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1140_1 | In amplitude modulation, the amplitude or strength of the radio frequency oscillations is varied. For example, in AM radio communication, a continuous wave radio-frequency signal has its amplitude modulated by an audio waveform before transmission. The audio waveform modifies the amplitude of the radio wave and determines the envelope of the waveform. In the frequency domain, amplitude modulation produces a signal with power concentrated at the carrier frequency and two adjacent sidebands. Each sideband is equal in bandwidth to that of the modulating signal, and is a mirror image of the other. Standard AM is thus sometimes called "double-sideband amplitude modulation" (DSBAM).
A disadvantage of all amplitude modulation techniques, not only standard AM, is that the receiver amplifies and detects noise and electromagnetic interference in equal proportion to the signal. Increasing the received signal-to-noise ratio, say, by a factor of 10 (a 10 decibel improvement), thus would require increasing the transmitter power by a factor of 10. This is in contrast to frequency modulation (FM) and digital radio where the effect of such noise following demodulation is strongly reduced so long as the received signal is well above the threshold for reception. For this reason AM broadcast is not favored for music and high fidelity broadcasting, but rather for voice communications and broadcasts (sports, news, talk radio etc.). | [
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1140_2 | AM is also inefficient in power usage; at least two-thirds of the power is concentrated in the carrier signal. The carrier signal contains none of the original information being transmitted (voice, video, data, etc.). However its presence provides a simple means of demodulation using envelope detection, providing a frequency and phase reference to extract the modulation from the sidebands. In some modulation systems based on AM, a lower transmitter power is required through partial or total elimination of the carrier component, however receivers for these signals are more complex because they must provide a precise carrier frequency reference signal (usually as shifted to the intermediate frequency) from a greatly reduced "pilot" carrier (in reduced-carrier transmission or DSB-RC) to use in the demodulation process. Even with the carrier totally eliminated in double-sideband suppressed-carrier transmission, carrier regeneration is possible using a Costas phase-locked loop. This does not work for single-sideband suppressed-carrier transmission (SSB-SC), leading to the characteristic "Donald Duck" sound from such receivers when slightly detuned. Single-sideband AM is nevertheless used widely in amateur radio and other voice communications because it has power and bandwidth efficiency (cutting the RF bandwidth in half compared to standard AM). On the other hand, in medium wave and short wave broadcasting, standard AM with the full carrier allows for reception using inexpensive receivers. The broadcaster absorbs the extra power cost to greatly increase potential audience.
An additional function provided by the carrier in standard AM, but which is lost in either single or double-sideband suppressed-carrier transmission, is that it provides an amplitude reference. In the receiver, the automatic gain control (AGC) responds to the carrier so that the reproduced audio level stays in a fixed proportion to the original modulation. On the other hand, with suppressed-carrier transmissions there is no transmitted power during pauses in the modulation, so the AGC must respond to peaks of the transmitted power during peaks in the modulation. This typically involves a so-called fast attack, slow decay circuit which holds the AGC level for a second or more following such peaks, in between syllables or short pauses in the program. This is very acceptable for communications radios, where compression of the audio aids intelligibility. However it is absolutely undesired for music or normal broadcast programming, where a faithful reproduction of the original program, including its varying modulation levels, is expected. | [
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1140_3 | A simple form of amplitude modulation is the transmission of speech signals from the traditional analog telephone set using a common battery local loop. The direct current provided by the central office battery is a carrier with a frequency of 0 Hz, that is modulated by a microphone (transmitter) in the telephone set according to the acoustic signal from the mouth of the speaker. The result is a varying amplitude direct current, whose AC-component is the speech signal extracted at the central office for transmission to another subscriber.
A simple form of digital amplitude modulation which can be used for transmitting binary data is on-off keying, the simplest form of amplitude-shift keying, in which ones and zeros are represented by the presence or absence of a carrier. On-off keying is likewise used by radio amateurs to transmit Morse code where it is known as continuous wave (CW) operation, even though the transmission is not strictly "continuous." A more complex form of AM, quadrature amplitude modulation is now more commonly used with digital data, while making more efficient use of the available bandwidth.
ITU designations
In 1982, the International Telecommunication Union (ITU) designated the types of amplitude modulation:
History
Although AM was used in a few crude experiments in multiplex telegraph and telephone transmission in the late 1800s, the practical development of amplitude modulation is synonymous with the development between 1900 and 1920 of "radiotelephone" transmission, that is, the effort to send sound (audio) by radio waves. The first radio transmitters, called spark gap transmitters, transmitted information by wireless telegraphy, using different length pulses of carrier wave to spell out text messages in Morse code. They couldn't transmit audio because the carrier consisted of strings of damped waves, pulses of radio waves that declined to zero, that sounded like a buzz in receivers. In effect they were already amplitude modulated.
Continuous waves
The first AM transmission was made by Canadian researcher Reginald Fessenden on 23 December 1900 using a spark gap transmitter with a specially designed high frequency 10 kHz interrupter, over a distance of 1 mile (1.6 km) at Cobb Island, Maryland, US. His first transmitted words were, "Hello. One, two, three, four. Is it snowing where you are, Mr. Thiessen?". The words were barely intelligible above the background buzz of the spark. | [
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1140_4 | Fessenden was a significant figure in the development of AM radio. He was one of the first researchers to realize, from experiments like the above, that the existing technology for producing radio waves, the spark transmitter, was not usable for amplitude modulation, and that a new kind of transmitter, one that produced sinusoidal continuous waves, was needed. This was a radical idea at the time, because experts believed the impulsive spark was necessary to produce radio frequency waves, and Fessenden was ridiculed. He invented and helped develop one of the first continuous wave transmitters - the Alexanderson alternator, with which he made what is considered the first AM public entertainment broadcast on Christmas Eve, 1906. He also discovered the principle on which AM is based, heterodyning, and invented one of the first detectors able to rectify and receive AM, the electrolytic detector or "liquid baretter", in 1902. Other radio detectors invented for wireless telegraphy, such as the Fleming valve (1904) and the crystal detector (1906) also proved able to rectify AM signals, so the technological hurdle was generating AM waves; receiving them was not a problem.
Early technologies
Early experiments in AM radio transmission, conducted by Fessenden, Valdemar Poulsen, Ernst Ruhmer, Quirino Majorana, Charles Herrold, and Lee de Forest, were hampered by the lack of a technology for amplification. The first practical continuous wave AM transmitters were based on either the huge, expensive Alexanderson alternator, developed 1906–1910, or versions of the Poulsen arc transmitter (arc converter), invented in 1903. The modifications necessary to transmit AM were clumsy and resulted in very low quality audio. Modulation was usually accomplished by a carbon microphone inserted directly in the antenna or ground wire; its varying resistance varied the current to the antenna. The limited power handling ability of the microphone severely limited the power of the first radiotelephones; many of the microphones were water-cooled. | [
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] |
1140_5 | Vacuum tubes
The 1912 discovery of the amplifying ability of the Audion tube, invented in 1906 by Lee de Forest, solved these problems. The vacuum tube feedback oscillator, invented in 1912 by Edwin Armstrong and Alexander Meissner, was a cheap source of continuous waves and could be easily modulated to make an AM transmitter. Modulation did not have to be done at the output but could be applied to the signal before the final amplifier tube, so the microphone or other audio source didn't have to modulate a high-power radio signal. Wartime research greatly advanced the art of AM modulation, and after the war the availability of cheap tubes sparked a great increase in the number of radio stations experimenting with AM transmission of news or music. The vacuum tube was responsible for the rise of AM broadcasting around 1920, the first electronic mass communication medium. Amplitude modulation was virtually the only type used for radio broadcasting until FM broadcasting began after World War II.
At the same time as AM radio began, telephone companies such as AT&T were developing the other large application for AM: sending multiple telephone calls through a single wire by modulating them on separate carrier frequencies, called frequency division multiplexing.
Single-sideband
John Renshaw Carson in 1915 did the first mathematical analysis of amplitude modulation, showing that a signal and carrier frequency combined in a nonlinear device would create two sidebands on either side of the carrier frequency, and passing the modulated signal through another nonlinear device would extract the original baseband signal. His analysis also showed only one sideband was necessary to transmit the audio signal, and Carson patented single-sideband modulation (SSB) on 1 December 1915. This more advanced variant of amplitude modulation was adopted by AT&T for longwave transatlantic telephone service beginning 7 January 1927. After WW2 it was developed by the military for aircraft communication.
Analysis
The carrier wave (sine wave) of frequency fc and amplitude A is expressed by
.
The message signal, such as an audio signal that is used for modulating the carrier, is m(t), and has a frequency fm, much lower than fc:
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1140_6 | ,
where m is the amplitude sensitivity, M is the amplitude of modulation. If m < 1, (1 + m(t)/A) is always positive for undermodulation. If m > 1 then overmodulation occurs and reconstruction of message signal from the transmitted signal would lead in loss of original signal. Amplitude modulation results when the carrier c(t) is multiplied by the positive quantity (1 + m(t)/A):
In this simple case m is identical to the modulation index, discussed below. With m = 0.5 the amplitude modulated signal y(t) thus corresponds to the top graph (labelled "50% Modulation") in figure 4.
Using prosthaphaeresis identities, y(t) can be shown to be the sum of three sine waves:
Therefore, the modulated signal has three components: the carrier wave c(t) which is unchanged in frequency, and two sidebands with frequencies slightly above and below the carrier frequency fc.
Spectrum
A useful modulation signal m(t) is usually more complex than a single sine wave, as treated above. However, by the principle of Fourier decomposition, m(t) can be expressed as the sum of a set of sine waves of various frequencies, amplitudes, and phases. Carrying out the multiplication of 1 + m(t) with c(t) as above, the result consists of a sum of sine waves. Again, the carrier c(t) is present unchanged, but each frequency component of m at fi has two sidebands at frequencies fc + fi and fc - fi. The collection of the former frequencies above the carrier frequency is known as the upper sideband, and those below constitute the lower sideband. The modulation m(t) may be considered to consist of an equal mix of positive and negative frequency components, as shown in the top of figure 2. One can view the sidebands as that modulation m(t) having simply been shifted in frequency by fc as depicted at the bottom right of figure 2. | [
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1140_7 | The short-term spectrum of modulation, changing as it would for a human voice for instance, the frequency content (horizontal axis) may be plotted as a function of time (vertical axis), as in figure 3. It can again be seen that as the modulation frequency content varies, an upper sideband is generated according to those frequencies shifted above the carrier frequency, and the same content mirror-imaged in the lower sideband below the carrier frequency. At all times, the carrier itself remains constant, and of greater power than the total sideband power.
Power and spectrum efficiency
The RF bandwidth of an AM transmission (refer to figure 2, but only considering positive frequencies) is twice the bandwidth of the modulating (or "baseband") signal, since the upper and lower sidebands around the carrier frequency each have a bandwidth as wide as the highest modulating frequency. Although the bandwidth of an AM signal is narrower than one using frequency modulation (FM), it is twice as wide as single-sideband techniques; it thus may be viewed as spectrally inefficient. Within a frequency band, only half as many transmissions (or "channels") can thus be accommodated. For this reason analog television employs a variant of single-sideband (known as vestigial sideband, somewhat of a compromise in terms of bandwidth) in order to reduce the required channel spacing. | [
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1140_8 | Another improvement over standard AM is obtained through reduction or suppression of the carrier component of the modulated spectrum. In figure 2 this is the spike in between the sidebands; even with full (100%) sine wave modulation, the power in the carrier component is twice that in the sidebands, yet it carries no unique information. Thus there is a great advantage in efficiency in reducing or totally suppressing the carrier, either in conjunction with elimination of one sideband (single-sideband suppressed-carrier transmission) or with both sidebands remaining (double sideband suppressed carrier). While these suppressed carrier transmissions are efficient in terms of transmitter power, they require more sophisticated receivers employing synchronous detection and regeneration of the carrier frequency. For that reason, standard AM continues to be widely used, especially in broadcast transmission, to allow for the use of inexpensive receivers using envelope detection. Even (analog) television, with a (largely) suppressed lower sideband, includes sufficient carrier power for use of envelope detection. But for communications systems where both transmitters and receivers can be optimized, suppression of both one sideband and the carrier represent a net advantage and are frequently employed.
A technique used widely in broadcast AM transmitters is an application of the Hapburg carrier, first proposed in the 1930s but impractical with the technology then available. During periods of low modulation the carrier power would be reduced and would return to full power during periods of high modulation levels. This has the effect of reducing the overall power demand of the transmitter and is most effective on speech type programmes. Various trade names are used for its implementation by the transmitter manufacturers from the late 80's onwards.
Modulation index
The AM modulation index is a measure based on the ratio of the modulation excursions of the RF signal to the level of the unmodulated carrier. It is thus defined as:
where and are the modulation amplitude and carrier amplitude, respectively; the modulation amplitude is the peak (positive or negative) change in the RF amplitude from its unmodulated value. Modulation index is normally expressed as a percentage, and may be displayed on a meter connected to an AM transmitter. | [
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] |
1140_9 | So if , carrier amplitude varies by 50% above (and below) its unmodulated level, as is shown in the first waveform, below. For , it varies by 100% as shown in the illustration below it. With 100% modulation the wave amplitude sometimes reaches zero, and this represents full modulation using standard AM and is often a target (in order to obtain the highest possible signal-to-noise ratio) but mustn't be exceeded. Increasing the modulating signal beyond that point, known as overmodulation, causes a standard AM modulator (see below) to fail, as the negative excursions of the wave envelope cannot become less than zero, resulting in distortion ("clipping") of the received modulation. Transmitters typically incorporate a limiter circuit to avoid overmodulation, and/or a compressor circuit (especially for voice communications) in order to still approach 100% modulation for maximum intelligibility above the noise. Such circuits are sometimes referred to as a vogad.
However it is possible to talk about a modulation index exceeding 100%, without introducing distortion, in the case of double-sideband reduced-carrier transmission. In that case, negative excursions beyond zero entail a reversal of the carrier phase, as shown in the third waveform below. This cannot be produced using the efficient high-level (output stage) modulation techniques (see below) which are widely used especially in high power broadcast transmitters. Rather, a special modulator produces such a waveform at a low level followed by a linear amplifier. What's more, a standard AM receiver using an envelope detector is incapable of properly demodulating such a signal. Rather, synchronous detection is required. Thus double-sideband transmission is generally not referred to as "AM" even though it generates an identical RF waveform as standard AM as long as the modulation index is below 100%. Such systems more often attempt a radical reduction of the carrier level compared to the sidebands (where the useful information is present) to the point of double-sideband suppressed-carrier transmission where the carrier is (ideally) reduced to zero. In all such cases the term "modulation index" loses its value as it refers to the ratio of the modulation amplitude to a rather small (or zero) remaining carrier amplitude.
Modulation methods | [
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1140_10 | Modulation methods
Modulation circuit designs may be classified as low- or high-level (depending on whether they modulate in a low-power domain—followed by amplification for transmission—or in the high-power domain of the transmitted signal).
Low-level generation
In modern radio systems, modulated signals are generated via digital signal processing (DSP). With DSP many types of AM are possible with software control (including DSB with carrier, SSB suppressed-carrier and independent sideband, or ISB). Calculated digital samples are converted to voltages with a digital-to-analog converter, typically at a frequency less than the desired RF-output frequency. The analog signal must then be shifted in frequency and linearly amplified to the desired frequency and power level (linear amplification must be used to prevent modulation distortion).
This low-level method for AM is used in many Amateur Radio transceivers.
AM may also be generated at a low level, using analog methods described in the next section.
High-level generation
High-power AM transmitters (such as those used for AM broadcasting) are based on high-efficiency class-D and class-E power amplifier stages, modulated by varying the supply voltage.
Older designs (for broadcast and amateur radio) also generate AM by controlling the gain of the transmitter's final amplifier (generally class-C, for efficiency). The following types are for vacuum tube transmitters (but similar options are available with transistors): | [
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1140_11 | Plate modulation In plate modulation, the plate voltage of the RF amplifier is modulated with the audio signal. The audio power requirement is 50 percent of the RF-carrier power.
Heising (constant-current) modulation RF amplifier plate voltage is fed through a choke (high-value inductor). The AM modulation tube plate is fed through the same inductor, so the modulator tube diverts current from the RF amplifier. The choke acts as a constant current source in the audio range. This system has a low power efficiency.
Control grid modulation The operating bias and gain of the final RF amplifier can be controlled by varying the voltage of the control grid. This method requires little audio power, but care must be taken to reduce distortion.
Clamp tube (screen grid) modulation The screen-grid bias may be controlled through a clamp tube, which reduces voltage according to the modulation signal. It is difficult to approach 100-percent modulation while maintaining low distortion with this system.
Doherty modulation One tube provides the power under carrier conditions and another operates only for positive modulation peaks. Overall efficiency is good, and distortion is low.
Outphasing modulation Two tubes are operated in parallel, but partially out of phase with each other. As they are differentially phase modulated their combined amplitude is greater or smaller. Efficiency is good and distortion low when properly adjusted.
Pulse-width modulation (PWM) or pulse-duration modulation (PDM) A highly efficient high voltage power supply is applied to the tube plate. The output voltage of this supply is varied at an audio rate to follow the program. This system was pioneered by Hilmer Swanson and has a number of variations, all of which achieve high efficiency and sound quality.
Digital methods The Harris Corporation obtained a patent for synthesizing a modulated high-power carrier wave from a set of digitally selected low-power amplifiers, running in phase at the same carrier frequency. The input signal is sampled by a conventional audio analog-to-digital converter (ADC), and fed to a digital exciter, which modulates overall transmitter output power by switching a series of low-power solid-state RF amplifiers on and off. The combined output drives the antenna system.
Demodulation methods
The simplest form of AM demodulator consists of a diode which is configured to act as envelope detector. Another type of demodulator, the product detector, can provide better-quality demodulation with additional circuit complexity. | [
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1140_12 | See also
AM stereo
Shortwave radio
Amplitude modulation signalling system (AMSS)
Modulation sphere
Types of radio emissions
Airband
DSB-SC
References
Bibliography
Newkirk, David and Karlquist, Rick (2004). Mixers, modulators and demodulators. In D. G. Reed (ed.), The ARRL Handbook for Radio Communications (81st ed.), pp. 15.1–15.36. Newington: ARRL. .
