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The arago–poisson spot: new applications for an old concept.

1. Introduction

2.1. theoretical considerations, 2.2. experiments, 2.3. properties, 2.3.1. ultimate arago–poisson beam size, 2.3.2. self-healing and nondiffractive properties, 2.3.3. faster-than-light properties, 3. discussion, 3.1. particle trapping, 3.2. changing nature of the arago–poisson spot and application to signal addressing, 4. conclusions, author contributions, data availability statement, acknowledgments, conflicts of interest.

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Emile, O.; Emile, J. The Arago–Poisson Spot: New Applications for an Old Concept. Photonics 2024 , 11 , 55. https://doi.org/10.3390/photonics11010055

Emile O, Emile J. The Arago–Poisson Spot: New Applications for an Old Concept. Photonics . 2024; 11(1):55. https://doi.org/10.3390/photonics11010055

Emile, Olivier, and Janine Emile. 2024. "The Arago–Poisson Spot: New Applications for an Old Concept" Photonics 11, no. 1: 55. https://doi.org/10.3390/photonics11010055

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Arago's Spot or Fresnel's, or Poisson's: Exploring the Nature of Light

Have you ever wondered if there could be a bright spot at the center of a shadow? It seems counterintuitive, doesn't it? Well, this intriguing phenomenon known as Arago's Spot, or sometimes referred to as Fresnel's or Poisson's Spot, has puzzled scientists for centuries. In this article, we will delve into the experiment that helped decide the nature of light and explore the intricacies of this fascinating optical phenomenon.

Shedding Light on the Experiment

To understand Arago's Spot, let's take a look at an experiment conducted by Michiel de Boer. In his setup, a laser beam shines on a sphere, casting a shadow. Surprisingly, both the sphere and its shadow exhibit a bright spot at their centers. This phenomenon challenges common-sense notions as we would expect the center of a shadow to be completely dark.

The Mathematics Behind the Phenomenon

The presence of Arago's Spot can be explained by the diffraction of light waves around the edge of the sphere. While it takes some complex mathematics to fully grasp the concept, it essentially boils down to the interaction between the waves and the shape of the object. Interestingly, if we were to use Newton's corpuscular theory, which suggests that light consists of tiny particles traveling in straight lines, we would expect a completely dark shadow. However, the diffraction of light waves around the sphere's edge creates a spot in the center of the shadow.

Visualizing Arago's Spot

To better visualize Arago's Spot, Michiel de Boer defocused the camera lens in one of his images, leaving only the diffraction pattern. In the center of this pattern, we can clearly observe the Arago-Fresnel-Poisson spot. Additionally, we can see vertical striations caused by interference patterns from laser light scattered by the material supporting the sphere.

The Complex Nature of the Spot

In a less than perfect world, the structure of Arago's Spot can become quite complex. Irregularities in the laser beam source contribute to the diffraction patterns, adding further intricacy to the phenomenon. Nevertheless, despite these complexities, the presence of the bright spot remains consistent.

A Historical Debate: Corpuscles vs. Waves

The discovery of Arago's Spot played a significant role in settling a long-standing debate about the nature of light. In the 18th century, renowned physicist Isaac Newton proposed that light consisted of tiny corpuscles traveling in straight lines. However, this theory struggled to explain interference fringes and diffraction phenomena. On the other side of the debate was Christiaan Huygens, who proposed that light was composed of longitudinal waves. Huygens' wave theory provided a reasonable explanation for refraction, interference, and diffraction.

The Competition to Settle the Debate

In 1818, the French Academy of Sciences organized a competition to determine whether light was composed of corpuscles or waves. Engineer Augustin Jean Fresnel, known for his work on lighthouse lenses, submitted his wave theory. One of the judges, Siméon Poisson, a strong supporter of Newton's corpuscular theory, sought to find a flaw in Fresnel's paper. To his surprise, while extending Fresnel's analysis, Poisson deduced that wave theory predicted the existence of a spot of light directly behind a lit disk or sphere. This seemingly absurd result led Poisson to believe that wave theory was flawed and unsupported.

