home Consultations Fresnel parking lens - a budget alternative to parking sensors and a rear view camera? Optics. Lens. Fresnel lens. Homemade LCD projector for home theater Fresnel lens operating principle

Fresnel parking lens - a budget alternative to parking sensors and a rear view camera? Optics. Lens. Fresnel lens. Homemade LCD projector for home theater Fresnel lens operating principle

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St. Petersburg

National Research University

Information Technology, Mechanics and Optics

Essay

"Fresnel lenses, their calculation, modeling and application"

Completed:

student gr. 4251

Elezov Andrey

Introduction

1. Fresnel lenses

2. Calculation of Fresnel lenses

3. Modeling and application of Fresnel lenses

Conclusion

List of used literature

Introduction

One of the creators of the wave theory of light, the outstanding French physicist Augustin Jean Fresnel was born in a small town near Paris in 1788. He grew up as a sickly boy.

Teachers considered him stupid: at the age of eight he could not read and could hardly remember the lesson. However, in high school, Fresnel showed remarkable abilities in mathematics, especially geometry. Having received an engineering education, from 1809 he participated in the design and construction of roads and bridges in various departments of the country.

However, his interests and capabilities were much broader than simple engineering activities in the provincial wilderness. Fresnel wanted to do science; He was especially interested in optics, the theoretical foundations of which were just beginning to take shape. He studied the behavior of light rays passing through narrow holes, bending around thin threads and the edges of plates.

Having explained the features of the resulting pictures, Fresnel in 1818-1819 created his theory of optical interference and diffraction - phenomena arising due to the wave nature of light.

One interesting fact from history related to Fresnel.

At the beginning of the 19th century, European maritime states decided to jointly improve lighthouses - the most important navigation devices of that time.

In France, a special commission was created for this purpose, and Fresnel was invited to work on it due to his rich engineering experience and deep knowledge of optics. The light of the lighthouse should be visible far away, so the lighthouse lantern is raised to a high tower. And in order to collect its light into rays, the flashlight must be placed at the focus of either a concave mirror or a collecting lens, and quite a large one. The mirror, of course, can be made of any size, but it gives only one beam, and the light of the lighthouse must be visible from everywhere. Therefore, sometimes a dozen and a half mirrors were placed on lighthouses with a separate lantern at the focus of each mirror. Several lenses can be mounted around one lantern, but making them of the required - large - size is almost impossible. The glass of a massive lens will inevitably have inhomogeneities, it will lose its shape under the influence of its own gravity, and due to uneven heating it may burst.

New ideas were needed, and the commission, having invited Fresnel, made the right choice: in 1819, he proposed the design of a composite lens, devoid of all the disadvantages inherent in a conventional lens. Fresnel probably reasoned this way. A lens can be thought of as a set of prisms that refract parallel light rays - deflect them at such angles that after refraction they converge at the focal point. This means that instead of one large lens, you can assemble a structure in the form of thin rings from individual prisms of triangular cross-section.

Fresnel not only calculated the shape of the ring profiles, he also developed the technology and supervised the entire process of their creation, often performing the duties of a simple worker (the subordinates turned out to be extremely inexperienced). His efforts yielded brilliant results. “The brightness of the light produced by the new device surprised the sailors,” Fresnel wrote to friends. And even the British - longtime competitors of the French at sea - admitted that the designs of French lighthouses turned out to be the best.

Augustin Fresnel entered the history of science and technology not only and not so much thanks to the invention of his lens.

His research and the theory created on its basis finally confirmed the wave nature of light and solved the most important problem in physics of that time - they found the reason for the rectilinear propagation of light.

Fresnel's work formed the basis of modern optics. Along the way, he predicted and explained several paradoxical optical phenomena, which, nevertheless, are easy to verify even now.