External links
Amplitude Modulation by Jakub Serych, Wolfram Demonstrations Project.
Amplitude Modulation, by S Sastry.
Amplitude Modulation, an introduction by Federation of American Scientists.
Amplitude Modulation tutorial including related topics of modulators, demodulators, etc...
Analog Modulation online interactive demonstration using Python in Google Colab Platform, by C Foh.
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1141_0 | Augustin-Jean Fresnel ( ; ; or ; ; 10 May 1788 – 14 July 1827) was a French civil engineer and physicist whose research in optics led to the almost unanimous acceptance of the wave theory of light, excluding any remnant of Newton's corpuscular theory, from the late 1830s until the end of the 19th century. He is perhaps better known for inventing the catadioptric (reflective/refractive) Fresnel lens and for pioneering the use of "stepped" lenses to extend the visibility of lighthouses, saving countless lives at sea. The simpler dioptric (purely refractive) stepped lens, first proposed by Count Buffon and independently reinvented by Fresnel, is used in screen magnifiers and in condenser lenses for overhead projectors.
By expressing Huygens's principle of secondary waves and Young's principle of interference in quantitative terms, and supposing that simple colors consist of sinusoidal waves, Fresnel gave the first satisfactory explanation of diffraction by straight edges, including the first satisfactory wave-based explanation of rectilinear propagation. Part of his argument was a proof that the addition of sinusoidal functions of the same frequency but different phases is analogous to the addition of forces with different directions. By further supposing that light waves are purely transverse, Fresnel explained the nature of polarization, the mechanism of chromatic polarization, and the transmission and reflection coefficients at the interface between two transparent isotropic media. Then, by generalizing the direction-speed-polarization relation for calcite, he accounted for the directions and polarizations of the refracted rays in doubly-refractive crystals of the biaxial class (those for which Huygens's secondary wavefronts are not axisymmetric). The period between the first publication of his pure-transverse-wave hypothesis, and the submission of his first correct solution to the biaxial problem, was less than a year. | [
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1141_1 | Later, he coined the terms linear polarization, circular polarization, and elliptical polarization, explained how optical rotation could be understood as a difference in propagation speeds for the two directions of circular polarization, and (by allowing the reflection coefficient to be complex) accounted for the change in polarization due to total internal reflection, as exploited in the Fresnel rhomb. Defenders of the established corpuscular theory could not match his quantitative explanations of so many phenomena on so few assumptions.
Fresnel had a lifelong battle with tuberculosis, to which he succumbed at the age of 39. Although he did not become a public celebrity in his lifetime, he lived just long enough to receive due recognition from his peers, including (on his deathbed) the Rumford Medal of the Royal Society of London, and his name is ubiquitous in the modern terminology of optics and waves. After the wave theory of light was subsumed by Maxwell's electromagnetic theory in the 1860s, some attention was diverted from the magnitude of Fresnel's contribution. In the period between Fresnel's unification of physical optics and Maxwell's wider unification, a contemporary authority, Humphrey Lloyd, described Fresnel's transverse-wave theory as "the noblest fabric which has ever adorned the domain of physical science, Newton's system of the universe alone excepted."
Early life
Family
Augustin-Jean Fresnel (also called Augustin Jean or simply Augustin), born in Broglie, Normandy, on 10 May 1788, was the second of four sons of the architect Jacques Fresnel (1755–1805) and his wife Augustine, née Mérimée (1755–1833). In 1790, following the Revolution, Broglie became part of the département of Eure. The family moved twice – in 1789/90 to Cherbourg, and in 1794 to Jacques's home town of Mathieu, where Madame Fresnel would spend 25 years as a widow, outliving two of her sons. | [
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1141_2 | The first son, Louis (1786–1809), was admitted to the École Polytechnique, became a lieutenant in the artillery, and was killed in action at Jaca, Spain, the day before his 23rd birthday. The third, Léonor (1790–1869), followed Augustin into civil engineering, succeeded him as secretary of the Lighthouse Commission, and helped to edit his collected works. The fourth, Fulgence Fresnel (1795–1855), became a noted linguist, diplomat, and orientalist, and occasionally assisted Augustin with negotiations. Fulgence died in Bagdad in 1855 having led a mission to explore Babylon. Léonor apparently was the only one of the four who married.
Their mother's younger brother, Jean François "Léonor" Mérimée (1757–1836), father of the writer Prosper Mérimée (1803–1870), was a paint artist who turned his attention to the chemistry of painting. He became the Permanent Secretary of the École des Beaux-Arts and (until 1814) a professor at the École Polytechnique, and was the initial point of contact between Augustin and the leading optical physicists of the day .
Education
The Fresnel brothers were initially home-schooled by their mother. The sickly Augustin was considered the slow one, not inclined to memorization; but the popular story that he hardly began to read until the age of eight is disputed. At the age of nine or ten he was undistinguished except for his ability to turn tree-branches into toy bows and guns that worked far too well, earning himself the title l'homme de génie (the man of genius) from his accomplices, and a united crackdown from their elders. | [
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1141_3 | In 1801, Augustin was sent to the École Centrale at Caen, as company for Louis. But Augustin lifted his performance: in late 1804 he was accepted into the École Polytechnique, being placed 17th in the entrance examination. As the detailed records of the École Polytechnique begin in 1808, we know little of Augustin's time there, except that he made few if any friends and – in spite of continuing poor health – excelled in drawing and geometry: in his first year he took a prize for his solution to a geometry problem posed by Adrien-Marie Legendre. Graduating in 1806, he then enrolled at the École Nationale des Ponts et Chaussées (National School of Bridges and Roads, also known as "ENPC" or "École des Ponts"), from which he graduated in 1809, entering the service of the Corps des Ponts et Chaussées as an ingénieur ordinaire aspirant (ordinary engineer in training). Directly or indirectly, he was to remain in the employment of the "Corps des Ponts" for the rest of his life.
Religious formation
Augustin Fresnel's parents were Roman Catholics of the Jansenist sect, characterized by an extreme Augustinian view of original sin. Religion took first place in the boys' home-schooling. In 1802, Mme Fresnel reportedly said:
Augustin remained a Jansenist. He indeed regarded his intellectual talents as gifts from God, and considered it his duty to use them for the benefit of others. Plagued by poor health, and determined to do his duty before death thwarted him, he shunned pleasures and worked to the point of exhaustion. According to his fellow engineer Alphonse Duleau, who helped to nurse him through his final illness, Fresnel saw the study of nature as part of the study of the power and goodness of God. He placed virtue above science and genius. Yet in his last days he needed "strength of soul," not against death alone, but against "the interruption of discoveries… of which he hoped to derive useful applications." | [
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] |
1141_4 | Jansenism is considered heretical by the Roman Catholic Church , and this may be part of the explanation why Fresnel, in spite of his scientific achievements and his royalist credentials, never gained a permanent academic teaching post; his only teaching appointment was at the Athénée in the winter of 1819–20. Be that as it may, the brief article on Fresnel in the old Catholic Encyclopedia does not mention his Jansenism, but describes him as "a deeply religious man and remarkable for his keen sense of duty."
Engineering assignments
Fresnel was initially posted to the western département of Vendée. There, in 1811, he anticipated what became known as the Solvay process for producing soda ash, except that recycling of the ammonia was not considered. That difference may explain why leading chemists, who learned of his discovery through his uncle Léonor, eventually thought it uneconomic.
About 1812, Fresnel was sent to Nyons, in the southern département of Drôme, to assist with the imperial highway that was to connect Spain and Italy. It is from Nyons that we have the first evidence of his interest in optics. On 15 May 1814, while work was slack due to Napoleon's defeat, Fresnel wrote a "P.S." to his brother Léonor, saying in part:
As late as 28 December he was still waiting for information, but he had received Biot's memoir by 10 February 1815. (The Institut de France had taken over the functions of the French Académie des Sciences and other académies in 1795. In 1816 the Académie des Sciences regained its name and autonomy, but remained part of the institute.)
In March 1815, perceiving Napoleon's return from Elba as "an attack on civilization", Fresnel departed without leave, hastened to Toulouse and offered his services to the royalist resistance, but soon found himself on the sick list. Returning to Nyons in defeat, he was threatened and had his windows broken. During the Hundred Days he was placed on suspension, which he was eventually allowed to spend at his mother's house in Mathieu. There he used his enforced leisure to begin his optical experiments.
Contributions to physical optics
Historical context: From Newton to Biot | [
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1141_5 | Historical context: From Newton to Biot
The appreciation of Fresnel's reconstruction of physical optics might be assisted by an overview of the fragmented state in which he found the subject. In this subsection, optical phenomena that were unexplained or whose explanations were disputed are named in bold type.
The corpuscular theory of light, favored by Isaac Newton and accepted by nearly all of Fresnel's seniors, easily explained rectilinear propagation: the corpuscles obviously moved very fast, so that their paths were very nearly straight. The wave theory, as developed by Christiaan Huygens in his Treatise on Light (1690), explained rectilinear propagation on the assumption that each point crossed by a traveling wavefront becomes the source of a secondary wavefront. Given the initial position of a traveling wavefront, any later position (according to Huygens) was the common tangent surface (envelope) of the secondary wavefronts emitted from the earlier position. As the extent of the common tangent was limited by the extent of the initial wavefront, the repeated application of Huygens's construction to a plane wavefront of limited extent (in a uniform medium) gave a straight, parallel beam. While this construction indeed predicted rectilinear propagation, it was difficult to reconcile with the common observation that wavefronts on the surface of water can bend around obstructions, and with the similar behavior of sound waves – causing Newton to maintain, to the end of his life, that if light consisted of waves it would "bend and spread every way" into the shadows.
Huygens's theory neatly explained the law of ordinary reflection and the law of ordinary refraction ("Snell's law"), provided that the secondary waves traveled slower in denser media (those of higher refractive index). The corpuscular theory, with the hypothesis that the corpuscles were subject to forces acting perpendicular to surfaces, explained the same laws equally well, albeit with the implication that light traveled faster in denser media; that implication was wrong, but could not be directly disproven with the technology of Newton's time or even Fresnel's time . | [
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1141_6 | Similarly inconclusive was stellar aberration—that is, the apparent change in the position of a star due to the velocity of the earth across the line of sight (not to be confused with stellar parallax, which is due to the displacement of the earth across the line of sight). Identified by James Bradley in 1728, stellar aberration was widely taken as confirmation of the corpuscular theory. But it was equally compatible with the wave theory, as Euler noted in 1746 – tacitly assuming that the aether (the supposed wave-bearing medium) near the earth was not disturbed by the motion of the earth.
The outstanding strength of Huygens's theory was his explanation of the birefringence (double refraction) of "Iceland crystal" (transparent calcite), on the assumption that the secondary waves are spherical for the ordinary refraction (which satisfies Snell's law) and spheroidal for the extraordinary refraction (which does not). In general, Huygens's common-tangent construction implies that rays are paths of least time between successive positions of the wavefront, in accordance with Fermat's principle. In the special case of isotropic media, the secondary wavefronts must be spherical, and Huygens's construction then implies that the rays are perpendicular to the wavefront; indeed, the law of ordinary refraction can be separately derived from that premise, as Ignace-Gaston Pardies did before Huygens. | [
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1141_7 | Although Newton rejected the wave theory, he noticed its potential to explain colors, including the colors of "thin plates" (e.g., "Newton's rings", and the colors of skylight reflected in soap bubbles), on the assumption that light consists of periodic waves, with the lowest frequencies (longest wavelengths) at the red end of the spectrum, and the highest frequencies (shortest wavelengths) at the violet end. In 1672 he published a heavy hint to that effect, but contemporary supporters of the wave theory failed to act on it: Robert Hooke treated light as a periodic sequence of pulses but did not use frequency as the criterion of color, while Huygens treated the waves as individual pulses without any periodicity; and Pardies died young in 1673. Newton himself tried to explain colors of thin plates using the corpuscular theory, by supposing that his corpuscles had the wavelike property of alternating between "fits of easy transmission" and "fits of easy reflection", the distance between like "fits" depending on the color and the medium and, awkwardly, on the angle of refraction or reflection into that medium. More awkwardly still, this theory required thin plates to reflect only at the back surface, although thick plates manifestly reflected also at the front surface. It was not until 1801 that Thomas Young, in the Bakerian Lecture for that year, cited Newton's hint, and accounted for the colors of a thin plate as the combined effect of the front and back reflections, which reinforce or cancel each other according to the wavelength and the thickness. Young similarly explained the colors of "striated surfaces" (e.g., gratings) as the wavelength-dependent reinforcement or cancellation of reflections from adjacent lines. He described this reinforcement or cancellation as interference. | [
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1141_8 | Neither Newton nor Huygens satisfactorily explained diffraction—the blurring and fringing of shadows where, according to rectilinear propagation, they ought to be sharp. Newton, who called diffraction "inflexion", supposed that rays of light passing close to obstacles were bent ("inflected"); but his explanation was only qualitative. Huygens's common-tangent construction, without modifications, could not accommodate diffraction at all. Two such modifications were proposed by Young in the same 1801 Bakerian Lecture: first, that the secondary waves near the edge of an obstacle could diverge into the shadow, but only weakly, due to limited reinforcement from other secondary waves; and second, that diffraction by an edge was caused by interference between two rays: one reflected off the edge, and the other inflected while passing near the edge. The latter ray would be undeviated if sufficiently far from the edge, but Young did not elaborate on that case. These were the earliest suggestions that the degree of diffraction depends on wavelength. Later, in the 1803 Bakerian Lecture, Young ceased to regard inflection as a separate phenomenon, and produced evidence that diffraction fringes inside the shadow of a narrow obstacle were due to interference: when the light from one side was blocked, the internal fringes disappeared. But Young was alone in such efforts until Fresnel entered the field. | [
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1141_9 | Huygens, in his investigation of double refraction, noticed something that he could not explain: when light passes through two similarly oriented calcite crystals at normal incidence, the ordinary ray emerging from the first crystal suffers only the ordinary refraction in the second, while the extraordinary ray emerging from the first suffers only the extraordinary refraction in the second; but when the second crystal is rotated 90° about the incident rays, the roles are interchanged, so that the ordinary ray emerging from the first crystal suffers only the extraordinary refraction in the second, and vice versa. This discovery gave Newton another reason to reject the wave theory: rays of light evidently had "sides". Corpuscles could have sides (or poles, as they would later be called); but waves of light could not, because (so it seemed) any such waves would need to be longitudinal (with vibrations in the direction of propagation). Newton offered an alternative "Rule" for the extraordinary refraction, which rode on his authority through the 18th century, although he made "no known attempt to deduce it from any principles of optics, corpuscular or otherwise." | [
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1141_10 | In 1808, the extraordinary refraction of calcite was investigated experimentally, with unprecedented accuracy, by Étienne-Louis Malus, and found to be consistent with Huygens's spheroid construction, not Newton's "Rule". Malus, encouraged by Pierre-Simon Laplace, then sought to explain this law in corpuscular terms: from the known relation between the incident and refracted ray directions, Malus derived the corpuscular velocity (as a function of direction) that would satisfy Maupertuis's "least action" principle. But, as Young pointed out, the existence of such a velocity law was guaranteed by Huygens's spheroid, because Huygens's construction leads to Fermat's principle, which becomes Maupertuis's principle if the ray speed is replaced by the reciprocal of the particle speed! The corpuscularists had not found a force law that would yield the alleged velocity law, except by a circular argument in which a force acting at the surface of the crystal inexplicably depended on the direction of the (possibly subsequent) velocity within the crystal. Worse, it was doubtful that any such force would satisfy the conditions of Maupertuis's principle. In contrast, Young proceeded to show that "a medium more easily compressible in one direction than in any direction perpendicular to it, as if it consisted of an infinite number of parallel plates connected by a substance somewhat less elastic" admits spheroidal longitudinal wavefronts, as Huygens supposed. | [
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1141_11 | But Malus, in the midst of his experiments on double refraction, noticed something else: when a ray of light is reflected off a non-metallic surface at the appropriate angle, it behaves like one of the two rays emerging from a calcite crystal. It was Malus who coined the term polarization to describe this behavior, although the polarizing angle became known as Brewster's angle after its dependence on the refractive index was determined experimentally by David Brewster in 1815. Malus also introduced the term plane of polarization. In the case of polarization by reflection, his "plane of polarization" was the plane of the incident and reflected rays; in modern terms, this is the plane normal to the electric vibration. In 1809, Malus further discovered that the intensity of light passing through two polarizers is proportional to the squared cosine of the angle between their planes of polarization (Malus's law), whether the polarizers work by reflection or double refraction, and that all birefringent crystals produce both extraordinary refraction and polarization. As the corpuscularists started trying to explain these things in terms of polar "molecules" of light, the wave-theorists had no working hypothesis on the nature of polarization, prompting Young to remark that Malus's observations "present greater difficulties to the advocates of the undulatory theory than any other facts with which we are acquainted."
Malus died in February 1812, at the age of 36, shortly after receiving the Rumford Medal for his work on polarization. | [
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1141_12 | In August 1811, François Arago reported that if a thin plate of mica was viewed against a white polarized backlight through a calcite crystal, the two images of the mica were of complementary colors (the overlap having the same color as the background). The light emerging from the mica was "depolarized" in the sense that there was no orientation of the calcite that made one image disappear; yet it was not ordinary ("unpolarized") light, for which the two images would be of the same color. Rotating the calcite around the line of sight changed the colors, though they remained complementary. Rotating the mica changed the saturation (not the hue) of the colors. This phenomenon became known as chromatic polarization. Replacing the mica with a much thicker plate of quartz, with its faces perpendicular to the optic axis (the axis of Huygens's spheroid or Malus's velocity function), produced a similar effect, except that rotating the quartz made no difference. Arago tried to explain his observations in corpuscular terms.
In 1812, as Arago pursued further qualitative experiments and other commitments, Jean-Baptiste Biot reworked the same ground using a gypsum lamina in place of the mica, and found empirical formulae for the intensities of the ordinary and extraordinary images. The formulae contained two coefficients, supposedly representing colors of rays "affected" and "unaffected" by the plate – the "affected" rays being of the same color mix as those reflected by amorphous thin plates of proportional, but lesser, thickness.