Arago's Discovery

Shortly after the competition, Dominique Arago, the head of the judging committee, made a remarkable discovery. He found the elusive Arago's Spot that Fresnel's wave theory had predicted. Arago's discovery provided undeniable evidence in favor of the wave theory of light, solidifying its acceptance in the scientific community.

A Modern Perspective: Particles and Waves

As physics progressed, new perspectives emerged. James Clerk Maxwell's work in 1865 mathematically described electricity and magnetism, leading to the understanding that light was composed of transverse electromagnetic waves. Quantum theory further expanded our understanding by suggesting that particles and waves are two different ways to interpret the behavior of matter and energy. In fact, using an electron microscope adjusted appropriately, we can observe an Arago spot.

Observing Arago's Spot Today

Even today, we can witness Arago's Spot under certain conditions. For example, when using a modern telescope with a central obstruction, a bright star that is well out of focus can produce a large disk of light that reveals the spot. However, it is important to note that the experiment is challenging without lasers, as the occulting disk or sphere must be smooth and round, meeting specific conditions for Fresnel diffraction to occur.

In conclusion, Arago's Spot, also known as Fresnel's or Poisson's Spot, has captivated scientists for centuries. Through experiments and mathematical analysis, we have come to understand this intriguing phenomenon as a result of the diffraction of light waves around the edge of an object. This discovery played a pivotal role in settling the historical debate between corpuscular and wave theories of light. Today, Arago's Spot continues to fascinate researchers and reminds us of the complex nature of light and its behavior.

Arago's Spot or Fresnel's, or Poisson's. Is there a bright spot in the centre of a shadow? An experiment crucis that helped decide the nature of light.

Optics experiments and images by Michiel de Boer (site). Video.

At left a laser beam shines on a sphere. We are in its shadow looking towards the laser. The sphere�s dark side has a bright spot at its centre. In the above right image a steel sphere is held up by magnetic beads. That too has a bright spot on its dark side.

At least one eminent French academician said it should not exist. Common-sense says it is absurd. How can a bright spot exist in the centre of a shadow?

All images ©Michiel de Boer, shown with permission

The experiment at its very simplest.

Light waves diffract around the sphere's edge. It takes some complex maths to show that a spot forms.

Newton's corpuscles would leave a completely dark shadow..

Michiel de Boer has kept the camera lens for this image but on an extension tube to grossly defocus the sphere itself to leave the diffraction pattern only.

In the centre is the Arago-Fresnel-Poisson spot.

The vertical striations are interference patterns from laser light scattered by the sphere support material.

The sphere's dark side. The rim shines brightly by diffracted light.

The spot structure in a less than perfect world is complex.

Irregularities in the laser beam source also contribute to the diffraction patterns.

In science, as in other activities, eminence and authority can carry great weight.

Isaac Newton in his landmark book �Opticks� of 1704 proposed that light was tiny corpuscles travelling in straight lines. Newton hesitated over the decision. It struggled to explain already known interference fringes or diffraction. And across the North Sea was the scientific giant, Christiaan Huygens. He had in 1678 already published a rival theory that light was longitudinal waves (like sound). Huygens provided a reasonable explanation of refraction, interference and diffraction. Nonetheless, and in spite of mounting evidence, Newton's corpuscular theory held sway for the next hundred years and more.

It came to a competition. In 1818 the French Academy of Sciences launched one to settle the question - was light corpuscles or waves?

Engineer Augustin Jean Fresnel (lighthouse lenses) submitted his wave theory. A brilliant scientist, Sim�on Poisson was one of the judges. He was also an ardent supporter of corpuscular theory. He sought a flaw in Fresnels's paper. He extended Fresnel's analysis and deduced that wave theory predicted a spot of light directly behind a lit disk or sphere. An impossible and absurd result! The spot was not visible and that was the end of wave theory.

Too clever! Shortly afterwards Dominique Arago, head of the judging committee, found the spot.

To be fair to Poissan, the experiment without lasers. is very difficult. Also, the occulting disk or sphere must be very smooth and round (witness the irregularities in the images here). Its placement must meet certain conditions for Fresnel diffraction to hold.

Physics advances come from unexpected quarters. Using Michael Faraday's experimental findings, James Clerk Maxwell in 1865 developed an elegant mathematical description of electricity and magnetism. His concise set of equations showed that light was transverse electromagnetc waves.