1. Fresnel lenses

The Fresnel lens is a complex compound lens. It does not consist of a single polished piece of glass with spherical or other surfaces (like conventional lenses), but of separate concentric rings of small thickness adjacent to each other, which in cross-section have the shape of prisms of a special profile. Proposed by Augustin Fresnel.

This design ensures that the Fresnel lens is thin (and therefore lightweight) even with a large angular aperture. The sections of the lens rings are constructed in such a way that the spherical aberration of the Fresnel lens is small, the rays from a point source placed at the focus of the lens, after refraction in the rings, emerge as an almost parallel beam (in ring Fresnel lenses).

2. Calculation of Fresnel lenses

The Fresnel lens is one of the first devices whose operation is based on the physical principle of light diffraction.

This device has not lost its practical significance to this day. The general diagram of the physical model on which its operation is based is presented in (Fig. 1).

Rice. 1 Scheme of constructing Fresnel zones for an infinitely distant observation point (plane wave)

Let us assume that at point O there is a point source of optical radiation of wavelength l. Naturally, like any point source, it emits a spherical wave, the wave front of which is depicted in the figure by a circle. Let us set the condition to change this wave to a plane one, which will propagate along the dotted axis. Several wavefronts of this variable wave, lagging each other by l/2, are depicted in (Fig. 1). To begin with, we note that we are considering a variable plane wave from an existing spherical one in free space. Therefore, in accordance with the Huygens-Fresnel principle, the “sources” of a given variable wave can only be electromagnetic oscillations in the existing one. And if this does not suit the spatial distribution of the phase of these oscillations, that is, the wave front (spherical) of the original wave. Let's try to correct it. Let's walk you through everything step by step.

Action one: note that from the point of view of secondary Huygens-Fresnel waves (which are spherical), a spatial displacement of an entire wavelength in any direction does not change the phase of the secondary sources. Therefore, we can allow ourselves, for example, to “break” the wave front of the original wave as shown in (Fig. 2).

Rice. 2 Equivalent phase distribution of secondary emitters in space

Thus, we have “disassembled” the original spherical wave front into “ring parts” number 1, 2... and so on. The boundaries of these rings, called Fresnel zones, are determined by the intersection of the wavefront of the original wave with a sequence of wavefronts of the “projected wave” shifted relative to each other by l/2. The resulting picture is already significantly “simpler”, and represents 2 slightly “rough” flat secondary emitters (green and red in Fig. 2), which, however, cancel each other due to the mentioned half-wave mutual displacement.

So, we see that Fresnel zones with odd numbers not only do not contribute to the accomplishment of the task, but are even actively harmful. There are two ways to combat this.

The first method (amplitude Fresnel lens). You can simply geometrically cover these odd zones with opaque rings. This is what is done in large-sized focusing systems of marine beacons. Of course, this may not achieve ideal beam collimation. You can see that the remaining, green, part of the secondary emitters is, firstly, not completely flat, and secondly, discontinuous (with zero dips in place of the former odd Fresnel zones).

Therefore, the strictly collimated part of the radiation (and its amplitude is nothing more than the zero two-dimensional Fourier component of the spatial distribution of the phase of green emitters along a flat wavefront with zero displacement, see (Fig. 2)) will be accompanied by wide-angle noise (all other Fourier components except zero). Therefore, it is almost impossible to use a Fresnel lens for imaging - only for collimation of radiation. However, nevertheless, the collimated part of the beam will be significantly more powerful than in the absence of a Fresnel lens, since we at least got rid of the negative contribution to the zero Fourier component from odd Fresnel zones.

Second method (Fresnel phase lens). It is possible to make the rings covering the odd Fresnel zones transparent, with a thickness corresponding to the additional phase shift l/2. In this case, the wave front of the “red” secondary emitters will shift and become “green”, see Fig. 3.

Fig.3 Wave front of secondary emitters behind the Fresnel phase lens

In reality, phase Fresnel lenses have two versions. The first is a flat substrate with deposited half-wave layers in the regions of odd Fresnel zones (a more expensive option). The second is a three-dimensional turning part (or even a polymer stamping based on a once-made matrix, like a gramophone record), made in the form of a “stepped conical pedestal” with a step half the length of the phase incursion wave.