Arago protested, declaring that he had made some of the same discoveries but had not had time to write them up. In fact the overlap between Arago's work and Biot's was minimal, Arago's being only qualitative and wider in scope (attempting to include polarization by reflection). But the dispute triggered a notorious falling-out between the two men. | [
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1141_13 | Later that year, Biot tried to explain the observations as an oscillation of the alignment of the "affected" corpuscles at a frequency proportional to that of Newton's "fits", due to forces depending on the alignment. This theory became known as mobile polarization. To reconcile his results with a sinusoidal oscillation, Biot had to suppose that the corpuscles emerged with one of two permitted orientations, namely the extremes of the oscillation, with probabilities depending on the phase of the oscillation. Corpuscular optics was becoming expensive on assumptions. But in 1813, Biot reported that the case of quartz was simpler: the observable phenomenon (now called optical rotation or optical activity or sometimes rotary polarization) was a gradual rotation of the polarization direction with distance, and could be explained by a corresponding rotation (not oscillation) of the corpuscles.
Early in 1814, reviewing Biot's work on chromatic polarization, Young noted that the periodicity of the color as a function of the plate thickness – including the factor by which the period exceeded that for a reflective thin plate, and even the effect of obliquity of the plate (but not the role of polarization)—could be explained by the wave theory in terms of the different propagation times of the ordinary and extraordinary waves through the plate. But Young was then the only public defender of the wave theory. | [
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1141_14 | In summary, in the spring of 1814, as Fresnel tried in vain to guess what polarization was, the corpuscularists thought that they knew, while the wave-theorists (if we may use the plural) literally had no idea. Both theories claimed to explain rectilinear propagation, but the wave explanation was overwhelmingly regarded as unconvincing. The corpuscular theory could not rigorously link double refraction to surface forces; the wave theory could not yet link it to polarization. The corpuscular theory was weak on thin plates and silent on gratings; the wave theory was strong on both, but under-appreciated. Concerning diffraction, the corpuscular theory did not yield quantitative predictions, while the wave theory had begun to do so by considering diffraction as a manifestation of interference, but had only considered two rays at a time. Only the corpuscular theory gave even a vague insight into Brewster's angle, Malus's law, or optical rotation. Concerning chromatic polarization, the wave theory explained the periodicity far better than the corpuscular theory, but had nothing to say about the role of polarization; and its explanation of the periodicity was largely ignored. And Arago had founded the study of chromatic polarization, only to lose the lead, controversially, to Biot. Such were the circumstances in which Arago first heard of Fresnel's interest in optics.
Rêveries
Fresnel's letters from later in 1814 reveal his interest in the wave theory, including his awareness that it explained the constancy of the speed of light and was at least compatible with stellar aberration. Eventually he compiled what he called his rêveries (musings) into an essay and submitted it via Léonor Mérimée to André-Marie Ampère, who did not respond directly. But on 19 December, Mérimée dined with Ampère and Arago, with whom he was acquainted through the École Polytechnique; and Arago promised to look at Fresnel's essay.
In mid 1815, on his way home to Mathieu to serve his suspension, Fresnel met Arago in Paris and spoke of the wave theory and stellar aberration. He was informed that he was trying to break down open doors ("il enfonçait des portes ouvertes"), and directed to classical works on optics. | [
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1141_15 | Diffraction
First attempt (1815)
On 12 July 1815, as Fresnel was about to leave Paris, Arago left him a note on a new topic:
Fresnel would not have ready access to these works outside Paris, and could not read English. But, in Mathieu – with a point-source of light made by focusing sunlight with a drop of honey, a crude micrometer of his own construction, and supporting apparatus made by a local locksmith – he began his own experiments. His technique was novel: whereas earlier investigators had projected the fringes onto a screen, Fresnel soon abandoned the screen and observed the fringes in space, through a lens with the micrometer at its focus, allowing more accurate measurements while requiring less light.
Later in July, after Napoleon's final defeat, Fresnel was reinstated with the advantage of having backed the winning side. He requested a two-month leave of absence, which was readily granted because roadworks were in abeyance.
On 23 September he wrote to Arago, beginning "I think I have found the explanation and the law of colored fringes which one notices in the shadows of bodies illuminated by a luminous point." In the same paragraph, however, Fresnel implicitly acknowledged doubt about the novelty of his work: noting that he would need to incur some expense in order to improve his measurements, he wanted to know "whether this is not useless, and whether the law of diffraction has not already been established by sufficiently exact experiments." He explained that he had not yet had a chance to acquire the items on his reading lists, with the apparent exception of "Young's book", which he could not understand without his brother's help. Not surprisingly, he had retraced many of Young's steps. | [
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1141_16 | In a memoir sent to the institute on 15 October 1815, Fresnel mapped the external and internal fringes in the shadow of a wire. He noticed, like Young before him, that the internal fringes disappeared when the light from one side was blocked, and concluded that "the vibrations of two rays that cross each other under a very small angle can contradict each other…" But, whereas Young took the disappearance of the internal fringes as confirmation of the principle of interference, Fresnel reported that it was the internal fringes that first drew his attention to the principle. To explain the diffraction pattern, Fresnel constructed the internal fringes by considering the intersections of circular wavefronts emitted from the two edges of the obstruction, and the external fringes by considering the intersections between direct waves and waves reflected off the nearer edge. For the external fringes, to obtain tolerable agreement with observation, he had to suppose that the reflected wave was inverted; and he noted that the predicted paths of the fringes were hyperbolic. In the part of the memoir that most clearly surpassed Young, Fresnel explained the ordinary laws of reflection and refraction in terms of interference, noting that if two parallel rays were reflected or refracted at other than the prescribed angle, they would no longer have the same phase in a common perpendicular plane, and every vibration would be cancelled by a nearby vibration. He noted that his explanation was valid provided that the surface irregularities were much smaller than the wavelength.
On 10 November, Fresnel sent a supplementary note dealing with Newton's rings and with gratings, including, for the first time, transmission gratings – although in that case the interfering rays were still assumed to be "inflected", and the experimental verification was inadequate because it used only two threads.
As Fresnel was not a member of the institute, the fate of his memoir depended heavily on the report of a single member. The reporter for Fresnel's memoir turned out to be Arago (with Poinsot as the other reviewer). On 8 November, Arago wrote to Fresnel: | [
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1141_17 | Fresnel was troubled, wanting to know more precisely where he had collided with Young. Concerning the curved paths of the "colored bands", Young had noted the hyperbolic paths of the fringes in the two-source interference pattern, corresponding roughly to Fresnel's internal fringes, and had described the hyperbolic fringes that appear on the screen within rectangular shadows. He had not mentioned the curved paths of the external fringes of a shadow; but, as he later explained, that was because Newton had already done so. Newton evidently thought the fringes were caustics. Thus Arago erred in his belief that the curved paths of the fringes were fundamentally incompatible with the corpuscular theory.
Arago's letter went on to request more data on the external fringes. Fresnel complied, until he exhausted his leave and was assigned to Rennes in the département of Ille-et-Vilaine. At this point Arago interceded with Gaspard de Prony, head of the École des Ponts, who wrote to Louis-Mathieu Molé, head of the Corps des Ponts, suggesting that the progress of science and the prestige of the Corps would be enhanced if Fresnel could come to Paris for a time. He arrived in March 1816, and his leave was subsequently extended through the middle of the year.
Meanwhile, in an experiment reported on 26 February 1816, Arago verified Fresnel's prediction that the internal fringes were shifted if the rays on one side of the obstacle passed through a thin glass lamina. Fresnel correctly attributed this phenomenon to the lower wave velocity in the glass. Arago later used a similar argument to explain the colors in the scintillation of stars.
Fresnel's updated memoir was eventually published in the March 1816 issue of Annales de Chimie et de Physique, of which Arago had recently become co-editor. That issue did not actually appear until May. In March, Fresnel already had competition: Biot read a memoir on diffraction by himself and his student Claude Pouillet, containing copious data and arguing that the regularity of diffraction fringes, like the regularity of Newton's rings, must be linked to Newton's "fits". But the new link was not rigorous, and Pouillet himself would become a distinguished early adopter of the wave theory. | [
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1141_18 | "Efficacious ray", double-mirror experiment (1816)
On 24 May 1816, Fresnel wrote to Young (in French), acknowledging how little of his own memoir was new. But in a "supplement" signed on 14 July and read the next day, Fresnel noted that the internal fringes were more accurately predicted by supposing that the two interfering rays came from some distance outside the edges of the obstacle. To explain this, he divided the incident wavefront at the obstacle into what we now call Fresnel zones, such that the secondary waves from each zone were spread over half a cycle when they arrived at the observation point. The zones on one side of the obstacle largely canceled out in pairs, except the first zone, which was represented by an "efficacious ray". This approach worked for the internal fringes, but the superposition of the efficacious ray and the direct ray did not work for the external fringes.
The contribution from the "efficacious ray" was thought to be only partly canceled, for reasons involving the dynamics of the medium: where the wavefront was continuous, symmetry forbade oblique vibrations; but near the obstacle that truncated the wavefront, the asymmetry allowed some sideways vibration towards the geometric shadow. This argument showed that Fresnel had not (yet) fully accepted Huygens's principle, which would have permitted oblique radiation from all portions of the front.
In the same supplement, Fresnel described his well-known double mirror, comprising two flat mirrors joined at an angle of slightly less than 180°, with which he produced a two-slit interference pattern from two virtual images of the same slit. A conventional double-slit experiment required a preliminary single slit to ensure that the light falling on the double slit was coherent (synchronized). In Fresnel's version, the preliminary single slit was retained, and the double slit was replaced by the double mirror – which bore no physical resemblance to the double slit and yet performed the same function. This result (which had been announced by Arago in the March issue of the Annales) made it hard to believe that the two-slit pattern had anything to do with corpuscles being deflected as they passed near the edges of the slits. | [
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] |
1141_19 | But 1816 was the "Year Without a Summer": crops failed; hungry farming families lined the streets of Rennes; the central government organized "charity workhouses" for the needy; and in October, Fresnel was sent back to Ille-et-Vilaine to supervise charity workers in addition to his regular road crew. According to Arago,
Fresnel's letters from December 1816 reveal his consequent anxiety. To Arago he complained of being "tormented by the worries of surveillance, and the need to reprimand…" And to Mérimée he wrote: "I find nothing more tiresome than having to manage other men, and I admit that I have no idea what I'm doing."
Prize memoir (1818) and sequel
On 17 March 1817, the Académie des Sciences announced that diffraction would be the topic for the biannual physics Grand Prix to be awarded in 1819. The deadline for entries was set at 1 August 1818 to allow time for replication of experiments. Although the wording of the problem referred to rays and inflection and did not invite wave-based solutions, Arago and Ampère encouraged Fresnel to enter.
In the fall of 1817, Fresnel, supported by de Prony, obtained a leave of absence from the new head of the Corp des Ponts, Louis Becquey, and returned to Paris. He resumed his engineering duties in the spring of 1818; but from then on he was based in Paris, first on the Canal de l'Ourcq, and then (from May 1819) with the cadastre of the pavements.
On 15 January 1818, in a different context (revisited below), Fresnel showed that the addition of sinusoidal functions of the same frequency but different phases is analogous to the addition of forces with different directions. His method was similar to the phasor representation, except that the "forces" were plane vectors rather than complex numbers; they could be added, and multiplied by scalars, but not (yet) multiplied and divided by each other. The explanation was algebraic rather than geometric. | [
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1141_20 | Knowledge of this method was assumed in a preliminary note on diffraction, dated 19 April 1818 and deposited on 20 April, in which Fresnel outlined the elementary theory of diffraction as found in modern textbooks. He restated Huygens's principle in combination with the superposition principle, saying that the vibration at each point on a wavefront is the sum of the vibrations that would be sent to it at that moment by all the elements of the wavefront in any of its previous positions, all elements acting separately . For a wavefront partly obstructed in a previous position, the summation was to be carried out over the unobstructed portion. In directions other than the normal to the primary wavefront, the secondary waves were weakened due to obliquity, but weakened much more by destructive interference, so that the effect of obliquity alone could be ignored. For diffraction by a straight edge, the intensity as a function of distance from the geometric shadow could then be expressed with sufficient accuracy in terms of what are now called the normalized Fresnel integrals:
The same note included a table of the integrals, for an upper limit ranging from 0 to 5.1 in steps of 0.1, computed with a mean error of 0.0003, plus a smaller table of maxima and minima of the resulting intensity. | [
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1141_21 | In his final "Memoir on the diffraction of light", deposited on 29 July and bearing the Latin epigraph "Natura simplex et fecunda" ("Nature simple and fertile"), Fresnel slightly expanded the two tables without changing the existing figures, except for a correction to the first minimum of intensity. For completeness, he repeated his solution to "the problem of interference", whereby sinusoidal functions are added like vectors. He acknowledged the directionality of the secondary sources and the variation in their distances from the observation point, chiefly to explain why these things make negligible difference in the context, provided of course that the secondary sources do not radiate in the retrograde direction. Then, applying his theory of interference to the secondary waves, he expressed the intensity of light diffracted by a single straight edge (half-plane) in terms of integrals which involved the dimensions of the problem, but which could be converted to the normalized forms above. With reference to the integrals, he explained the calculation of the maxima and minima of the intensity (external fringes), and noted that the calculated intensity falls very rapidly as one moves into the geometric shadow. The last result, as Olivier Darrigol says, "amounts to a proof of the rectilinear propagation of light in the wave theory, indeed the first proof that a modern physicist would still accept."
For the experimental testing of his calculations, Fresnel used red light with a wavelength of 638nm, which he deduced from the diffraction pattern in the simple case in which light incident on a single slit was focused by a cylindrical lens. For a variety of distances from the source to the obstacle and from the obstacle to the field point, he compared the calculated and observed positions of the fringes for diffraction by a half-plane, a slit, and a narrow strip – concentrating on the minima, which were visually sharper than the maxima. For the slit and the strip, he could not use the previously computed table of maxima and minima; for each combination of dimensions, the intensity had to be expressed in terms of sums or differences of Fresnel integrals and calculated from the table of integrals, and the extrema had to be calculated anew. The agreement between calculation and measurement was better than 1.5% in almost every case. | [
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1141_22 | Near the end of the memoir, Fresnel summed up the difference between Huygens's use of secondary waves and his own: whereas Huygens says there is light only where the secondary waves exactly agree, Fresnel says there is complete darkness only where the secondary waves exactly cancel out.
The judging committee comprised Laplace, Biot, and Poisson (all corpuscularists), Gay-Lussac (uncommitted), and Arago, who eventually wrote the committee's report. Although entries in the competition were supposed to be anonymous to the judges, Fresnel's must have been recognizable by the content. There was only one other entry, of which neither the manuscript nor any record of the author has survived. That entry (identified as "no.1") was mentioned only in the last paragraph of the judges' report, noting that the author had shown ignorance of the relevant earlier works of Young and Fresnel, used insufficiently precise methods of observation, overlooked known phenomena, and made obvious errors. In the words of John Worrall, "The competition facing Fresnel could hardly have been less stiff." We may infer that the committee had only two options: award the prize to Fresnel ("no. 2"), or withhold it.
The committee deliberated into the new year. Then Poisson, exploiting a case in which Fresnel's theory gave easy integrals, predicted that if a circular obstacle were illuminated by a point-source, there should be (according to the theory) a bright spot in the center of the shadow, illuminated as brightly as the exterior. This seems to have been intended as a reductio ad absurdum. Arago, undeterred, assembled an experiment with an obstacle 2mm in diameter – and there, in the center of the shadow, was Poisson's spot.
The unanimous report of the committee, read at the meeting of the Académie on 15 March 1819, awarded the prize to "the memoir marked no. 2, and bearing as epigraph: Natura simplex et fecunda." At the same meeting, after the judgment was delivered, the president of the Académie opened a sealed note accompanying the memoir, revealing the author as Fresnel. The award was announced at the public meeting of the Académie a week later, on 22 March. | [
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1141_23 | Arago's verification of Poisson's counter-intuitive prediction passed into folklore as if it had decided the prize. That view, however, is not supported by the judges' report, which gave the matter only two sentences in the penultimate paragraph. Neither did Fresnel's triumph immediately convert Laplace, Biot, and Poisson to the wave theory, for at least four reasons. First, although the professionalization of science in France had established common standards, it was one thing to acknowledge a piece of research as meeting those standards, and another thing to regard it as conclusive. Second, it was possible to interpret Fresnel's integrals as rules for combining rays. Arago even encouraged that interpretation, presumably in order to minimize resistance to Fresnel's ideas. Even Biot began teaching the Huygens-Fresnel principle without committing himself to a wave basis. Third, Fresnel's theory did not adequately explain the mechanism of generation of secondary waves or why they had any significant angular spread; this issue particularly bothered Poisson. Fourth, the question that most exercised optical physicists at that time was not diffraction, but polarization – on which Fresnel had been working, but was yet to make his critical breakthrough.
Polarization
Background: Emissionism and selectionism | [
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1141_24 | Polarization
Background: Emissionism and selectionism
An emission theory of light was one that regarded the propagation of light as the transport of some kind of matter. While the corpuscular theory was obviously an emission theory, the converse did not follow: in principle, one could be an emissionist without being a corpuscularist. This was convenient because, beyond the ordinary laws of reflection and refraction, emissionists never managed to make testable quantitative predictions from a theory of forces acting on corpuscles of light. But they did make quantitative predictions from the premises that rays were countable objects, which were conserved in their interactions with matter (except absorbent media), and which had particular orientations with respect to their directions of propagation. According to this framework, polarization and the related phenomena of double refraction and partial reflection involved altering the orientations of the rays and/or selecting them according to orientation, and the state of polarization of a beam (a bundle of rays) was a question of how many rays were in what orientations: in a fully polarized beam, the orientations were all the same. This approach, which Jed Buchwald has called selectionism, was pioneered by Malus and diligently pursued by Biot.
Fresnel, in contrast, decided to introduce polarization into interference experiments.