Quantum theory added another perspective. Depending on circumstances, we might interpret the world as particles or waves. An electron microscope suitably adjusted will show a very nice Arago spot!

. A star is another source of parallel light and under very steady conditions a modern telescope with a central obstruction can show the spot if a bright star is racked well out of focus into a large disk of light.

Note: this article has been automatically converted from the old site and may not appear as intended. You can find the original article here .

Reference Atmospheric Optics

If you use any of the definitions, information, or data presented on Atmospheric Optics, please copy the link or reference below to properly credit us as the reference source. Thank you!

<a href="https://atoptics.co.uk/blog/aragos-spot-or-fresnels-or-poissons-opod/">Arago's Spot or Fresnel's, or Poisson's - OPOD</a>

"Arago's Spot or Fresnel's, or Poisson's - OPOD". Atmospheric Optics. Accessed on July 1, 2024. https://atoptics.co.uk/blog/aragos-spot-or-fresnels-or-poissons-opod/.

"Arago's Spot or Fresnel's, or Poisson's - OPOD". Atmospheric Optics, https://atoptics.co.uk/blog/aragos-spot-or-fresnels-or-poissons-opod/. Accessed 1 July, 2024

Arago's Spot or Fresnel's, or Poisson's - OPOD. Atmospheric Optics. Retrieved from https://atoptics.co.uk/blog/aragos-spot-or-fresnels-or-poissons-opod/.

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How did Arago find the Arago Spot without a laser?

Famously, Poisson showed that Fresnel's wave model of light would predict a bright spot in the very center of a circular shadow, which he interpreted as an absurd result. But Arago was able to perform the experiment, giving strong evidence toward the wave theory of light.

Nowadays, we can replicate the experiment with a laser and any small, sufficiently circular object.

But... Arago didn't have lasers in his time. The Wikipedia article (and general internet sources) says that he molded a metallic circle to a glass plate with wax, but mentions nothing about the light source. How did he generate a coherent light source, or if he didn't, how did he perform the experiment? (Is it even documented?)

• visible-light
• diffraction

• 1 $\begingroup$ It seems remarkably hard to find any information on this. Apparently the details are in a report published by Arago in 1819 and called simple "Arago report". $\endgroup$ –  John Rennie Commented Nov 3, 2016 at 7:24
• 2 $\begingroup$ kth.se/social/files/55f1b177f276540261b6a04b/arago092015.pdf Modern experiment, but used white light. $\endgroup$ –  BowlOfRed Commented Nov 3, 2016 at 7:29
• 1 $\begingroup$ point sources were used for coherent light. see page 5 here optics.hanyang.ac.kr/~shsong/9-Coherence.pdf . see also Young's eperiment en.wikipedia.org/wiki/Young%27s_interference_experiment .Also if the source were far away the plane wave approximation would be good. $\endgroup$ –  anna v Commented Nov 3, 2016 at 7:49
• $\begingroup$ Are point sources really coherent though? :/ [oh @JohnRennie I guess it doesn't need to be, interesting] $\endgroup$ –  oink Commented Nov 3, 2016 at 19:41
• 2 $\begingroup$ Here is Arago's memo on the experiement, arago too verbose for me, enjoy if you can: books.google.com.au/… $\endgroup$ –  Manu de Hanoi Commented Sep 17, 2018 at 21:46

2 Answers 2

How did he generate a coherent light source, or if he didn't, how did he perform the experiment? (Is it even documented?)

It is most important that the focusing object be round, next the light source must be small enough that the center of the projection area is not lit by incident rays - for example the Sun and the Moon do not produce this effect on the Earth's surface.

For an Aragon spot to be seen:

"The dimensions of the setup must comply with the requirements for Fresnel diffraction . Namely, the Fresnel number must satisfy $$ F={\frac {d^{2}}{\ell \lambda }}\gtrsim 1,$$ where $d$ is the diameter of the circular object, $ℓ$ is the distance between the object and the screen, $λ$ the wavelength of the source. Finally, the edge of the circular object must be sufficiently smooth. These conditions together explain why the bright spot is not encountered in everyday life.