Thus, Fresnel lenses can cope with the collimation of beams of large transverse aperture, while at the same time being flat parts of low weight and relatively low manufacturing complexity. An ordinary glass lens for a lighthouse, equivalent in efficiency, weighs half a ton and costs little less than a lens for an astronomical telescope.

Let us now turn to the question of what will happen when the light source is displaced along the axis relative to the Fresnel lens, originally designed to collimate the source radiation in position O (Fig. 1). Let us agree in advance to call the initial distance from the source to the lens (that is, the initial curvature of the wave front on the lens) the focal length F by analogy with a conventional lens, see (Fig. 4).

Rice. 4 Constructing an image of a point source with a Fresnel lens

So, in order for the Fresnel lens to continue to be a Fresnel lens when the source is shifted from position O to position A, it is necessary that the boundaries of the Fresnel zones on it remain the same. And these boundaries are the distances from the axis at which the wave fronts of the incident and “projected” waves intersect. The initially incident one had a front with a radius of curvature F, and the “projected” one was flat (in red in Fig. 4). At a distance h from the axis, these fronts intersect, defining the boundary of one of the Fresnel zones,

where n is the number of the zone starting at this distance from the axis.

When the source moved to point A, the radius of the incident wavefront increased and became R1 (blue color in the figure). This means that we need to come up with a new wavefront surface, such that it intersects with the blue one at the same distance h from the axis, giving the same MN on the axis itself. We suspect that such a surface of the projected wavefront could be a sphere with radius R2 (green color in the figure). Let's prove it.

The distance h is easily calculated from the “red” part of the figure:

Here we neglect the small square of the wavelength compared to the square of the focus - an approximation completely analogous to the parabolic approximation in deriving the usual thin lens formula. On the other hand, we want to find a new boundary of the nth Fresnel zone as a result of the intersection of the blue and green wavefronts, let's call it h1. Based on the fact that we require the same length of the segment MN:

Finally, requiring h=h1, we get:

This equation is the same as the usual thin lens formula. Moreover, it does not contain the number n of the considered boundary of the Fresnel zones, and therefore is valid for all Fresnel zones.

Thus, we see that the Fresnel lens can not only collimate beams, but also construct images. True, you need to keep in mind that the lens is still stepped, and not continuous. Therefore, the image quality will be noticeably degraded due to the admixture of higher Fourier wavefront components discussed at the beginning of this section.

That is, a Fresnel lens can be used to focus radiation to a given point, but not for precision imaging in microscopic and telescopic devices.

All of the above applied to monochromatic radiation. However, it can be shown that by careful selection of the diameters of the rings discussed, reasonable focusing quality can be achieved for natural light as well.

3. Modeling and application of Fresnel lenses

Modeling

The calculation can be carried out for lenses with a square shape in terms of plan and two types of receivers (RE): round and square. User-defined lens design parameters include:

· side size;

· focal length;

· profile pitch (constant);

· thickness of the supporting layer.

All calculations are made for the conditions of lens illumination by solar radiation with a spectrum specified by the user in tabular form (instead of the solar spectrum, you can use the spectrum of another source, for example, a solar radiation simulator). Calculations can be performed both for lenses with and without protective glass.

The flow of incident radiation is simulated by a large number of conical beams of rays with a solid angle corresponding to the apparent angular size of the Sun.

The beams are located on the input surface of the glass (or lens, if there is no glass) randomly in accordance with the uniform distribution law. The angle between the axis of the conical beam of solar rays and the optical axis of the lens is determined by the given accuracy of the orientation of the concentrating system to the Sun.

Through each finite element of the input aperture, the path of 1280 rays is traced, which corresponds to 64 points on the solar disk and 20 wavelengths of its radiation spectrum for each point on the disk.