Interference of polarized light, chromatic polarization (1816–21)
In July or August 1816, Fresnel discovered that when a birefringent crystal produced two images of a single slit, he could not obtain the usual two-slit interference pattern, even if he compensated for the different propagation times. A more general experiment, suggested by Arago, found that if the two beams of a double-slit device were separately polarized, the interference pattern appeared and disappeared as the polarization of one beam was rotated, giving full interference for parallel polarizations, but no interference for perpendicular polarizations . These experiments, among others, were eventually reported in a brief memoir published in 1819 and later translated into English. | [
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1141_25 | In a memoir drafted on 30 August 1816 and revised on 6 October, Fresnel reported an experiment in which he placed two matching thin laminae in a double-slit apparatus – one over each slit, with their optic axes perpendicular – and obtained two interference patterns offset in opposite directions, with perpendicular polarizations. This, in combination with the previous findings, meant that each lamina split the incident light into perpendicularly polarized components with different velocities – just like a normal (thick) birefringent crystal, and contrary to Biot's "mobile polarization" hypothesis.
Accordingly, in the same memoir, Fresnel offered his first attempt at a wave theory of chromatic polarization. When polarized light passed through a crystal lamina, it was split into ordinary and extraordinary waves (with intensities described by Malus's law), and these were perpendicularly polarized and therefore did not interfere, so that no colors were produced (yet). But if they then passed through an analyzer (second polarizer), their polarizations were brought into alignment (with intensities again modified according to Malus's law), and they would interfere. This explanation, by itself, predicts that if the analyzer is rotated 90°, the ordinary and extraordinary waves simply switch roles, so that if the analyzer takes the form of a calcite crystal, the two images of the lamina should be of the same hue (this issue is revisited below). But in fact, as Arago and Biot had found, they are of complementary colors. To correct the prediction, Fresnel proposed a phase-inversion rule whereby one of the constituent waves of one of the two images suffered an additional 180° phase shift on its way through the lamina. This inversion was a weakness in the theory relative to Biot's, as Fresnel acknowledged, although the rule specified which of the two images had the inverted wave. Moreover, Fresnel could deal only with special cases, because he had not yet solved the problem of superposing sinusoidal functions with arbitrary phase differences due to propagation at different velocities through the lamina. | [
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1141_26 | He solved that problem in a "supplement" signed on 15 January 1818 (mentioned above). In the same document, he accommodated Malus's law by proposing an underlying law: that if polarized light is incident on a birefringent crystal with its optic axis at an angle θ to the "plane of polarization", the ordinary and extraordinary vibrations (as functions of time) are scaled by the factors cosθ and sinθ, respectively. Although modern readers easily interpret these factors in terms of perpendicular components of a transverse oscillation, Fresnel did not (yet) explain them that way. Hence he still needed the phase-inversion rule. He applied all these principles to a case of chromatic polarization not covered by Biot's formulae, involving two successive laminae with axes separated by 45°, and obtained predictions that disagreed with Biot's experiments (except in special cases) but agreed with his own.
Fresnel applied the same principles to the standard case of chromatic polarization, in which one birefringent lamina was sliced parallel to its axis and placed between a polarizer and an analyzer. If the analyzer took the form of a thick calcite crystal with its axis in the plane of polarization, Fresnel predicted that the intensities of the ordinary and extraordinary images of the lamina were respectively proportional to
where is the angle from the initial plane of polarization to the optic axis of the lamina, is the angle from the initial plane of polarization to the plane of polarization of the final ordinary image, and is the phase lag of the extraordinary wave relative to the ordinary wave due to the difference in propagation times through the lamina. The terms in are the frequency-dependent terms and explain why the lamina must be thin in order to produce discernible colors: if the lamina is too thick, will pass through too many cycles as the frequency varies through the visible range, and the eye (which divides the visible spectrum into only three bands) will not be able to resolve the cycles.
From these equations it is easily verified that for all so that the colors are complementary. Without the phase-inversion rule, there would be a plus sign in front of the last term in the second equation, so that the -dependent term would be the same in both equations, implying (incorrectly) that the colors were of the same hue. | [
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] |
1141_27 | These equations were included in an undated note that Fresnel gave to Biot, to which Biot added a few lines of his own. If we substitute
and
then Fresnel's formulae can be rewritten as
which are none other than Biot's empirical formulae of 1812, except that Biot interpreted and as the "unaffected" and "affected" selections of the rays incident on the lamina. If Biot's substitutions were accurate, they would imply that his experimental results were more fully explained by Fresnel's theory than by his own.
Arago delayed reporting on Fresnel's works on chromatic polarization until June 1821, when he used them in a broad attack on Biot's theory. In his written response, Biot protested that Arago's attack went beyond the proper scope of a report on the nominated works of Fresnel. But Biot also claimed that the substitutions for and and therefore Fresnel's expressions for and were empirically wrong because when Fresnel's intensities of spectral colors were mixed according to Newton's rules, the squared cosine and sine functions varied too smoothly to account for the observed sequence of colors. That claim drew a written reply from Fresnel, who disputed whether the colors changed as abruptly as Biot claimed, and whether the human eye could judge color with sufficient objectivity for the purpose. On the latter question, Fresnel pointed out that different observers may give different names to the same color. Furthermore, he said, a single observer can only compare colors side by side; and even if they are judged to be the same, the identity is of sensation, not necessarily of composition. Fresnel's oldest and strongest point – that thin crystals were subject to the same laws as thick ones and did not need or allow a separate theory – Biot left unanswered. Arago and Fresnel were seen to have won the debate.
Moreover, by this time Fresnel had a new, simpler explanation of his equations on chromatic polarization.
Breakthrough: Pure transverse waves (1821) | [
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1141_28 | Breakthrough: Pure transverse waves (1821)
In the draft memoir of 30 August 1816, Fresnel mentioned two hypotheses – one of which he attributed to Ampère – by which the non-interference of orthogonally-polarized beams could be explained if polarized light waves were partly transverse. But Fresnel could not develop either of these ideas into a comprehensive theory. As early as September 1816, according to his later account, he realized that the non-interference of orthogonally-polarized beams, together with the phase-inversion rule in chromatic polarization, would be most easily explained if the waves were purely transverse, and Ampère "had the same thought" on the phase-inversion rule. But that would raise a new difficulty: as natural light seemed to be unpolarized and its waves were therefore presumed to be longitudinal, one would need to explain how the longitudinal component of vibration disappeared on polarization, and why it did not reappear when polarized light was reflected or refracted obliquely by a glass plate.
Independently, on 12 January 1817, Young wrote to Arago (in English) noting that a transverse vibration would constitute a polarization, and that if two longitudinal waves crossed at a significant angle, they could not cancel without leaving a residual transverse vibration. Young repeated this idea in an article published in a supplement to the Encyclopædia Britannica in February 1818, in which he added that Malus's law would be explained if polarization consisted in a transverse motion.
Thus Fresnel, by his own testimony, may not have been the first person to suspect that light waves could have a transverse component, or that polarized waves were exclusively transverse. And it was Young, not Fresnel, who first published the idea that polarization depends on the orientation of a transverse vibration. But these incomplete theories had not reconciled the nature of polarization with the apparent existence of unpolarized light; that achievement was to be Fresnel's alone. | [
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1141_29 | In a note that Buchwald dates in the summer of 1818, Fresnel entertained the idea that unpolarized waves could have vibrations of the same energy and obliquity, with their orientations distributed uniformly about the wave-normal, and that the degree of polarization was the degree of non-uniformity in the distribution. Two pages later he noted, apparently for the first time in writing, that his phase-inversion rule and the non-interference of orthogonally-polarized beams would be easily explained if the vibrations of fully polarized waves were "perpendicular to the normal to the wave"—that is, purely transverse.
But if he could account for lack of polarization by averaging out the transverse component, he did not also need to assume a longitudinal component. It was enough to suppose that light waves are purely transverse, hence always polarized in the sense of having a particular transverse orientation, and that the "unpolarized" state of natural or "direct" light is due to rapid and random variations in that orientation, in which case two coherent portions of "unpolarized" light will still interfere because their orientations will be synchronized.
It is not known exactly when Fresnel made this last step, because there is no relevant documentation from 1820 or early 1821 (perhaps because he was too busy working on lighthouse-lens prototypes; see below). But he first published the idea in a paper on "Calcul des teintes…" ("calculation of the tints…"), serialized in Arago's Annales for May, June, and July 1821. In the first installment, Fresnel described "direct" (unpolarized) light as "the rapid succession of systems of waves polarized in all directions", and gave what is essentially the modern explanation of chromatic polarization, albeit in terms of the analogy between polarization and the resolution of forces in a plane, mentioning transverse waves only in a footnote. The introduction of transverse waves into the main argument was delayed to the second installment, in which he revealed the suspicion that he and Ampère had harbored since 1816, and the difficulty it raised. He continued:
According to this new view, he wrote, "the act of polarization consists not in creating these transverse movements, but in decomposing them into two fixed perpendicular directions and in separating the two components". | [
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1141_30 | While selectionists could insist on interpreting Fresnel's diffraction integrals in terms of discrete, countable rays, they could not do the same with his theory of polarization. For a selectionist, the state of polarization of a beam concerned the distribution of orientations over the population of rays, and that distribution was presumed to be static. For Fresnel, the state of polarization of a beam concerned the variation of a displacement over time. That displacement might be constrained but was not static, and rays were geometric constructions, not countable objects. The conceptual gap between the wave theory and selectionism had become unbridgeable.
The other difficulty posed by pure transverse waves, of course, was the apparent implication that the aether was an elastic solid, except that, unlike other elastic solids, it was incapable of transmitting longitudinal waves. The wave theory was cheap on assumptions, but its latest assumption was expensive on credulity. If that assumption was to be widely entertained, its explanatory power would need to be impressive.
Partial reflection (1821)
In the second installment of "Calcul des teintes" (June 1821), Fresnel supposed, by analogy with sound waves, that the density of the aether in a refractive medium was inversely proportional to the square of the wave velocity, and therefore directly proportional to the square of the refractive index. For reflection and refraction at the surface between two isotropic media of different indices, Fresnel decomposed the transverse vibrations into two perpendicular components, now known as the s and p components, which are parallel to the surface and the plane of incidence, respectively; in other words, the s and p components are respectively square and parallel to the plane of incidence. For the s component, Fresnel supposed that the interaction between the two media was analogous to an elastic collision, and obtained a formula for what we now call the reflectivity: the ratio of the reflected intensity to the incident intensity. The predicted reflectivity was non-zero at all angles. | [
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1141_31 | The third installment (July 1821) was a short "postscript" in which Fresnel announced that he had found, by a "mechanical solution", a formula for the reflectivity of the p component, which predicted that the reflectivity was zero at the Brewster angle. So polarization by reflection had been accounted for – but with the proviso that the direction of vibration in Fresnel's model was perpendicular to the plane of polarization as defined by Malus. (On the ensuing controversy, see Plane of polarization.) The technology of the time did not allow the s and p reflectivities to be measured accurately enough to test Fresnel's formulae at arbitrary angles of incidence. But the formulae could be rewritten in terms of what we now call the reflection coefficient: the signed ratio of the reflected amplitude to the incident amplitude. Then, if the plane of polarization of the incident ray was at 45° to the plane of incidence, the tangent of the corresponding angle for the reflected ray was obtainable from the ratio of the two reflection coefficients, and this angle could be measured. Fresnel had measured it for a range of angles of incidence, for glass and water, and the agreement between the calculated and measured angles was better than 1.5° in all cases.
Fresnel gave details of the "mechanical solution" in a memoir read to the Académie des Sciences on 7 January 1823. Conservation of energy was combined with continuity of the tangential vibration at the interface. The resulting formulae for the reflection coefficients and reflectivities became known as the Fresnel equations. The reflection coefficients for the s and p polarizations are most succinctly expressed as
and
where and are the angles of incidence and refraction; these equations are known respectively as Fresnel's sine law and Fresnel's tangent law. By allowing the coefficients to be complex, Fresnel even accounted for the different phase shifts of the s and p components due to total internal reflection.
This success inspired James MacCullagh and Augustin-Louis Cauchy, beginning in 1836, to analyze reflection from metals by using the Fresnel equations with a complex refractive index. The same technique is applicable to non-metallic opaque media. With these generalizations, the Fresnel equations can predict the appearance of a wide variety of objects under illumination – for example, in computer graphics . | [
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1141_32 | Circular and elliptical polarization, optical rotation (1822)
In a memoir dated 9 December 1822, Fresnel coined the terms linear polarization (French: polarisation rectiligne) for the simple case in which the perpendicular components of vibration are in phase or 180° out of phase, circular polarization for the case in which they are of equal magnitude and a quarter-cycle (±90°) out of phase, and elliptical polarization for other cases in which the two components have a fixed amplitude ratio and a fixed phase difference. He then explained how optical rotation could be understood as a species of birefringence. Linearly-polarized light could be resolved into two circularly-polarized components rotating in opposite directions. If these components propagated at slightly different speeds, the phase difference between them – and therefore the direction of their linearly-polarized resultant – would vary continuously with distance.
These concepts called for a redefinition of the distinction between polarized and unpolarized light. Before Fresnel, it was thought that polarization could vary in direction, and in degree (e.g., due to variation in the angle of reflection off a transparent body), and that it could be a function of color (chromatic polarization), but not that it could vary in kind. Hence it was thought that the degree of polarization was the degree to which the light could be suppressed by an analyzer with the appropriate orientation. Light that had been converted from linear to elliptical or circular polarization (e.g., by passage through a crystal lamina, or by total internal reflection) was described as partly or fully "depolarized" because of its behavior in an analyzer. After Fresnel, the defining feature of polarized light was that the perpendicular components of vibration had a fixed ratio of amplitudes and a fixed difference in phase. By that definition, elliptically or circularly polarized light is fully polarized although it cannot be fully suppressed by an analyzer alone. The conceptual gap between the wave theory and selectionism had widened again.
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1141_33 | Total internal reflection (1817–23)
By 1817 it had been discovered by Brewster, but not adequately reported, that plane-polarized light was partly depolarized by total internal reflection if initially polarized at an acute angle to the plane of incidence. Fresnel rediscovered this effect and investigated it by including total internal reflection in a chromatic-polarization experiment. With the aid of his first theory of chromatic polarization, he found that the apparently depolarized light was a mixture of components polarized parallel and perpendicular to the plane of incidence, and that the total reflection introduced a phase difference between them. Choosing an appropriate angle of incidence (not yet exactly specified) gave a phase difference of 1/8 of a cycle (45°). Two such reflections from the "parallel faces" of "two coupled prisms" gave a phase difference of 1/4 of a cycle (90°). These findings were contained in a memoir submitted to the Académie on 10 November 1817 and read a fortnight later. An undated marginal note indicates that the two coupled prisms were later replaced by a single "parallelepiped in glass"—now known as a Fresnel rhomb.
This was the memoir whose "supplement", dated January 1818, contained the method of superposing sinusoidal functions and the restatement of Malus's law in terms of amplitudes. In the same supplement, Fresnel reported his discovery that optical rotation could be emulated by passing the polarized light through a Fresnel rhomb (still in the form of "coupled prisms"), followed by an ordinary birefringent lamina sliced parallel to its axis, with the axis at 45° to the plane of reflection of the Fresnel rhomb, followed by a second Fresnel rhomb at 90° to the first. In a further memoir read on 30 March, Fresnel reported that if polarized light was fully "depolarized" by a Fresnel rhomb – now described as a parallelepiped – its properties were not further modified by a subsequent passage through an optically rotating medium or device. | [
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1141_34 | The connection between optical rotation and birefringence was further explained in 1822, in the memoir on elliptical and circular polarization. This was followed by the memoir on reflection, read in January 1823, in which Fresnel quantified the phase shifts in total internal reflection, and thence calculated the precise angle at which a Fresnel rhomb should be cut in order to convert linear polarization to circular polarization. For a refractive index of 1.51, there were two solutions: about 48.6° and 54.6°.
Double refraction
Background: Uniaxial and biaxial crystals; Biot's laws
When light passes through a slice of calcite cut perpendicular to its optic axis, the difference between the propagation times of the ordinary and extraordinary waves has a second-order dependence on the angle of incidence. If the slice is observed in a highly convergent cone of light, that dependence becomes significant, so that a chromatic-polarization experiment will show a pattern of concentric rings. But most minerals, when observed in this manner, show a more complicated pattern of rings involving two foci and a lemniscate curve, as if they had two optic axes. The two classes of minerals naturally become known as uniaxal and biaxal—or, in later literature, uniaxial and biaxial.
In 1813, Brewster observed the simple concentric pattern in "beryl, emerald, ruby &c." The same pattern was later observed in calcite by Wollaston, Biot, and Seebeck. Biot, assuming that the concentric pattern was the general case, tried to calculate the colors with his theory of chromatic polarization, and succeeded better for some minerals than for others. In 1818, Brewster belatedly explained why: seven of the twelve minerals employed by Biot had the lemniscate pattern, which Brewster had observed as early as 1812; and the minerals with the more complicated rings also had a more complicated law of refraction. | [
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1141_35 | In a uniform crystal, according to Huygens's theory, the secondary wavefront that expands from the origin in unit time is the ray-velocity surface—that is, the surface whose "distance" from the origin in any direction is the ray velocity in that direction. In calcite, this surface is two-sheeted, consisting of a sphere (for the ordinary wave) and an oblate spheroid (for the extraordinary wave) touching each other at opposite points of a common axis—touching at the north and south poles, if we may use a geographic analogy. But according to Malus's corpuscular theory of double refraction, the ray velocity was proportional to the reciprocal of that given by Huygens's theory, in which case the velocity law was of the form
where and were the ordinary and extraordinary ray velocities according to the corpuscular theory, and was the angle between the ray and the optic axis. By Malus's definition, the plane of polarization of a ray was the plane of the ray and the optic axis if the ray was ordinary, or the perpendicular plane (containing the ray) if the ray was extraordinary. In Fresnel's model, the direction of vibration was normal to the plane of polarization. Hence, for the sphere (the ordinary wave), the vibration was along the lines of latitude (continuing the geographic analogy); and for the spheroid (the extraordinary wave), the vibration was along the lines of longitude. | [
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1141_36 | On 29 March 1819, Biot presented a memoir in which he proposed simple generalizations of Malus's rules for a crystal with two axes, and reported that both generalizations seemed to be confirmed by experiment. For the velocity law, the squared sine was replaced by the product of the sines of the angles from the ray to the two axes (Biot's sine law). And for the polarization of the ordinary ray, the plane of the ray and the axis was replaced by the plane bisecting the dihedral angle between the two planes each of which contained the ray and one axis (Biot's dihedral law). Biot's laws meant that a biaxial crystal with axes at a small angle, cleaved in the plane of those axes, behaved nearly like a uniaxial crystal at near-normal incidence; this was fortunate because gypsum, which had been used in chromatic-polarization experiments, is biaxial.