See Physics World's article: " The spot in the shadow ":

"According to Fresnel’s work, if light were shone on a circular obstruction, a bright spot would appear in the centre of the shadow, as bright as if the obstruction were not there at all. Obvious nonsense! Not only that, Fresnel’s equations indicated that light shining through a circular hole could produce a dark spot in the middle. The committee’s head was, however, François Arago – one of the few French scientists besides Fresnel acquainted with Young’s work, and therefore able to appreciate Fresnel’s contributions. Arago carried out the experiment with a flame, filters and a 2 mm metal disc attached to a glass plate with wax. To everyone’s surprise, and Poisson’s chagrin, Arago observed the spot and Fresnel won the competition. ... If the demonstration is so simple, I asked Metcalf, why wasn’t it discovered earlier in things like eclipses? “The Moon’s not nearly round enough,” he snorted. “All those mountains! The Sun’s not a point source of coherent light. People didn’t always have laser pointers.” The critical point The episode illustrates the ambiguities of discovery. Who’s the discoverer? Fresnel, who produced the original framework? Poisson, who showed the spot was a direct consequence but was firmly convinced that it didn’t exist? Arago, who did the experiment? Moreover, two other scientists turned out to have noticed the spot a century earlier but did not know what to make of it. What about the French Academy, whose actions set the discovery in motion? Didn’t Young play a role? Even Newton? Moreover, the spot is just an illustration of a more general phenomenon that complementary obstruction patterns produce complementary diffraction results, described by Jacques Babinet’s theorem.".

My understanding is that the important characteristic of the light source is its size, not its coherence. The wikipedia article refers to a "point source". A laser is a good approximation to a point source.

But, I think the size of the source just hast to be small relative to the object blocking the light, so the requirements are not so stringent. (It would be difficult if the size of the source should be small relative to the wavelength.) You can make a simple point source by inverting a camera obscura. Basically a bright light in a box with one very small hole in one side will give you something which is a good enough point source for the Arago experiment.

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Light is beautiful

Thoughts of a graphics programmer, demoscener and spare time photographer, fresnel and the poisson spot.

The casting of the following story is remarkable. The year is 1818. On one side, Augustin Fresnel (1788 – 1827) has just handed to the French Academy of Sciences (Académie des Sciences) an essay defending a theory completely opposed to the widely accepted one; on the other side, François Arago (1786 – 1853), Jean-Baptiste Biot (1774 – 1862), Louis Joseph Gay-Lussac (1778 – 1850), Pierre-Simon Laplace (1749 – 1827) and Siméon Denis Poisson (1781 – 1840) are the panel in charge of assessing it. These are all major theorem names. Men who built Science, the giants whose shoulders we stand upon. But the context is peculiar: the scientists are here to fight, as the battle is raging between partisans of the particle theory and partisans of the wave theory.

It all starts three years earlier, in July of 1815, when Fresnel (then 27) meets the person who would later become his mentor, Arago. The political background is rough: the Hundred Days have ended just a month before with the defeat of Napoleon at the battle of Waterloo, and Fresnel, a royalist, is under police scrutiny and has been dismissed from his title as a state engineer. The scientific background is the status quo: Isaac Newton’s corpuscular theory of light is prevailing and unshakeable.

Pushed forward by Arago who sees great potential in him, Fresnel performs rudimentary experiments with light diffraction at his mother’s home, in a town north of Caen . There, with gear made by a local worker and consisting of wires and drops of honey serving as lenses, he observes and measures hyperbolic fringed patterns that cannot be explained by the particle theory (which should lead to linear patterns). He thus builds upon the wave theory by Hyugens and on October 26th, sends to the French Academy of Sciences a first paper reporting his observations. He will later send more of these papers, prompting strong reactions from the community, especially Laplace.

The competition organized by the Academy and aimed at rewarding the best work on a given topic is seen as the perfect opportunity to put an end to the battle. Proposed on the 17th of March 1817, and ending on the 1st of August of the next year, it focuses on diffraction phenomenons, and while rigorous, it seems to have been written by a supporter of the corpuscular theory. Opponents to the wave theory are hoping to see someone present a work that will put a stop to it.