The total number of traced rays is more than 2 million (with the possibility of increasing to 3.2 million with a slight decrease in the computation speed), which allows one to correctly take into account the features of the spectrum of the radiation source, the geometry of the teeth of the lens profile and simulate its chromatic aberration (Fig. 5).

Rice. 5 Diagram of the passage of light rays through the refractive surfaces of a Fresnel lens.

Modeling is carried out in two stages:

· At the first stage, using an optimization procedure, a lens (and matrix) profile is determined that allows minimizing the negative impact of chromatic aberration on the concentrating ability of the lens-receiver system (cell) at its given efficiency.

· At the second stage, for a lens with an optimal profile, by specifying the size and shape of the solar element located in the focal plane of the Fresnel lens, and the misorientation angle, it is possible to determine how these parameters affect the concentration coefficient and the optical efficiency of the lens-solar cell system.

Solar radiation concentrator based on Fresnel lenses

This device is designed to directly convert solar energy into electrical energy. A solar radiation concentrator is known, consisting of a primary parabolic-cylindrical reflector, a confocal secondary parabolic reflector and a set of triangular refractive prisms that decompose solar radiation into a spectrum.

Solar radiation, after reflection from the secondary concentrator, enters in the form of a pseudo-parallel flow onto triangular prisms, where it is decomposed into a spectrum.

Solar cells (SCs) of heterogeneous spectral sensitivity are installed in the corresponding parts of the spectrum, which increases the efficiency of solar radiation energy conversion by matching the spectral sensitivity of the SC with the radiation in the spectrum.

Application

Nevertheless, there is already positive experience in constructing such optical systems. A promising direction may be the construction of space telescopes with a diameter of tens and hundreds of meters, using Fresnel lenses based on thin membranes.

It is widely used in lighting devices, especially mobile ones, to minimize weight and moving costs.

Fresnel lenses are used in large-sized focusing systems of marine lighthouses, in projection televisions, overhead projectors (overhead projectors),

Fresnel lenses in lighthouses, photo flashes, navigation lights, traffic lights, railway lens traffic lights and semaphore and passenger car lights.

The ultra-flat, lightweight magnifying glass, a thin sheet of plastic molded into the shape of a Fresnel lens, turns out to be a convenient magnifying glass for people with low vision who have to read text in small print. Due to its small thickness, this magnifying glass is used as a bookmark and ruler.

Acoustic Fresnel lenses (actually not lenses, but acoustic Fresnel zone plates) are used to form a sound field in acoustics. Made from sound-absorbing materials.

A plastic film in the form of a Fresnel lens, applied to the rear window of a car, reduces the blind spot (invisible) behind the car when viewed through the rearview mirror.

The use of Fresnel lenses as a solar energy concentrator for solar cells is currently considered promising, making it possible to increase the efficiency of solar cells to 44.7%.

Fresnel lenses are used in infrared (pyrometric) motion sensors for security alarms and in lens antennas.

Conclusion

In this essay, we examined the main issues regarding Fresnel lenses, described the calculation of lenses, determined how modeling occurs during calculations, and determined the areas of application of Fresnel lenses.

fresnel lens light beam

List of used literature

1. http://www.nkj.ru/archive/articles/15766/ (link to article from the archive of the journal “SCIENCE AND LIFE”)

2. http://technoexan.ru/products/photovoltaika/cat7.php

3. R. Leutz, A. Suzuki, Nonimaging Fresnel Lenses: Design and Performance of Solar Concentrators (2001), Springer

4. Landsberg G.S. Optics. Tutorial. 6th ed. (2003)

5. Sivukhin D.V. General physics course. Optics. - M.: Nauka, 1985.

6. Landsberg G.S. Optics. - M.: Nauka, 1976.

7. Physics. Big encyclopedic dictionary.- M.: Big Russian Encyclopedia, 1999.- P.90, 460.

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What is a Fresnel lens?