First memoir and supplements (1821–22)
Until Fresnel turned his attention to biaxial birefringence, it was assumed that one of the two refractions was ordinary, even in biaxial crystals. But, in a memoir submitted on 19 November 1821, Fresnel reported two experiments on topaz showing that neither refraction was ordinary in the sense of satisfying Snell's law; that is, neither ray was the product of spherical secondary waves. | [
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1141_37 | The same memoir contained Fresnel's first attempt at the biaxial velocity law. For calcite, if we interchange the equatorial and polar radii of Huygens's oblate spheroid while preserving the polar direction, we obtain a prolate spheroid touching the sphere at the equator. A plane through the center/origin cuts this prolate spheroid in an ellipse whose major and minor semi-axes give the magnitudes of the extraordinary and ordinary ray velocities in the direction normal to the plane, and (said Fresnel) the directions of their respective vibrations. The direction of the optic axis is the normal to the plane for which the ellipse of intersection reduces to a circle. So, for the biaxial case, Fresnel simply replaced the prolate spheroid with a triaxial ellipsoid, which was to be sectioned by a plane in the same way. In general there would be two planes passing through the center of the ellipsoid and cutting it in a circle, and the normals to these planes would give two optic axes. From the geometry, Fresnel deduced Biot's sine law (with the ray velocities replaced by their reciprocals). | [
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1141_38 | The ellipsoid indeed gave the correct ray velocities (although the initial experimental verification was only approximate). But it did not give the correct directions of vibration, for the biaxial case or even for the uniaxial case, because the vibrations in Fresnel's model were tangential to the wavefront—which, for an extraordinary ray, is not generally normal to the ray. This error (which is small if, as in most cases, the birefringence is weak) was corrected in an "extract" that Fresnel read to the Académie a week later, on 26 November. Starting with Huygens's spheroid, Fresnel obtained a 4th-degree surface which, when sectioned by a plane as above, would yield the wave-normal velocities for a wavefront in that plane, together with their vibration directions. For the biaxial case, he generalized the equation to obtain a surface with three unequal principal dimensions; this he subsequently called the "surface of elasticity". But he retained the earlier ellipsoid as an approximation, from which he deduced Biot's dihedral law.
Fresnel's initial derivation of the surface of elasticity had been purely geometric, and not deductively rigorous. His first attempt at a mechanical derivation, contained in a "supplement" dated 13 January 1822, assumed that (i) there were three mutually perpendicular directions in which a displacement produced a reaction in the same direction, (ii) the reaction was otherwise a linear function of the displacement, and (iii) the radius of the surface in any direction was the square root of the component, in that direction, of the reaction to a unit displacement in that direction. The last assumption recognized the requirement that if a wave was to maintain a fixed direction of propagation and a fixed direction of vibration, the reaction must not be outside the plane of those two directions. | [
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] |
1141_39 | In the same supplement, Fresnel considered how he might find, for the biaxial case, the secondary wavefront that expands from the origin in unit time—that is, the surface that reduces to Huygens's sphere and spheroid in the uniaxial case. He noted that this "wave surface" (surface de l'onde) is tangential to all possible plane wavefronts that could have crossed the origin one unit of time ago, and he listed the mathematical conditions that it must satisfy. But he doubted the feasibility of deriving the surface from those conditions.
In a "second supplement", Fresnel eventually exploited two related facts: (i) the "wave surface" was also the ray-velocity surface, which could be obtained by sectioning the ellipsoid that he had initially mistaken for the surface of elasticity, and (ii) the "wave surface" intersected each plane of symmetry of the ellipsoid in two curves: a circle and an ellipse. Thus he found that the "wave surface" is described by the 4th-degree equation
where and are the propagation speeds in directions normal to the coordinate axes for vibrations along the axes (the ray and wave-normal speeds being the same in those special cases). Later commentators put the equation in the more compact and memorable form
Earlier in the "second supplement", Fresnel modeled the medium as an array of point-masses and found that the force-displacement relation was described by a symmetric matrix, confirming the existence of three mutually perpendicular axes on which the displacement produced a parallel force. Later in the document, he noted that in a biaxial crystal, unlike a uniaxial crystal, the directions in which there is only one wave-normal velocity are not the same as those in which there is only one ray velocity. Nowadays we refer to the former directions as the optic axes or binormal axes, and the latter as the ray axes or biradial axes .
Fresnel's "second supplement" was signed on 31 March 1822 and submitted the next day – less than a year after the publication of his pure-transverse-wave hypothesis, and just less than a year after the demonstration of his prototype eight-panel lighthouse lens .
Second memoir (1822–26) | [
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] |
1141_40 | Second memoir (1822–26)
Having presented the pieces of his theory in roughly the order of discovery, Fresnel needed to rearrange the material so as to emphasize the mechanical foundations; and he still needed a rigorous treatment of Biot's dihedral law. He attended to these matters in his "second memoir" on double refraction, published in the Recueils of the Académie des Sciences for 1824; this was not actually printed until late 1827, a few months after his death. In this work, having established the three perpendicular axes on which a displacement produces a parallel reaction, and thence constructed the surface of elasticity, he showed that Biot's dihedral law is exact provided that the binormals are taken as the optic axes, and the wave-normal direction as the direction of propagation.
As early as 1822, Fresnel discussed his perpendicular axes with Cauchy. Acknowledging Fresnel's influence, Cauchy went on to develop the first rigorous theory of elasticity of non-isotropic solids (1827), hence the first rigorous theory of transverse waves therein (1830) — which he promptly tried to apply to optics. The ensuing difficulties drove a long competitive effort to find an accurate mechanical model of the aether. Fresnel's own model was not dynamically rigorous; for example, it deduced the reaction to a shear strain by considering the displacement of one particle while all others were fixed, and it assumed that the stiffness determined the wave velocity as in a stretched string, whatever the direction of the wave-normal. But it was enough to enable the wave theory to do what selectionist theory could not: generate testable formulae covering a comprehensive range of optical phenomena, from mechanical assumptions.
Photoelasticity, multiple-prism experiments (1822)
In 1815, Brewster reported that colors appear when a slice of isotropic material, placed between crossed polarizers, is mechanically stressed. Brewster himself immediately and correctly attributed this phenomenon to stress-induced birefringence — now known as photoelasticity. | [
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1141_41 | In a memoir read in September 1822, Fresnel announced that he had verified Brewster's diagnosis more directly, by compressing a combination of glass prisms so severely that one could actually see a double image through it. In his experiment, Fresnel lined up seven 45°-90°-45° prisms, short side to short side, with their 90° angles pointing in alternating directions. Two half-prisms were added at the ends to make the whole assembly rectangular. The prisms were separated by thin films of turpentine (térébenthine) to suppress internal reflections, allowing a clear line of sight along the row. When the four prisms with similar orientations were compressed in a vise across the line of sight, an object viewed through the assembly produced two images with perpendicular polarizations, with an apparent spacing of 1.5mm at one metre.
At the end of that memoir, Fresnel predicted that if the compressed prisms were replaced by (unstressed) monocrystalline quartz prisms with matching directions of optical rotation, and with their optic axes aligned along the row, an object seen by looking along the common optic axis would give two images, which would seem unpolarized when viewed through an analyzer but, when viewed through a Fresnel rhomb, would be polarized at ±45° to the plane of reflection of the rhomb (indicating that they were initially circularly polarized in opposite directions). This would show directly that optical rotation is a form of birefringence. In the memoir of December 1822, in which he introduced the term circular polarization, he reported that he had confirmed this prediction using only one 14°-152°-14° prism and two glass half-prisms. But he obtained a wider separation of the images by replacing the glass half-prism with quartz half-prisms whose rotation was opposite to that of the 14°-152°-14° prism. He added in passing that one could further increase the separation by increasing the number of prisms.
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] |
1141_42 | Reception
For the supplement to Riffault's translation of Thomson's System of Chemistry, Fresnel was chosen to contribute the article on light. The resulting 137-page essay, titled De la Lumière (On Light), was apparently finished in June 1821 and published by February 1822. With sections covering the nature of light, diffraction, thin-film interference, reflection and refraction, double refraction and polarization, chromatic polarization, and modification of polarization by reflection, it made a comprehensive case for the wave theory to a readership that was not restricted to physicists.
To examine Fresnel's first memoir and supplements on double refraction, the Académie des Sciences appointed Ampère, Arago, Fourier, and Poisson. Their report, of which Arago was clearly the main author, was delivered at the meeting of 19 August 1822. Then, in the words of Émile Verdet, as translated by Ivor Grattan-Guinness:
Whether Laplace was announcing his conversion to the wave theory – at the age of 73 – is uncertain. Grattan-Guinness entertained the idea. Buchwald, noting that Arago failed to explain that the "ellipsoid of elasticity" did not give the correct planes of polarization, suggests that Laplace may have merely regarded Fresnel's theory as a successful generalization of Malus's ray-velocity law, embracing Biot's laws. | [
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1141_43 | In the following year, Poisson, who did not sign Arago's report, disputed the possibility of transverse waves in the aether. Starting from assumed equations of motion of a fluid medium, he noted that they did not give the correct results for partial reflection and double refraction – as if that were Fresnel's problem rather than his own – and that the predicted waves, even if they were initially transverse, became more longitudinal as they propagated. In reply Fresnel noted, inter alia, that the equations in which Poisson put so much faith did not even predict viscosity. The implication was clear: given that the behavior of light had not been satisfactorily explained except by transverse waves, it was not the responsibility of the wave-theorists to abandon transverse waves in deference to pre-conceived notions about the aether; rather, it was the responsibility of the aether modelers to produce a model that accommodated transverse waves. According to Robert H. Silliman, Poisson eventually accepted the wave theory shortly before his death in 1840.
Among the French, Poisson's reluctance was an exception. According to Eugene Frankel, "in Paris no debate on the issue seems to have taken place after 1825. Indeed, almost the entire generation of physicists and mathematicians who came to maturity in the 1820s – Pouillet, Savart, Lamé, Navier, Liouville, Cauchy – seem to have adopted the theory immediately." Fresnel's other prominent French opponent, Biot, appeared to take a neutral position in 1830, and eventually accepted the wave theory – possibly by 1846 and certainly by 1858. | [
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1141_44 | In 1826, the British astronomer John Herschel, who was working on a book-length article on light for the Encyclopædia Metropolitana, addressed three questions to Fresnel concerning double refraction, partial reflection, and their relation to polarization. The resulting article, titled simply "Light", was highly sympathetic to the wave theory, although not entirely free of selectionist language. It was circulating privately by 1828 and was published in 1830. Meanwhile, Young's translation of Fresnel's De la Lumière was published in installments from 1827 to 1829. George Biddell Airy, the former Lucasian Professor at Cambridge and future Astronomer Royal, unreservedly accepted the wave theory by 1831. In 1834, he famously calculated the diffraction pattern of a circular aperture from the wave theory, thereby explaining the limited angular resolution of a perfect telescope . By the end of the 1830s, the only prominent British physicist who held out against the wave theory was Brewster, whose objections included the difficulty of explaining photochemical effects and (in his opinion) dispersion.
A German translation of De la Lumière was published in installments in 1825 and 1828. The wave theory was adopted by Fraunhofer in the early 1820s and by Franz Ernst Neumann in the 1830s, and then began to find favor in German textbooks.
The economy of assumptions under the wave theory was emphasized by William Whewell in his History of the Inductive Sciences, first published in 1837. In the corpuscular system, "every new class of facts requires a new supposition," whereas in the wave system, a hypothesis devised in order to explain one phenomenon is then found to explain or predict others. In the corpuscular system there is "no unexpected success, no happy coincidence, no convergence of principles from remote quarters"; but in the wave system, "all tends to unity and simplicity."
Hence, in 1850, when Foucault and Fizeau found by experiment that light travels more slowly in water than in air, in accordance with the wave explanation of refraction and contrary to the corpuscular explanation, the result came as no surprise.
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1141_45 | Lighthouses and the Fresnel lens
Fresnel was not the first person to focus a lighthouse beam using a lens. That distinction apparently belongs to the London glass-cutter Thomas Rogers, whose first lenses, 53cm in diameter and 14cm thick at the center, were installed at the Old Lower Lighthouse at Portland Bill in 1789. Further samples were installed in about half a dozen other locations by 1804. But much of the light was wasted by absorption in the glass.
Nor was Fresnel the first to suggest replacing a convex lens with a series of concentric annular prisms, to reduce weight and absorption. In 1748, Count Buffon proposed grinding such prisms as steps in a single piece of glass. In 1790, the Marquis de Condorcet suggested that it would be easier to make the annular sections separately and assemble them on a frame; but even that was impractical at the time. These designs were intended not for lighthouses, but for burning glasses. Brewster, however, proposed a system similar to Condorcet's in 1811, and by 1820 was advocating its use in British lighthouses.
Meanwhile, on 21 June 1819, Fresnel was "temporarily" seconded by the Commission des Phares (Commission of Lighthouses) on the recommendation of Arago (a member of the Commission since 1813), to review possible improvements in lighthouse illumination. The commission had been established by Napoleon in 1811 and placed under the Corps des Ponts – Fresnel's employer. | [
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1141_46 | By the end of August 1819, unaware of the Buffon-Condorcet-Brewster proposal, Fresnel made his first presentation to the commission, recommending what he called lentilles à échelons (lenses by steps) to replace the reflectors then in use, which reflected only about half of the incident light. One of the assembled commissioners, Jacques Charles, recalled Buffon's suggestion, leaving Fresnel embarrassed for having again "broken through an open door". But, whereas Buffon's version was biconvex and in one piece, Fresnel's was plano-convex and made of multiple prisms for easier construction. With an official budget of 500 francs, Fresnel approached three manufacturers. The third, François Soleil, produced the prototype. Finished in March 1820, it had a square lens panel 55cm on a side, containing 97 polygonal (not annular) prisms – and so impressed the Commission that Fresnel was asked for a full eight-panel version. This model, completed a year later in spite of insufficient funding, had panels 76cm square. In a public spectacle on the evening of 13 April 1821, it was demonstrated by comparison with the most recent reflectors, which it suddenly rendered obsolete. | [
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1141_47 | Fresnel's next lens was a rotating apparatus with eight "bull's-eye" panels, made in annular arcs by Saint-Gobain, giving eight rotating beams – to be seen by mariners as a periodic flash. Above and behind each main panel was a smaller, sloping bull's-eye panel of trapezoidal outline with trapezoidal elements. This refracted the light to a sloping plane mirror, which then reflected it horizontally, 7 degrees ahead of the main beam, increasing the duration of the flash. Below the main panels were 128 small mirrors arranged in four rings, stacked like the slats of a louver or Venetian blind. Each ring, shaped as a frustum of a cone, reflected the light to the horizon, giving a fainter steady light between the flashes. The official test, conducted on the unfinished Arc de Triomphe on 20 August 1822, was witnessed by the commission – and by Louis and his entourage – from 32km away. The apparatus was stored at Bordeaux for the winter, and then reassembled at Cordouan Lighthouse under Fresnel's supervision. On 25 July 1823, the world's first lighthouse Fresnel lens was lit. Soon afterwards, Fresnel started coughing up blood.
In May 1824, Fresnel was promoted to secretary of the Commission des Phares, becoming the first member of that body to draw a salary, albeit in the concurrent role of Engineer-in-Chief. He was also an examiner (not a teacher) at the École Polytechnique since 1821; but poor health, long hours during the examination season, and anxiety about judging others induced him to resign that post in late 1824, to save his energy for his lighthouse work. | [
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1141_48 | In the same year he designed the first fixed lens – for spreading light evenly around the horizon while minimizing waste above or below. Ideally the curved refracting surfaces would be segments of toroids about a common vertical axis, so that the dioptric panel would look like a cylindrical drum. If this was supplemented by reflecting (catoptric) rings above and below the refracting (dioptric) parts, the entire apparatus would look like a beehive. The second Fresnel lens to enter service was indeed a fixed lens, of third order, installed at Dunkirk by 1 February 1825. However, due to the difficulty of fabricating large toroidal prisms, this apparatus had a 16-sided polygonal plan.
In 1825, Fresnel extended his fixed-lens design by adding a rotating array outside the fixed array. Each panel of the rotating array was to refract part of the fixed light from a horizontal fan into a narrow beam.
Also in 1825, Fresnel unveiled the Carte des Phares (Lighthouse Map), calling for a system of 51 lighthouses plus smaller harbor lights, in a hierarchy of lens sizes (called orders, the first order being the largest), with different characteristics to facilitate recognition: a constant light (from a fixed lens), one flash per minute (from a rotating lens with eight panels), and two per minute (sixteen panels).
In late 1825, to reduce the loss of light in the reflecting elements, Fresnel proposed to replace each mirror with a catadioptric prism, through which the light would travel by refraction through the first surface, then total internal reflection off the second surface, then refraction through the third surface. The result was the lighthouse lens as we now know it. In 1826 he assembled a small model for use on the Canal Saint-Martin, but he did not live to see a full-sized version. | [
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1141_49 | The first fixed lens with toroidal prisms was a first-order apparatus designed by the Scottish engineer Alan Stevenson under the guidance of Léonor Fresnel, and fabricated by Isaac Cookson & Co. from French glass; it entered service at the Isle of May in 1836. The first large catadioptric lenses were fixed third-order lenses made in 1842 for the lighthouses at Gravelines and Île Vierge. The first fully catadioptric first-order lens, installed at Ailly in 1852, gave eight rotating beams assisted by eight catadioptric panels at the top (to lengthen the flashes), plus a fixed light from below. The first fully catadioptric lens with purely revolving beams – also of first order – was installed at Saint-Clément-des-Baleines in 1854, and marked the completion of Augustin Fresnel's original Carte des Phares.
Production of one-piece stepped dioptric lenses—roughly as envisaged by Buffon—became practical in 1852, when John L. Gilliland of the Brooklyn Flint-Glass Company patented a method of making such lenses from press-molded glass. By the 1950s, the substitution of plastic for glass made it economic to use fine-stepped Fresnel lenses as condensers in overhead projectors. Still finer steps can be found in low-cost plastic "sheet" magnifiers.