Arago, originally convinced by the particle theory, sees Fresnel as the one who can best defend the wave theory. He helps him any way he can, and in particular helps him move to Paris to enter the competition. Even André-Marie Ampère (1775 – 1836), although a openly partisan of Newton’s theory (possibly for political reason related to the Academy), gives him full support. Both push him to publish his new results. The three will become close friends in the process.

Finally this essay handed at the last minute (29th of July 1818) is the only one selected out of two submitted. Natura simplex et fecunda is much more thorough than the previous works, and it is nowadays described as a masterpiece. Going beyond the work of Thomas Young (1773 – 1829), the author proposes a model that predicts with precision the position and size of the fringes, and presents the experiment now known as Fresnel double mirror.

Among the jury, Biot, Laplace and Poisson are the most resolutely opposed to wave theory. Poisson in particular, fascinated by Fresnel’s theory, studies it in detail, looking for weaknesses. From it he derives a counter intuitive result beyond Fresnel’s own predictions: by placing a disc at a certain distance between a source of light and a screen, a bright spot should appear in the center of the disc’s shadow. To Poisson, this apparently absurd consequence is a proof that invalidates Fresnel’s work.

But Arago decides to proceed and perform the experiment. To everyone’s surprise, the spot predicted by Poisson is indeed observed. The anecdote, recorded by Arago, would be the strawberry on the shortcake to Fresnel’s success that day. Ironically, although it still didn’t convince Poisson, the experiment is since then often referred to as the Poisson spot .

Some references:

Augustin Fresnel’s essay used to be available on the website of the Académie des Sciences, but the link seems to be broken recently.

“Mémoire sur la diffraction de la lumière” on the website of the French Academy of Science (fr, PDF)

André Marie Ampère et Augustin Fresnel (fr)

Final word:

Before opening this space specifically dedicated to light and rendering, I was posting from time to (increasingly distant) time on another blog in French. One post that attracted attention was the story of Augustin Fresnel defending his thesis in front of the Académie des Sciences. Given the impact his ground breaking work has on rendering, I thought it made sense to translate it and post it here.

I have tried my best to bring the pieces together from different sources, but some of them were disagreeing on some details, and unfortunately I haven’t noted all the references so it is possible some part isn’t 100% faithful to the events. Please leave a comment if you have some material on the topic.

5 thoughts on “ Fresnel and the Poisson spot ”

Since Fresnel’s white spot plays such a major example in Kuhn’s “Structure of Scientific Revolutions” I urge you to describe the experimental set up better and how it works to address the wave-particle debate in that historical context as I think many non-physicists would appreciate knowing much more about this great revolutionary case.

This is an experiment we successfully used for thirty years at the University of Queensland, Australia. We used a laser beam incident on a ball bearing suspended from a magnetic needle. The spot was always clearly apparent.

Nice! I have never seen the experiment myself, but that must be a very counter intuitive sight.

Such a beautifully written account I was looking for background on the white spot and found you. Many thanks

Thank you for you comment, appreciated.

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Instructional Resources and Lecture Demonstrations

6c20.10 - poisson's spot.

The expandable beam laser pointer, round headed pins, screen, and video camera are permanently mounted on an optics rail.  Viewing the diffraction patterns around the object with the video camera can be done by focusing the camera onto the back side of the screen.  Adjustment of the 2 axis stage may be needed to get the most intense central spot.  In some cases it will work much better if instead of using the small screen and the video camera, you dispense with these and direct the diffraction pattern onto the screen at the other end of the lecture room.