Due to the small spherical aberration, the refracted light rays emerge as almost a single parallel beam. That is, the lens can be imagined as a set of thin rings of individual prisms of triangular cross-section, refracting parallel rays and deflecting them at such an angle that after refraction they converge at a single focal point.

There is not only a converging or positive lens, but also a diverging (negative) one. In the negative ring prism-grooves are made of a different shape. Due to the short focal length, the field of view is wide and, in a reduced form, an image area 2-3 times larger than can be covered with the naked eye can fit in it.

History of creation

At the beginning of the 19th century, a commission was assembled in France, whose task was to improve the design of lighthouses. At that time, the lighthouse was an indispensable navigation device, so European maritime states were interested in improving them.

In order for the light of the lighthouse to be visible at a great distance, the lantern must not only be placed on a high tower, but also its light must be collected into rays. To do this, light was placed at the focus of a concave mirror or a large converging lens, but these methods had a number of disadvantages. With the help of a mirror, only one beam is obtained, and since the light must be visible everywhere, it was necessary to install many mirrors with separate lanterns in each. If you ignore the option with mirrors, you can install several lenses around one lantern, the size of which should be quite impressive. A massive lens can simply lose its shape or burst from heat, and there is also a high probability of material heterogeneity.

To elegantly solve this problem, the outstanding French physicist Auguste Jean Fresnel was invited to the commission. In 1819, he proposed a composite lens that eliminated the disadvantages of a conventional one: it is a lightweight design in the form of thin rings from individual prisms of triangular cross-section. Fresnel not only calculated the ideal shape. He developed the creation technology, supervised production, and sometimes even acted as a worker himself. The result was brilliant, and the resulting brightness of the light impressed the sailors. So French lighthouses became the best, which was recognized even by long-time maritime competitors - the British.

Device Application

An unsurpassed device, created almost 200 years ago, remains relevant to this day. It is used not only in lighthouses, but also for the manufacture of headlights, signal lights, projector parts, and traffic lights. Its low weight allows it to be built in as a part of portable lighting fixtures.

There are many variants of this amazing invention that are intended for household use. For example, a Fresnel reading lens made of lightweight transparent plastic with almost invisible circular grooves. These devices come in all shapes and many of them can even be bent.

The Fresnel parking lens is quite popular, which is used instead of a panoramic rear view mirror in a car. As a thin coating, it is applied to the rear window and thereby provides a wide viewing angle, reducing the visual blind spot. This is done for the purpose of safety, ease of reverse parking, and control of the trailer or tow.

The prism faces coated with an aluminum mirror layer can be used in X-ray telescopes. Such mirrors and lenses are produced very actively: for example, they can be produced from flexible plastic for almost kilometers and then used for design ideas.

The Fresnel lens comes in tabletop and backlit versions, similar to any other magnifying devices for home use. It is useful for a small (2-2.5 times) magnification of the image of small details in the process of doing handicrafts or hobbies.

Many travelers also use a Fresnel lens. The price and weight are quite modest, so you can always take such a device with you. Why is it needed when traveling? This lens can collect sunlight into a small spot that can ignite a fire from dry materials - paper, boards. Some experienced tourists adapt it to heat small quantities of water in the field.

One of the creators of the wave theory of light, the outstanding French physicist Augustin Jean Fresnel was born in a small town near Paris in 1788. He grew up as a sickly boy. Teachers considered him stupid: at the age of eight he could not read and could hardly remember the lesson. However, in high school, Fresnel showed remarkable abilities in mathematics, especially geometry. Having received an engineering education, from 1809 he participated in the design and construction of roads and bridges in various departments of the country. However, his interests and capabilities were much broader than simple engineering activities in the provincial wilderness. Fresnel wanted to do science; He was especially interested in optics, the theoretical foundations of which were just beginning to take shape. He studied the behavior of light rays passing through narrow holes, bending around thin threads and the edges of plates. Having explained the features of the resulting pictures, Fresnel in 1818-1819 created his theory of optical interference and diffraction - phenomena arising due to the wave nature of light.