Honors
Fresnel was elected to the Société Philomathique de Paris in April 1819, and in 1822 became one of the editors of the Société's Bulletin des Sciences. As early as May 1817, at Arago's suggestion, Fresnel applied for membership of the Académie des Sciences, but received only one vote. The successful candidate on that occasion was Joseph Fourier. In November 1822, Fourier's elevation to Permanent Secretary of the Académie created a vacancy in the physics section, which was filled in February 1823 by Pierre Louis Dulong, with 36 votes to Fresnel's 20. But in May 1823, after another vacancy was left by the death of Jacques Charles, Fresnel's election was unanimous. In 1824, Fresnel was made a chevalier de la Légion d'honneur (Knight of the Legion of Honour).
Meanwhile, in Britain, the wave theory was yet to take hold; Fresnel wrote to Thomas Young in November 1824, saying in part: | [
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1141_50 | But "the praise of English scholars" soon followed. On 9 June 1825, Fresnel was made a Foreign Member of the Royal Society of London. In 1827 he was awarded the society's Rumford Medal for the year 1824, "For his Development of the Undulatory Theory as applied to the Phenomena of Polarized Light, and for his various important discoveries in Physical Optics."
A monument to Fresnel at his birthplace was dedicated on 14 September 1884 with a speech by , Permanent Secretary of the Académie des Sciences. "" is among the 72 names embossed on the Eiffel Tower (on the south-east side, fourth from the left). In the 19th century, as every lighthouse in France acquired a Fresnel lens, every one acquired a bust of Fresnel, seemingly watching over the coastline that he had made safer. The lunar features Promontorium Fresnel and Rimae Fresnel were later named after him.
Decline and death
Fresnel's health, which had always been poor, deteriorated in the winter of 1822–1823, increasing the urgency of his original research, and (in part) preventing him from contributing an article on polarization and double refraction for the Encyclopædia Britannica. The memoirs on circular and elliptical polarization and optical rotation, and on the detailed derivation of the Fresnel equations and their application to total internal reflection, date from this period. In the spring he recovered enough, in his own view, to supervise the lens installation at Cordouan. Soon afterwards, it became clear that his condition was tuberculosis.
In 1824, he was advised that if he wanted to live longer, he needed to scale back his activities. Perceiving his lighthouse work to be his most important duty, he resigned as an examiner at the École Polytechnique, and closed his scientific notebooks. His last note to the Académie, read on 13 June 1825, described the first radiometer and attributed the observed repulsive force to a temperature difference. Although his fundamental research ceased, his advocacy did not; as late as August or September 1826, he found the time to answer Herschel's queries on the wave theory. It was Herschel who recommended Fresnel for the Royal Society's Rumford Medal. | [
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1141_51 | Fresnel's cough worsened in the winter of 1826–1827, leaving him too ill to return to Mathieu in the spring. The Académie meeting of 30 April 1827 was the last that he attended. In early June he was carried to Ville-d'Avray, 12km west of Paris. There his mother joined him. On 6 July, Arago arrived to deliver the Rumford Medal. Sensing Arago's distress, Fresnel whispered that "the most beautiful crown means little, when it is laid on the grave of a friend." Fresnel did not have the strength to reply to the Royal Society. He died eight days later, on Bastille Day.
He is buried at Père Lachaise Cemetery, Paris. The inscription on his headstone is partly eroded away; the legible part says, when translated, "To the memory of Augustin Jean Fresnel, member of the Institute of France".
Posthumous publications
Fresnel's "second memoir" on double refraction was not printed until late 1827, a few months after his death. Until then, the best published source on his work on double refraction was an extract of that memoir, printed in 1822. His final treatment of partial reflection and total internal reflection, read to the Académie in January 1823, was thought to be lost until it was rediscovered among the papers of the deceased Joseph Fourier (1768–1830), and was printed in 1831. Until then, it was known chiefly through an extract printed in 1823 and 1825. The memoir introducing the parallelepiped form of the Fresnel rhomb, read in March 1818, was mislaid until 1846, and then attracted such interest that it was soon republished in English. Most of Fresnel's writings on polarized light before 1821 – including his first theory of chromatic polarization (submitted 7 October 1816) and the crucial "supplement" of January 1818 — were not published in full until his Oeuvres complètes ("complete works") began to appear in 1866. The "supplement" of July 1816, proposing the "efficacious ray" and reporting the famous double-mirror experiment, met the same fate, as did the "first memoir" on double refraction. | [
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1141_52 | Publication of Fresnel's collected works was itself delayed by the deaths of successive editors. The task was initially entrusted to Félix Savary, who died in 1841. It was restarted twenty years later by the Ministry of Public Instruction. Of the three editors eventually named in the Oeuvres, Sénarmont died in 1862, Verdet in 1866, and Léonor Fresnel in 1869, by which time only two of the three volumes had appeared. At the beginning of vol. 3 (1870), the completion of the project is described in a long footnote by "J. Lissajous."
Not included in the Oeuvres are two short notes by Fresnel on magnetism, which were discovered among Ampère's manuscripts. In response to Ørsted's discovery of electromagnetism in 1820, Ampère initially supposed that the field of a permanent magnet was due to a macroscopic circulating current. Fresnel suggested instead that there was a microscopic current circulating around each particle of the magnet. In his first note, he argued that microscopic currents, unlike macroscopic currents, would explain why a hollow cylindrical magnet does not lose its magnetism when cut longitudinally. In his second note, dated 5 July 1821, he further argued that a macroscopic current had the counterfactual implication that a permanent magnet should be hot, whereas microscopic currents circulating around the molecules might avoid the heating mechanism. He was not to know that the fundamental units of permanent magnetism are even smaller than molecules . The two notes, together with Ampère's acknowledgment, were eventually published in 1885.
Lost works
Fresnel's essay Rêveries of 1814 has not survived. While its content would have been interesting to historians, its quality may perhaps be gauged from the fact that Fresnel himself never referred to it in his maturity. | [
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1141_53 | More disturbing is the fate of the late article "Sur les Différents Systèmes relatifs à la Théorie de la Lumière" ("On the Different Systems relating to the Theory of Light"), which Fresnel wrote for the newly launched English journal European Review. This work seems to have been similar in scope to the essay De la Lumière of 1821/22, except that Fresnel's views on double refraction, circular and elliptical polarization, optical rotation, and total internal reflection had developed since then. The manuscript was received by the publisher's agent in Paris in early September 1824, and promptly forwarded to London. But the journal failed before Fresnel's contribution could be published. Fresnel tried unsuccessfully to recover the manuscript. The editors of his collected works were also unable to find it, and admitted that it was probably lost.
Unfinished business
Aether drag and aether density
In 1810, Arago found experimentally that the degree of refraction of starlight does not depend on the direction of the earth's motion relative to the line of sight. In 1818, Fresnel showed that this result could be explained by the wave theory, on the hypothesis that if an object with refractive index moved at velocity relative to the external aether (taken as stationary), then the velocity of light inside the object gained the additional component . He supported that hypothesis by supposing that if the density of the external aether was taken as unity, the density of the internal aether was , of which the excess, namely , was dragged along at velocity , whence the average velocity of the internal aether was . The factor in parentheses, which Fresnel originally expressed in terms of wavelengths, became known as the Fresnel drag coefficient.
In his analysis of double refraction, Fresnel supposed that the different refractive indices in different directions within the same medium were due to a directional variation in elasticity, not density (because the concept of mass per unit volume is not directional). But in his treatment of partial reflection, he supposed that the different refractive indices of different media were due to different aether densities, not different elasticities. The latter decision, although puzzling in the context of double refraction, was consistent with the earlier treatment of aether drag. | [
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1141_54 | In 1846, George Gabriel Stokes pointed out that there was no need to divide the aether inside a moving object into two portions; all of it could be considered as moving at a common velocity. Then, if the aether was conserved while its density changed in proportion to , the resulting velocity of the aether inside the object was equal to Fresnel's additional velocity component.
Dispersion
The analogy between light waves and transverse waves in elastic solids does not predict dispersion — that is, the frequency-dependence of the speed of propagation, which enables prisms to produce spectra and causes lenses to suffer from chromatic aberration. Fresnel, in De la Lumière and in the second supplement to his first memoir on double refraction, suggested that dispersion could be accounted for if the particles of the medium exerted forces on each other over distances that were significant fractions of a wavelength. Later, more than once, Fresnel referred to the demonstration of this result as being contained in a note appended to his "second memoir" on double refraction. But no such note appeared in print, and the relevant manuscripts found after his death showed only that, around 1824, he was comparing refractive indices (measured by Fraunhofer) with a theoretical formula, the meaning of which was not fully explained.
In the 1830s, Fresnel's suggestion was taken up by Cauchy, Powell, and Kelland, and it was indeed found to be tolerably consistent with the variation of refractive indices with wavelength over the visible spectrum, for a variety of transparent media . These investigations were enough to show that the wave theory was at least compatible with dispersion. However, if the model of dispersion was to be accurate over a wider range of frequencies, it needed to be modified so as to take account of resonances within the medium .
Conical refraction
The analytical complexity of Fresnel's derivation of the ray-velocity surface was an implicit challenge to find a shorter path to the result. This was answered by MacCullagh in 1830, and by William Rowan Hamilton in 1832. | [
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1141_55 | Hamilton went further, establishing two properties of the surface that Fresnel, in the short time given to him, had overlooked: (i) at each of the four points where the inner and outer sheets of the surface make contact, the surface has a tangent cone (tangential to both sheets), hence a cone of normals, indicating that a cone of wave-normal directions corresponds to a single ray-velocity vector; and (ii) around each of these points, the outer sheet has a circle of contact with a tangent plane, indicating that a cone of ray directions corresponds to a single wave-normal velocity vector. As Hamilton noted, these properties respectively imply that (i) a narrow beam propagating inside the crystal in the direction of the single ray velocity will, on exiting the crystal through a flat surface, break into a hollow cone (external conical refraction), and (ii) a narrow beam striking a flat surface of the crystal in the appropriate direction (corresponding to that of the single internal wave-normal velocity) will, on entering the crystal, break into a hollow cone (internal conical refraction).
Thus a new pair of phenomena, qualitatively different from anything previously observed or suspected, had been predicted by mathematics as consequences of Fresnel's theory. The prompt experimental confirmation of those predictions by Humphrey Lloyd brought Hamilton a prize that had never come to Fresnel: immediate fame.
Legacy
Within a century of Fresnel's initial stepped-lens proposal, more than 10,000 lights with Fresnel lenses were protecting lives and property around the world. Concerning the other benefits, the science historian Theresa H. Levitt has remarked:
In the history of physical optics, Fresnel's successful revival of the wave theory nominates him as the pivotal figure between Newton, who held that light consisted of corpuscles, and James Clerk Maxwell, who established that light waves are electromagnetic. Whereas Albert Einstein described Maxwell's work as "the most profound and the most fruitful that physics has experienced since the time of Newton," commentators of the era between Fresnel and Maxwell made similarly strong statements about Fresnel:
MacCullagh, as early as 1830, wrote that Fresnel's mechanical theory of double refraction "would do honour to the sagacity of Newton". | [
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1141_56 | Lloyd, in his Report on the progress and present state of physical optics (1834) for the British Association for the Advancement of Science, surveyed previous knowledge of double refraction and declared:The theory of Fresnel to which I now proceed,— and which not only embraces all the known phenomena, but has even outstripped observation, and predicted consequences which were afterwards fully verified,— will, I am persuaded, be regarded as the finest generalization in physical science which has been made since the discovery of universal gravitation.In 1841, Lloyd published his Lectures on the Wave-theory of Light, in which he described Fresnel's transverse-wave theory as "the noblest fabric which has ever adorned the domain of physical science, Newton's system of the universe alone excepted."
William Whewell, in all three editions of his History of the Inductive Sciences (1837, 1847, and 1857), at the end of Book , compared the histories of physical astronomy and physical optics and concluded:It would, perhaps, be too fanciful to attempt to establish a parallelism between the prominent persons who figure in these two histories. If we were to do this, we must consider Huyghens and Hooke as standing in the place of Copernicus, since, like him, they announced the true theory, but left it to a future age to give it development and mechanical confirmation; Malus and Brewster, grouping them together, correspond to Tycho Brahe and Kepler, laborious in accumulating observations, inventive and happy in discovering laws of phenomena; and Young and Fresnel combined, make up the Newton of optical science. | [
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1141_57 | What Whewell called the "true theory" has since undergone two major revisions. The first, by Maxwell, specified the physical fields whose variations constitute the waves of light. Without the benefit of this knowledge, Fresnel managed to construct the world's first coherent theory of light, showing in retrospect that his methods are applicable to multiple types of waves. The second revision, initiated by Einstein's explanation of the photoelectric effect, supposed that the energy of light waves was divided into quanta, which were eventually identified with particles called photons. But photons did not exactly correspond to Newton's corpuscles; for example, Newton's explanation of ordinary refraction required the corpuscles to travel faster in media of higher refractive index, which photons do not. Neither did photons displace waves; rather, they led to the paradox of wave–particle duality. Moreover, the phenomena studied by Fresnel, which included nearly all the optical phenomena known at his time, are still most easily explained in terms of the wave nature of light. So it was that, as late as 1927, the astronomer Eugène Michel Antoniadi declared Fresnel to be "the dominant figure in optics."
See also
Explanatory notes
References
Citations
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1141_58 | D.F.J. Arago (tr. B. Powell), 1857, "Fresnel" (elegy read at the Public Meeting of the Academy of Sciences, 26 July 1830), in D.F.J. Arago (tr. W.H. Smyth, B. Powell, and R. Grant), Biographies of Distinguished Scientific Men (single-volume edition), London: Longman, Brown, Green, Longmans, & Roberts, 1857, pp. 399–471. (On the translator's identity, see pp. 425n,452n.) Erratum: In the translator's note on p. 413, a plane tangent to the outer sphere at point t should intersect the refractive surface (assumed flat); then, through that intersection, tangent planes should be drawn to the inner sphere and spheroid (cf. Mach, 1926, p.263).
D.F.J. Arago and A. Fresnel, 1819, "Mémoire sur l'action que les rayons de lumière polarisée exercent les uns sur les autres", Annales de Chimie et de Physique, Ser.2, vol. 10, pp. 288–305, March 1819; reprinted in Fresnel, 1866–70, vol. 1, pp. 509–22; translated as "On the action of rays of polarized light upon each other", in Crew, 1900, pp. 145–55.
G.-A. Boutry, 1948, "Augustin Fresnel: His time, life and work, 1788–1827", Science Progress, vol. 36, no. 144 (October 1948), pp. 587–604; jstor.org/stable/43413515.
J.Z. Buchwald, 1989, The Rise of the Wave Theory of Light: Optical Theory and Experiment in the Early Nineteenth Century, University of Chicago Press, .
J.Z. Buchwald, 2013, "Optics in the Nineteenth Century", in J.Z. Buchwald and R. Fox (eds.), The Oxford Handbook of the History of Physics, Oxford, , pp. 445–72. | [
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] |
1141_59 | H. Crew (ed.), 1900, The Wave Theory of Light: Memoirs by Huygens, Young and Fresnel, American Book Company.
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1141_60 | A. Fresnel, 1818a, "Mémoire sur les couleurs développées dans les fluides homogènes par la lumière polarisée", read 30 March 1818 (according to Kipnis, 1991, p. 217), published 1846; reprinted in Fresnel, 1866–70, vol. 1, pp. 655–83; translated by E. Ronalds & H. Lloyd as "Memoir upon the colours produced in homogeneous fluids by polarized light", in Taylor, 1852, pp. 44–65. (Cited page numbers refer to the translation.)
A. Fresnel, 1818b, "Mémoire sur la diffraction de la lumière" ("Memoir on the diffraction of light"), deposited 29 July 1818, "crowned" 15 March 1819, published (with appended notes) in Mémoires de l'Académie Royale des Sciences de l'Institut de France, vol. (for 1821 & 1822, printed 1826), pp. 339–475; reprinted (with notes) in Fresnel, 1866–70, vol. 1, pp. 247–383; partly translated as "Fresnel's prize memoir on the diffraction of light", in Crew, 1900, pp. 81–144. Not to be confused with the earlier memoir with the same French title (Fresnel, 1816). | [
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1141_61 | A. Fresnel, 1818c, "Lettre de M. Fresnel à M. Arago sur l'influence du mouvement terrestre dans quelques phénomènes d'optique", Annales de Chimie et de Physique, Ser.2, vol. 9, pp. 57–66 & plate after p.111 (Sep. 1818), & p.286–7 (Nov. 1818); reprinted in Fresnel, 1866–70, vol. 2, pp. 627–36; translated as "Letter from Augustin Fresnel to François Arago, on the influence of the movement of the earth on some phenomena of optics" in K.F. Schaffner, Nineteenth-Century Aether Theories, Pergamon, 1972 (), pp. 125–35; also translated (with several errors) by R.R. Traill as "Letter from Augustin Fresnel to François Arago concerning the influence of terrestrial movement on several optical phenomena", General Science Journal, 23 January 2006 (PDF, 8pp.).
A. Fresnel, 1821a, "Note sur le calcul des teintes que la polarisation développe dans les lames cristallisées" et seq., Annales de Chimie et de Physique, Ser.2, vol. 17, pp. 102–11 (May 1821), 167–96 (June 1821), 312–15 ("Postscript", July 1821); reprinted (with added section nos.) in Fresnel, 1866–70, vol. 1, pp. 609–48; translated as "On the calculation of the tints that polarization develops in crystalline plates, & postscript", / , 2021.
A. Fresnel, 1821b, "Note sur les remarques de M. Biot...", Annales de Chimie et de Physique, Ser.2, vol. 17, pp. 393–403 (August 1821); reprinted (with added section nos.) in Fresnel, 1866–70, vol. 1, pp. 601–608; translated as "Note on the remarks of Mr. Biot relating to colors of thin plates", / , 2021. | [
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1141_62 | A. Fresnel, 1821c, Letter to D.F.J.Arago, 21 September 1821, in Fresnel, 1866–70, vol. 2, pp. 257–9; translated as "Letter to Arago on biaxial birefringence", Wikisource, April 2021.