• Matthew Hoover, Michael Everhart, Jose D'Arruda, "Poisson Spot with Magnetic Levitation", TPT, Vol. 48, # 2, Feb. 2010, p. 135.
• Michael E. Harrison, C. Thomas Marek, and James D. White, "Rediscovering Poisson's Spot", TPT, Vol.  35, # 1, p. 18-19, Jan. 1997.
• Jack Higbie, "More on Poisson's Spot", TPT, Vol. 35, # 4, Apr. 1997, p. 197.
• Ronald D. Wong, "Still More on Poisson's Spot", TPT, Vol. 35, # 4, Apr. 1997, p. 197.
• Gordon R. Gore, "Diffraction Photographs with a Laser Pointer", TPT, Vol. 32, # 3, March 1994, p. 174.
• Robert A. Barttett, "Poisson's Circles?", TPT, Vol. 32, # 6, Sept. 1994, p. 326.
• Andrew DePino Jr.  "Unusual Diffraction Patterns",  TPT, Vol. 25, # 4, p. 219, April 1987.
• Timothy Kersey, "The Poisson Bright Spot", TPT, Vol. 23, # 4, April 1985, back cover.
• John B. Johnston, "Projecting Poisson's Spot", TPT, Vol. 16, # 3, Mar. 1978, p. 179.
• R. C. Nicklin and J. Dinkins, "Laser Diffraction Photography", TPT, Vol. 12, # 5, May 1974, p. 295.
• John Dowling, Jr., and John Swanson, "A Short Note on "The Poisson Distribution" Lab", TPT, Vol. 11, # 9, Dec. 1973, p. 543.
• Mimi S. Lafleur and Peter F. Hinrichsen, "An Experimental Approach to Teaching Statistics", TPT, Vol. 10, # 6, Sept. 1972, p. 314.
• James Moore, "Viewing Diffraction Fringes", TPT, Vol. 9, # 3, March 1971, p. 153.
• Michel Gondran, Alexandre Gondran, "Energy Flow Lines and the Spot of Poisson-Arago", AJP, Vol. 77, # 6, June 2010, p. 598.
• W.R. Kelly, E.L. Shirley, A.L. Migdall, S.V. Polyakov, K. Hendrix, "First- and Second-Order Poisson Spots", AJP, Vol. 77, # 8, August 2009, p. 713.
• Andrzej Kolodziejczyk, Zbigniew Jaroszewicz, Rodrigo Henao and Orlando Quintero, "An Experimental Apparatus for White Light Imaging by Means of a Spherical Obstacle", AJP, Vol. 70, # 2, Feb. 2002, p. 169.
• P. M. Rinard, "Large-Scale Diffraction Patterns From Circular Objects", AJP, Vol. 44, # 1, Jan. 1976.
• O-530:  "Needle, Slit, and Razor Blade",  DICK and RAE Physics Demo Notebook.
• O-555:  "Poisson's Spot",  DICK and RAE Physics Demo Notebook.
• O-7f:  Wallace A. Hilton, Physics Demonstration Experiments.
• L-78:  Richard Manliffe Sutton, Demonstration Experiments in Physics.
• Jearl Walker,  "A Ball Bearing Aids in the Study of Light and Also Serves As a Lens",  The Amateur Scientist,  November, 1984.
• Robert Ehrlich, "11.4, Poisson's Bright Spot", Why Toast Lands Jelly-Side Down, p. 176.
• T. Kallard, "The Poisson - Arago Spot", Exploring Laser Light, p. 184.
• T. Kallard, "Simple Optical System for Fraunhofer Diffraction Experiments", Exploring Laser Light, p. 188.
• Wallace A. Hilton, "Arago White Spot", Apparatus Notes, July 1965-December 1972, p. 61.
• Borislaw Bilash II, David Maiullo, "Poisson Spot- The Inner Light", A Demo a Day: A Year of Physics Demonstrations, p. 351.
• Jearl Walker, "6.151, Using a Solid Metal Ball to Focus Light", The Flying Circus of Physics Ed. 2, p. 303.
• Yaakov Kraftmakher, "7.22, Poisson Spot", Experiments and Demonstrations in Physics, ISBN 981-256-602-3, p. 497.
• Richard E. Berg, "DEMO HINTS: Laser Diffraction", PIRA Newsletter, Vol. 3, # 11, March 31, 1989, p. 3.
• 5.98, Jearl Walker, "Poisson Spot", The Flying Circus of Physics with Answers.
• C. Harvey Palmer, "Experiment B13: Demonstration of Fresnel Diffraction by Circular Apertures and Obstructions",  Optics - Experiments and Demonstrations, John Hopkins Press, 1962.
• "Diffraction Grating, Simple", Selective Experiments in Physics, CENCO, 1962.

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