A. Fresnel, 1822a, De la Lumière (On Light), in J. Riffault (ed.), Supplément à la traduction française de la cinquième édition du "Système de Chimie" par Th.Thomson, Paris: Chez Méquignon-Marvis, 1822, pp. 1–137,535–9; reprinted in Fresnel, 1866–70, vol. 2, pp. 3–146; translated by T. Young as "Elementary view of the undulatory theory of light", Quarterly Journal of Science, Literature, and Art, vol. 22 (Jan.–Jun.1827), pp. 127–41, 441–54; vol. 23 (Jul.–Dec.1827), pp. 113–35, 431–48; vol. 24 (Jan.–Jun.1828), pp. 198–215; vol. 25 (Jul.–Dec.1828), pp. 168–91, 389–407; vol. 26 (Jan.–Jun.1829), pp. 159–65.
A. Fresnel, 1822b, "Mémoire sur un nouveau système d'éclairage des phares", read 29 July 1822; reprinted in Fresnel, 1866–70, vol. 3, pp. 97–126; translated by T. Tag as "Memoir upon a new system of lighthouse illumination", U.S. Lighthouse Society, accessed 26 August 2017; archived 19 August 2016. (Cited page numbers refer to the translation.) | [
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1141_63 | A. Fresnel, 1827, "Mémoire sur la double réfraction", Mémoires de l'Académie Royale des Sciences de l'Institut de France, vol. (for 1824, printed 1827), pp. 45–176; reprinted as "Second mémoire…" in Fresnel, 1866–70, vol. 2, pp. 479–596; translated by A.W. Hobson as "Memoir on double refraction", in Taylor, 1852, pp. 238–333. (Cited page numbers refer to the translation. For notable errata in the original edition, and consequently in the translation, see Fresnel, 1866–70, vol. 2, p. 596n.)
A. Fresnel (ed. H. de Sénarmont, E. Verdet, and L. Fresnel), 1866–70, Oeuvres complètes d'Augustin Fresnel (3 volumes), Paris: Imprimerie Impériale; vol. 1 (1866), vol. 2 (1868), vol. 3 (1870).
I. Grattan-Guinness, 1990, Convolutions in French Mathematics, 1800–1840, Basel: Birkhäuser, vol. 2, , chapter 13 (pp. 852–915, "The entry of Fresnel: Physical optics, 1815–1824") and chapter 15 (pp. 968–1045, "The entry of Navier and the triumph of Cauchy: Elasticity theory, 1819–1830").
C. Huygens, 1690, Traité de la Lumière (Leiden: Van der Aa), translated by S.P. Thompson as Treatise on Light, University of Chicago Press, 1912; Project Gutenberg, 2005. (Cited page numbers match the 1912 edition and the Gutenberg HTML edition.)
F.A. Jenkins and H.E. White, 1976, Fundamentals of Optics, 4th Ed., New York: McGraw-Hill, .
N. Kipnis, 1991, History of the Principle of Interference of Light, Basel: Birkhäuser, , chapters . | [
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1141_66 | Further reading
Some English translations of works by Fresnel are included in the above Bibliography. For a more comprehensive list, see "External links" below.
The most detailed secondary source on Fresnel in English is apparently Buchwald 1989 —in which Fresnel, although not named in the title, is clearly the central character.
On lighthouse lenses, this article heavily cites Levitt 2013, Elton 2009, and Thomas Tag at the U.S. Lighthouse Society (see "External links" below). All three authors deal not only with Fresnel's contributions but also with later innovations that are not mentioned here (see Fresnel lens: History).
By comparison with the volume and impact of his scientific and technical writings, biographical information on Fresnel is remarkably scarce. There is no book-length critical biography of him, and anyone who proposes to write one must confront the fact that the letters published in his Oeuvres complètes—contrary to the title—are heavily redacted. In the words of Robert H. Silliman (1967, p. 6n): "By an unhappy judgment of the editors, dictated in part, one suspects, by political expediency, the letters appear in fragmentary form, preserving almost nothing beyond the technical discussions of Fresnel and his correspondents." It is not clear from the secondary sources whether the manuscripts of those letters are still extant (cf. Grattan-Guinness, 1990, p.854n).
External links
List of English translations of works by Augustin Fresnel at Zenodo.
United States Lighthouse Society, especially "Fresnel Lenses".
.
.
1788 births
1827 deaths
19th-century deaths from tuberculosis
19th-century French physicists
Burials at Père Lachaise Cemetery
Corps des ponts
École des Ponts ParisTech alumni
École Polytechnique alumni
Foreign Members of the Royal Society
French civil engineers
French humanitarians
French Roman Catholics
History of physics
Tuberculosis deaths in France
Jansenists
Light
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Members of the French Academy of Sciences
Optical physicists
People from Eure
Physical optics | [
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1143_0 | Abbot (from the Aramaic Abba meaning "father") is an ecclesiastical title given to the male head of a monastery in various Western religious traditions, including Christianity. The office may also be given as an honorary title to a clergyman who is not the head of a monastery. The female equivalent is abbess.
Origins
The title had its origin in the monasteries of Egypt and Syria, spread through the eastern Mediterranean, and soon became accepted generally in all languages as the designation of the head of a monastery. The word is derived from the Aramaic meaning "father" or , meaning "my father" (it still has this meaning in contemporary Israeli Hebrew: אבא) In the Septuagint, it was written as "abbas". At first it was employed as a respectful title for any monk, but it was soon restricted by canon law to certain priestly superiors. At times it was applied to various priests, e.g. at the court of the Frankish monarchy the ("of the palace"') and ("of the camp") were chaplains to the Merovingian and Carolingian sovereigns’ court and army respectively. The title of abbot came into fairly general use in western monastic orders whose members include priests.
Monastic history
An abbot (from , , from ("father"), from (), from / (, "father"); compare ; ) is the head and chief governor of a community of monks, called also in the East hegumen or archimandrite. The English version for a female monastic head is abbess.
Early history
In Egypt, the first home of monasticism, the jurisdiction of the abbot, or archimandrite, was but loosely defined. Sometimes he ruled over only one community, sometimes over several, each of which had its own abbot as well. Saint John Cassian speaks of an abbot of the Thebaid who had 500 monks under him. By the Rule of St Benedict, which, until the Cluniac reforms, was the norm in the West, the abbot has jurisdiction over only one community. The rule, as was inevitable, was subject to frequent violations; but it was not until the foundation of the Cluniac Order that the idea of a supreme abbot, exercising jurisdiction over all the houses of an order, was definitely recognised. | [
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1143_1 | Monks, as a rule, were laymen, nor at the outset was the abbot any exception. For the reception of the sacraments, and for other religious offices, the abbot and his monks were commanded to attend the nearest church. This rule proved inconvenient when a monastery was situated in a desert or at a distance from a city, and necessity compelled the ordination of some monks. This innovation was not introduced without a struggle, ecclesiastical dignity being regarded as inconsistent with the higher spiritual life, but, before the close of the 5th century, at least in the East, abbots seem almost universally to have become deacons, if not priests. The change spread more slowly in the West, where the office of abbot was commonly filled by laymen till the end of the 7th century. The ecclesiastical leadership exercised by abbots despite their frequent lay status is proved by their attendance and votes at ecclesiastical councils. Thus at the first Council of Constantinople, AD 448, 23 archimandrites or abbots sign, with 30 bishops.
The second Council of Nicaea, AD 787, recognized the right of abbots to ordain their monks to the inferior orders below the diaconate, a power usually reserved to bishops.
Abbots used to be subject to episcopal jurisdiction, and continued generally so, in fact, in the West till the 11th century. The Code of Justinian (lib. i. tit. iii. de Ep. leg. xl.) expressly subordinates the abbot to episcopal oversight. The first case recorded of the partial exemption of an abbot from episcopal control is that of Faustus, abbot of Lerins, at the council of Arles, AD 456; but the exorbitant claims and exactions of bishops, to which this repugnance to episcopal control is to be traced, far more than to the arrogance of abbots, rendered it increasingly frequent, and, in the 6th century, the practice of exempting religious houses partly or altogether from episcopal control, and making them responsible to the pope alone, received an impulse from Pope Gregory the Great. These exceptions, introduced with a good object, had grown into a widespread evil by the 12th century, virtually creating an imperium in imperio, and depriving the bishop of all authority over the chief centres of influence in his diocese.
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1143_2 | Later Middle Ages
In the 12th century, the abbots of Fulda claimed precedence of the archbishop of Cologne. Abbots more and more assumed almost episcopal state, and in defiance of the prohibition of early councils and the protests of St Bernard and others, adopted the episcopal insignia of mitre, ring, gloves and sandals.
It has been maintained that the right to wear mitres was sometimes granted by the popes to abbots before the 11th century, but the documents on which this claim is based are not genuine (J. Braun, Liturgische Gewandung, p. 453). The first undoubted instance is the bull by which Alexander II in 1063 granted the use of the mitre to Egelsinus, abbot of the monastery of St Augustine at Canterbury. The mitred abbots in England were those of Abingdon, St Alban's, Bardney, Battle, Bury St Edmunds, St Augustine's Canterbury, Colchester, Croyland, Evesham, Glastonbury, Gloucester, St Benet's Hulme, Hyde, Malmesbury, Peterborough, Ramsey, Reading, Selby, Shrewsbury, Tavistock, Thorney, Westminster, Winchcombe, and St Mary's York. Of these the precedence was yielded to the abbot of Glastonbury, until in AD 1154 Adrian IV (Nicholas Breakspear) granted it to the abbot of St Alban's, in which monastery he had been brought up. Next after the abbot of St Alban's ranked the abbot of Westminster and then Ramsey. Elsewhere, the mitred abbots that sat in the Estates of Scotland were of Arbroath, Cambuskenneth, Coupar Angus, Dunfermline, Holyrood, Iona, Kelso, Kilwinning, Kinloss, Lindores, Paisley, Melrose, Scone, St Andrews Priory and Sweetheart. To distinguish abbots from bishops, it was ordained that their mitre should be made of less costly materials, and should not be ornamented with gold, a rule which was soon entirely disregarded, and that the crook of their pastoral staff (the crosier) should turn inwards instead of outwards, indicating that their jurisdiction was limited to their own house. | [
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1143_3 | The adoption of certain episcopal insignia (pontificalia) by abbots was followed by an encroachment on episcopal functions, which had to be specially but ineffectually guarded against by the Lateran council, AD 1123. In the East abbots, if in priests' orders and with the consent of the bishop, were, as we have seen, permitted by the second Nicene council, AD 787, to confer the tonsure and admit to the order of reader; but gradually abbots, in the West also, advanced higher claims, until we find them in AD 1489 permitted by Innocent IV to confer both the subdiaconate and diaconate. Of course, they always and everywhere had the power of admitting their own monks and vesting them with the religious habit.
The power of the abbot was paternal but absolute, limited, however, by the canon law. One of the main goals of monasticism was the purgation of self and selfishness, and obedience was seen as a path to that perfection. It was sacred duty to execute the abbot's orders, and even to act without his orders was sometimes considered a transgression. Examples among the Egyptian monks of this submission to the commands of the superiors, exalted into a virtue by those who regarded the entire crushing of the individual will as a goal, are detailed by Cassian and others, e.g. a monk watering a dry stick, day after day, for months, or endeavoring to remove a huge rock immensely exceeding his powers. | [
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1143_4 | Appointments
When a vacancy occurred, the bishop of the diocese chose the abbot out of the monks of the monastery, but the right of election was transferred by jurisdiction to the monks themselves, reserving to the bishop the confirmation of the election and the benediction of the new abbot. In abbeys exempt from the archbishop's diocesan jurisdiction, the confirmation and benediction had to be conferred by the pope in person, the house being taxed with the expenses of the new abbot's journey to Rome. It was necessary that an abbot should be at least 30 years of age, of legitimate birth, a monk of the house for at least 10 years, unless it furnished no suitable candidate, when a liberty was allowed of electing from another monastery, well instructed himself, and able to instruct others, one also who had learned how to command by having practised obedience. In some exceptional cases an abbot was allowed to name his own successor. Cassian speaks of an abbot in Egypt doing this; and in later times we have another example in the case of St Bruno. Popes and sovereigns gradually encroached on the rights of the monks, until in Italy the pope had usurped the nomination of all abbots, and the king in France, with the exception of Cluny, Premontré and other houses, chiefs of their order. The election was for life, unless the abbot was canonically deprived by the chiefs of his order, or when he was directly subject to them, by the pope or the bishop, and also in England it was for a term of 8–12 years.
The ceremony of the formal admission of a Benedictine abbot in medieval times is thus prescribed by the consuetudinary of Abingdon. The newly elected abbot was to put off his shoes at the door of the church, and proceed barefoot to meet the members of the house advancing in a procession. After proceeding up the nave, he was to kneel and pray at the topmost step of the entrance of the choir, into which he was to be introduced by the bishop or his commissary, and placed in his stall. The monks, then kneeling, gave him the kiss of peace on the hand, and rising, on the mouth, the abbot holding his staff of office. He then put on his shoes in the vestry, and a chapter was held, and the bishop or his delegate preached a suitable sermon. | [
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1143_5 | General information
Before the late modern era, the abbot was treated with the utmost reverence by the brethren of his house. When he appeared either in church or chapter all present rose and bowed. His letters were received kneeling, as were those of the pope and the king. No monk might sit in his presence, or leave it without his permission, reflecting the hierarchical etiquette of families and society. The highest place was assigned to him, both in church and at table. In the East he was commanded to eat with the other monks. In the West the Rule of St Benedict appointed him a separate table, at which he might entertain guests and strangers. Because this permission opened the door to luxurious living, Synods of Aachen (816–819), decreed that the abbot should dine in the refectory, and be content with the ordinary fare of the monks, unless he had to entertain a guest. These ordinances proved, however, generally ineffectual to secure strictness of diet, and contemporaneous literature abounds with satirical remarks and complaints concerning the inordinate extravagance of the tables of the abbots. When the abbot condescended to dine in the refectory, his chaplains waited upon him with the dishes, a servant, if necessary, assisting them. When abbots dined in their own private hall, the Rule of St Benedict charged them to invite their monks to their table, provided there was room, on which occasions the guests were to abstain from quarrels, slanderous talk and idle gossiping. | [
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1143_6 | The ordinary attire of the abbot was according to rule to be the same as that of the monks. But by the 10th century the rule was commonly set aside, and we find frequent complaints of abbots dressing in silk, and adopting sumptuous attire. Some even laid aside the monastic habit altogether, and assumed a secular dress. With the increase of wealth and power, abbots had lost much of their special religious character, and become great lords, chiefly distinguished from lay lords by celibacy. Thus we hear of abbots going out to hunt, with their men carrying bows and arrows; keeping horses, dogs and huntsmen; and special mention is made of an abbot of Leicester, c. 1360, who was the most skilled of all the nobility in hare hunting. In magnificence of equipage and retinue the abbots vied with the first nobles of the realm. They rode on mules with gilded bridles, rich saddles and housings, carrying hawks on their wrist, followed by an immense train of attendants. The bells of the churches were rung as they passed. They associated on equal terms with laymen of the highest distinction, and shared all their pleasures and pursuits. This rank and power was, however, often used most beneficially. For instance, we read of Richard Whiting, the last abbot of Glastonbury, judicially murdered by Henry VIII, that his house was a kind of well-ordered court, where as many as 300 sons of noblemen and gentlemen, who had been sent to him for virtuous education, had been brought up, besides others of a lesser rank, whom he fitted for the universities. His table, attendance and officers were an honour to the nation. He would entertain as many as 500 persons of rank at one time, besides relieving the poor of the vicinity twice a week. He had his country houses and fisheries, and when he travelled to attend parliament his retinue amounted to upwards of 100 persons. The abbots of Cluny and Vendôme were, by virtue of their office, cardinals of the Roman church. | [
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1143_7 | In the process of time, the title abbot was extended to clerics who had no connection with the monastic system, as to the principal of a body of parochial clergy; and under the Carolingians to the chief chaplain of the king, , or military chaplain of the emperor, It even came to be adopted by purely secular officials. Thus the chief magistrate of the republic at Genoa was called .
Lay abbots (M. Lat. , , , , or , , or sometimes simply ) were the outcome of the growth of the feudal system from the 8th century onwards. The practice of commendation, by which—to meet a contemporary emergency—the revenues of the community were handed over to a lay lord, in return for his protection,
early suggested to the emperors and kings the expedient of rewarding their warriors with rich abbeys held in commendam.
During the Carolingian epoch, the custom grew up of granting these as regular heritable fiefs or benefices, and by the 10th century, before the great Cluniac reform, the system was firmly established. Even the abbey of St Denis was held in commendam by Hugh Capet. The example of the kings was followed by the feudal nobles, sometimes by making a temporary concession permanent, sometimes without any form of commendation whatever. In England the abuse was rife in the 8th century, as may be gathered from the acts of the council of Cloveshoe. These lay abbacies were not merely a question of overlordship, but implied the concentration in lay hands of all the rights, immunities and jurisdiction of the foundations, i.e. the more or less complete secularization of spiritual institutions. The lay abbot took his recognized rank in the feudal hierarchy, and was free to dispose of his fief as in the case of any other. The enfeoffment of abbeys differed in form and degree. Sometimes the monks were directly subject to the lay abbot; sometimes he appointed a substitute to perform the spiritual functions, known usually as dean (), but also as abbot (, , ). | [
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1143_8 | When the great reform of the 11th century had put an end to the direct jurisdiction of the lay abbots, the honorary title of abbot continued to be held by certain of the great feudal families, as late as the 13th century and later, with the head of the community retaining the title of dean. The connection of the lesser lay abbots with the abbeys, especially in the south of France, lasted longer; and certain feudal families retained the title of () for centuries, together with certain rights over the abbey lands or revenues. The abuse was not confined to the West. John, patriarch of Antioch at the beginning of the 12th century, informs us that in his time most monasteries had been handed over to laymen, , for life, or for part of their lives, by the emperors.
Giraldus Cambrensis reported (Itinerary, ii.iv) the common customs of lay abbots in the late 12th-century Church of Wales:
In conventual cathedrals, where the bishop occupied the place of the abbot, the functions usually devolving on the superior of the monastery were performed by a prior.
Modern practices
In the Roman Catholic Church, abbots continue to be elected by the monks of an abbey to lead them as their religious superior in those orders and monasteries that make use of the term (some orders of monks, as the Carthusians for instance, have no abbots, only priors). A monastery must have been granted the status of an abbey by the pope, and such monasteries are normally raised to this level after showing a degree of stability—a certain number of monks in vows, a certain number of years of establishment, a certain firmness to the foundation in economic, vocational and legal aspects. Prior to this, the monastery would be a mere priory, headed by a prior who acts as superior but without the same degree of legal authority that an abbot has. | [
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1143_9 | The abbot is chosen by the monks from among the fully professed monks. Once chosen, he must request blessing: the blessing of an abbot is celebrated by the bishop in whose diocese the monastery is or, with his permission, another abbot or bishop. The ceremony of such a blessing is similar in some aspects to the consecration of a bishop, with the new abbot being presented with the mitre, the ring, and the crosier as symbols of office and receiving the laying on of hands and blessing from the celebrant. Though the ceremony installs the new abbot into a position of legal authority, it does not confer further sacramental authority- it is not a further degree of Holy Orders (although some abbots have been ordained to the episcopacy).
Once he has received this blessing, the abbot not only becomes father of his monks in a spiritual sense, but their major superior under canon law, and has the additional authority to confer the ministries of acolyte and lector (formerly, he could confer the minor orders, which are not sacraments, that these ministries have replaced). The abbey is a species of "exempt religious" in that it is, for the most part, answerable to the pope, or to the abbot primate, rather than to the local bishop.
The abbot wears the same habit as his fellow monks, though by tradition he adds to it a pectoral cross.
Territorial abbots follow all of the above, but in addition must receive a mandate of authority from the pope over the territory around the monastery for which they are responsible.
Abbatial hierarchy
In some monastic families, there is a hierarchy of precedence or authority among abbots. In some cases, this is the result of an abbey being considered the "mother" of several "daughter" abbeys founded as dependent priories of the "mother." In other cases, abbeys have affiliated in networks known as "congregations." Some monastic families recognize one abbey as the motherhouse of the entire order. | [
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1143_10 | The abbot of Sant'Anselmo di Aventino, in Rome, is styled the "abbot primate," and is acknowledged the senior abbot for the Order of St. Benedict (O.S.B.)
An abbot president is the head of a congregation (federation) of abbeys within the Order of St. Benedict (for instance, the English Congregation, The American Cassinese Congregation, etc.), or of the Cistercians (O. Cist.)
An archabbot is the head of some monasteries which are the motherhouses of other monasteries (for instance, Saint Vincent Archabbey, Latrobe, Pennsylvania)
Mauro-Giuseppe Lepori O. Cist. is the current Abbot General of the Cistercians of the Common Observance.
Modern abbots not as superior
The title abbé (French; Ital. abate), as commonly used in the Catholic Church on the European continent, is the equivalent of the English "Father" (parallel etymology), being loosely applied to all who have received the tonsure. This use of the title is said to have originated in the right conceded to the king of France, by the concordat between Pope Leo X and Francis I (1516), to appoint commendatory abbots () to most of the abbeys in France. The expectation of obtaining these sinecures drew young men towards the church in considerable numbers, and the class of abbés so formed - they were sometimes called, and sometimes (ironically) ("abbés of holy hope; or in a jeu de mots, "of St. Hope") - came to hold a recognized position. The connection many of them had with the church was of the slenderest kind, consisting mainly in adopting the title of abbé, after a remarkably moderate course of theological study, practising celibacy and wearing distinctive dress, a short dark-violet coat with narrow collar. Being men of presumed learning and undoubted leisure, many of the class found admission to the houses of the French nobility as tutors or advisers. Nearly every great family had its abbé. The class did not survive the Revolution; but the courtesy title of abbé, having long lost all connection in people's minds with any special ecclesiastical function, remained as a convenient general term applicable to any clergyman.
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1143_11 | Eastern Christian
In the Eastern Orthodox and Eastern Catholic Churches, the abbot is referred to as the hegumen. The Superior of a monastery of nuns is called the Hēguménē. The title of archimandrite (literally the head of the enclosure) used to mean something similar.
In the East, the principle set forth in the Corpus Juris Civilis still applies, whereby most abbots are immediately subject to the local bishop. Those monasteries which enjoy the status of being stauropegic will be subject only to a primate or his Synod of Bishops and not the local bishop.
Honorary and other uses of the title
Although currently in the Western Church the title "abbot" is given only abbots of monasteries, the title archimandrite is given to "monastics" (i.e., celibate) priests in the East, even when not attached to a monastery, as an honor for service, similar to the title of monsignor in the Western/Latin Rite of the Catholic Church. In the Eastern Orthodox Church, only monastics are permitted to be elevated to the rank of archimandrite. Married priests are elevated to the parallel rank of Archpriest or Protopresbyter. Normally there are no celibate priests who are not monastics in the Orthodox Church, with the exception of married priests who have been widowed. Since the time of Catherine II the ranks of Abbot and Archimandrite have been given as honorary titles in the Russian Church, and may be given to any monastic, even if he does not in fact serve as the superior of a monastery. In Greek practice the title or function of Abbot corresponds to a person who serves as the head of a monastery, although the title of the Archimandrite may be given to any celibate priest who could serve as the head of a monastery. | [
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1143_12 | In the German Evangelical Church, the German title of Abt (abbot) is sometimes bestowed, like the French abbé, as an honorary distinction, and survives to designate the heads of some monasteries converted at the Reformation into collegiate foundations.
Of these the most noteworthy is Loccum Abbey in Hanover, founded as a Cistercian house in 1163 by Count Wilbrand of Hallermund, and reformed in 1593. The abbot of Loccum, who still carries a pastoral staff, takes precedence over all the clergy of Hanover, and was ex officio a member of the consistory of the kingdom. The governing body of the abbey consists of the abbot, prior and the "convent", or community, of Stiftsherren (canons).
In the Church of England, the Bishop of Norwich, by royal decree given by Henry VIII, also holds the honorary title of "Abbot of St. Benet." This title hails back to England's separation from the See of Rome, when King Henry, as supreme head of the newly independent church, took over all of the monasteries, mainly for their possessions, except for St. Benet, which he spared because the abbot and his monks possessed no wealth, and lived like simple beggars, deposing the incumbent Bishop of Norwich and seating the abbot in his place, thus the dual title still held to this day.
Additionally, at the enthronement of the Archbishop of Canterbury, there is a threefold enthronement, once in the throne the chancel as the diocesan bishop of Canterbury, once in the Chair of St. Augustine as the Primate of All England, and then once in the chapter-house as Titular Abbot of Canterbury.
There are several Benedictine abbeys throughout the Anglican Communion. Most of them have mitred abbots.
Abbots in art and literature
"The Abbot" is one of the archetypes traditionally illustrated in scenes of Danse Macabre.
The lives of numerous abbots make up a significant contribution to Christian hagiography, one of the most well-known being the Life of St. Benedict of Nursia by St. Gregory the Great. | [
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] |
1143_13 | During the years 1106–1107 AD, Daniel, a Russian Orthodox abbot, made a pilgrimage to the Holy Land and recorded his experiences. His diary was much-read throughout Russia, and at least seventy-five manuscript copies survive. Saint Joseph, Abbot of Volokolamsk, Russia (1439–1515), wrote a number of influential works against heresy, and about monastic and liturgical discipline, and Christian philanthropy.
In the Tales of Redwall series, the creatures of Redwall are led by an abbot or abbess. These "abbots" are appointed by the brothers and sisters of Redwall to serve as a superior and provide paternal care, much like real abbots.
"The Abbot" was a nickname of RZA from the Wu-Tang Clan.
See also
Abbé
Abbé Pierre
Abbot (Buddhism)
Abthain
Commendatory abbot
Notes
References
External links
Russian Orthodox Abbot of Valaam Monastery
The Pilgrimage of the Russian Abbot Daniel in the Holy Land
Religious terminology
Ecclesiastical titles
Monasticism
Organisation of Catholic religious orders
Religious leadership roles
Catholic ecclesiastical titles
Christian religious occupations | [
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1144_0 | Ardipithecus is a genus of an extinct hominine that lived during the Late Miocene and Early Pliocene epochs in the Afar Depression, Ethiopia. Originally described as one of the earliest ancestors of humans after they diverged from the chimpanzees, the relation of this genus to human ancestors and whether it is a hominin is now a matter of debate. Two fossil species are described in the literature: A. ramidus, which lived about 4.4 million years ago during the early Pliocene, and A. kadabba, dated to approximately 5.6 million years ago (late Miocene). Initial behavioral analysis indicated that Ardipithecus could be very similar to chimpanzees, however more recent analysis based on canine size and lack of canine sexual dimorphism indicates that Ardipithecus was characterised by reduced aggression, and that they more closely resemble bonobos.
Ardipithecus ramidus
A. ramidus was named in September 1994. The first fossil found was dated to 4.4 million years ago on the basis of its stratigraphic position between two volcanic strata: the basal Gaala Tuff Complex (G.A.T.C.) and the Daam Aatu Basaltic Tuff (D.A.B.T.). The name Ardipithecus ramidus stems mostly from the Afar language, in which Ardi means "ground/floor" and ramid means "root". The pithecus portion of the name is from the Greek word for "ape".
Like most hominids, but unlike all previously recognized hominins, it had a grasping hallux or big toe adapted for locomotion in the trees. It is not confirmed how many other features of its skeleton reflect adaptation to bipedalism on the ground as well. Like later hominins, Ardipithecus had reduced canine teeth and reduced canine sexual dimorphism. | [
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1144_1 | In 1992–1993 a research team headed by Tim White discovered the first A. ramidus fossils—seventeen fragments including skull, mandible, teeth and arm bones—from the Afar Depression in the Middle Awash river valley of Ethiopia. More fragments were recovered in 1994, amounting to 45% of the total skeleton. This fossil was originally described as a species of Australopithecus, but White and his colleagues later published a note in the same journal renaming the fossil under a new genus, Ardipithecus. Between 1999 and 2003, a multidisciplinary team led by Sileshi Semaw discovered bones and teeth of nine A. ramidus individuals at As Duma in the Gona area of Ethiopia's Afar Region. The fossils were dated to between 4.35 and 4.45 million years old.
Ardipithecus ramidus had a small brain, measuring between 300 and 350 cm3. This is slightly smaller than a modern bonobo or female common chimpanzee brain, but much smaller than the brain of australopithecines like Lucy (~400 to 550 cm3) and roughly 20% the size of the modern Homo sapiens brain. Like common chimpanzees, A. ramidus was much more prognathic than modern humans.
The teeth of A. ramidus lacked the specialization of other apes, and suggest that it was a generalized omnivore and frugivore (fruit eater) with a diet that did not depend heavily on foliage, fibrous plant material (roots, tubers, etc.), or hard and or abrasive food. The size of the upper canine tooth in A. ramidus males was not distinctly different from that of females. Their upper canines were less sharp than those of modern common chimpanzees in part because of this decreased upper canine size, as larger upper canines can be honed through wear against teeth in the lower mouth. The features of the upper canine in A. ramidus contrast with the sexual dimorphism observed in common chimpanzees, where males have significantly larger and sharper upper canine teeth than females. Of the living apes, bonobos have the smallest canine sexual dimorphism, although still greater than that displayed by A. ramidus. | [
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1144_2 | The less pronounced nature of the upper canine teeth in A. ramidus has been used to infer aspects of the social behavior of the species and more ancestral hominids. In particular, it has been used to suggest that the last common ancestor of hominids and African apes was characterized by relatively little aggression between males and between groups. This is markedly different from social patterns in common chimpanzees, among which intermale and intergroup aggression are typically high. Researchers in a 2009 study said that this condition "compromises the living chimpanzee as a behavioral model for the ancestral hominid condition." Bonobo canine size and canine sexual dimorphism more closely resembles that of A. ramidus, and as a result, bonobos are now suggested as a behavioural model.
A. ramidus existed more recently than the most recent common ancestor of humans and chimpanzees (CLCA or Pan-Homo LCA) and thus is not fully representative of that common ancestor. Nevertheless, it is in some ways unlike chimpanzees, suggesting that the common ancestor differs from the modern chimpanzee. After the chimpanzee and human lineages diverged, both underwent substantial evolutionary change. Chimp feet are specialized for grasping trees; A. ramidus feet are better suited for walking. The canine teeth of A. ramidus are smaller, and equal in size between males and females, which suggests reduced male-to-male conflict, increased pair-bonding, and increased parental investment. "Thus, fundamental reproductive and social behavioral changes probably occurred in hominids long before they had enlarged brains and began to use stone tools," the research team concluded.
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1144_3 | Ardi
On October 1, 2009, paleontologists formally announced the discovery of the relatively complete A. ramidus fossil skeleton first unearthed in 1994. The fossil is the remains of a small-brained 50-kilogram (110 lb) female, nicknamed "Ardi", and includes most of the skull and teeth, as well as the pelvis, hands, and feet. It was discovered in Ethiopia's harsh Afar desert at a site called Aramis in the Middle Awash region. Radiometric dating of the layers of volcanic ash encasing the deposits suggest that Ardi lived about 4.3-4.5 million years ago. This date, however, has been questioned by others. Fleagle and Kappelman suggest that the region in which Ardi was found is difficult to date radiometrically, and they argue that Ardi should be dated at 3.9 million years.
The fossil is regarded by its describers as shedding light on a stage of human evolution about which little was known, more than a million years before Lucy (Australopithecus afarensis), the iconic early human ancestor candidate who lived 3.2 million years ago, and was discovered in 1974 just away from Ardi's discovery site. However, because the "Ardi" skeleton is no more than 200,000 years older than the earliest fossils of Australopithecus, and may in fact be younger than they are, some researchers doubt that it can represent a direct ancestor of Australopithecus.
Some researchers infer from the form of her pelvis and limbs and the presence of her abductable hallux, that "Ardi" was a facultative biped: bipedal when moving on the ground, but quadrupedal when moving about in tree branches. A. ramidus had a more primitive walking ability than later hominids, and could not walk or run for long distances. The teeth suggest omnivory, and are more generalised than those of modern apes.
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1144_4 | Ardipithecus kadabba
Ardipithecus kadabba is "known only from teeth and bits and pieces of skeletal bones", and is dated to approximately 5.6 million years ago. It has been described as a "probable chronospecies" (i.e. ancestor) of A. ramidus. Although originally considered a subspecies of A. ramidus, in 2004 anthropologists Yohannes Haile-Selassie, Gen Suwa, and Tim D. White published an article elevating A. kadabba to species level on the basis of newly discovered teeth from Ethiopia. These teeth show "primitive morphology and wear pattern" which demonstrate that A. kadabba is a distinct species from A. ramidus.
The specific name comes from the Afar word for "basal family ancestor".
Classification
Due to several shared characteristics with chimpanzees, its closeness to ape divergence period, and due to its fossil incompleteness, the exact position of Ardipithecus in the fossil record is a subject of controversy. Primatologist Esteban Sarmiento had systematically compared and concluded that there is not sufficient anatomical evidence to support an exclusively human lineage. Sarmiento noted that Ardipithecus does not share any characteristics exclusive to humans, and some of its characteristics (those in the wrist and basicranium) suggest it diverged from humans prior to the human–gorilla last common ancestor. His comparative (narrow allometry) study in 2011 on the molar and body segment lengths (which included living primates of similar body size) noted that some dimensions including short upper limbs, and metacarpals are reminiscent of humans, but other dimensions such as long toes and relative molar surface area are great ape-like. Sarmiento concluded that such length measures can change back and forth during evolution and are not very good indicators of relatedness (homoplasy). | [
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1144_5 | However, some later studies still argue for its classification in the human lineage. In 2014, it was reported that the hand bones of Ardipithecus, Australopithecus sediba and A. afarensis have the third metacarpal styloid process, which is absent in other apes. Unique brain organisations (such as lateral shift of the carotid foramina, mediolateral abbreviation of the lateral tympanic, and a shortened, trapezoidal basioccipital element) in Ardipithecus are also found only in the Australopithecus and Homo. Comparison of the tooth root morphology with those of the earlier Sahelanthropus also indicated strong resemblance, also pointing to inclusion to the human line.
Evolutionary tree according to a 2019 study:
Paleobiology
The Ardipithecus length measures are good indicators of function and together with dental isotope data and the fauna and flora from the fossil site indicate Ardipithecus was mainly a terrestrial quadruped collecting a large portion of its food on the ground. Its arboreal behaviors would have been limited and suspension from branches solely from the upper limbs rare. A comparative study in 2013 on carbon and oxygen stable isotopes within modern and fossil tooth enamel revealed that Ardipithecus fed both arboreally (on trees) and on the ground in a more open habitat, unlike chimpanzees. | [
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1144_6 | In 2015, Australian anthropologists Gary Clark and Maciej Henneberg said that Ardipithecus adults have a facial anatomy more similar to chimpanzee subadults than adults, with a less-projecting face and smaller canines (large canines in primate males are used to compete within mating hierarchies), and attributed this to a decrease in craniofacial growth in favour of brain growth. This is only seen in humans, so they argued that the species may show the first trend towards human social, parenting and sexual psychology. Previously, it was assumed that such ancient human ancestors behaved much like chimps, but this is no longer considered to be a viable comparison. This view has yet to be corroborated by more detailed studies of the growth of A.ramidus. The study also provides support for Stephen Jay Gould's theory in Ontogeny and Phylogeny that the paedomorphic (childlike) form of early hominin craniofacial morphology results from dissociation of growth trajectories.
Clark and Henneberg also argued that such shortening of the skull—which may have caused a descension of the larynx—as well as lordosis—allowing better movement of the larynx—increased vocal ability, significantly pushing back the origin of language to well before the evolution of Homo. They argued that self domestication was aided by the development of vocalization, living in a pro-social society. They conceded that chimps and A. ramidus likely had the same vocal capabilities, but said that A. ramidus made use of more complex vocalizations, and vocalized at the same level as a human infant due to selective pressure to become more social. This would have allowed their society to become more complex. They also noted that the base of the skull stopped growing with the brain by the end of juvenility, whereas in chimps it continues growing with the rest of the body into adulthood; and considered this evidence of a switch from a gross skeletal anatomy trajectory to a neurological development trajectory due to selective pressure for sociability. Nonetheless, their conclusions are highly speculative. | [
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