At the beginning of the 19th century, European maritime states decided to jointly improve lighthouses - the most important navigation devices of that time. In France, a special commission was created for this purpose, and Fresnel was invited to work on it due to his rich engineering experience and deep knowledge of optics.

The light of the lighthouse should be visible far away, so the lighthouse lantern is raised to a high tower. And in order to collect its light into rays, the flashlight must be placed at the focus of either a concave mirror or a collecting lens, and quite a large one. The mirror, of course, can be made of any size, but it gives only one beam, and the light of the lighthouse must be visible from everywhere. Therefore, sometimes a dozen and a half mirrors were placed on lighthouses with a separate lantern at the focus of each mirror. You can mount several lenses around one lantern, but making them the required - large - size is almost impossible. The glass of a massive lens will inevitably have inhomogeneities, it will lose its shape under the influence of its own gravity, and due to uneven heating it may burst.
New ideas were needed, and the commission, having invited Fresnel, made the right choice: in 1819, he proposed the design of a composite lens, devoid of all the disadvantages inherent in a conventional lens. Fresnel probably reasoned this way. A lens can be imagined as a set of prisms that refract parallel light rays - deflect them at such angles that after refraction they converge at the focal point. This means that instead of one large lens, you can assemble a structure in the form of thin rings from individual prisms of triangular cross-section.

190 years have passed since then, but the designs proposed by Fresnel remain an unsurpassed technical device, and not only for lighthouses and river buoys. Until recently, glass of various signal lights, car headlights, traffic lights, and parts of lecture projectors were made in the form of Fresnel lenses. And just recently, magnifying glasses appeared in the form of rulers made of transparent plastic with barely noticeable circular grooves. Each such groove is a miniature annular prism; and all together they form a converging lens, which can work both as a magnifying glass, magnifying an object, and as a camera lens, creating an inverted image. Such a lens is capable of collecting the light of the Sun into a small spot and setting fire to a dry board, not to mention a piece of paper (especially black).

A Fresnel lens can be not only converging (positive), but also diverging (negative) - for this you need to make the annular prism-grooves on a piece of transparent plastic of a different shape. Moreover, a negative Fresnel lens with a very short focal length has a wide field of view; in it, in a reduced form, a piece of the landscape is placed, two to three times larger than what is covered by the naked eye. Such “minus” lens plates are used instead of panoramic rear-view mirrors in large cars such as minibuses and station wagons.

The edges of miniature prisms can be coated with a mirror layer - say, by sputtering aluminum. Then the Fresnel lens turns into a mirror, convex or concave. Manufactured using nanotechnology, such mirrors are used in telescopes operating in the X-ray range. And mirrors and lenses for visible light stamped in flexible plastic are so easy to manufacture and cheap that they are produced literally by the kilometer in the form of ribbons for window dressings or bathroom curtains.
There have been attempts to use Fresnel lenses to create flat lenses for cameras. But technical difficulties stood in the way of the designers. White light in a prism is decomposed into a spectrum; the same thing happens in the miniature prisms of the Fresnel lens. Therefore, it has a significant drawback - the so-called chromatic aberration. Because of it, a rainbow border appears on the edges of images of objects. In good lenses, the fringe is eliminated by installing additional lenses. The same could be done with a Fresnel lens, but then a flat lens would no longer be possible.

A Fresnel ruler lens focuses the sun's rays no worse, and even better (because it is larger) than a regular glass lens. The sun's rays collected by it instantly burn through a dry pine board.

Augustin Fresnel entered the history of science and technology not only and not so much thanks to the invention of his lens. His research and the theory created on its basis finally confirmed the wave nature of light and solved the most important problem in physics of that time - they found the reason for the rectilinear propagation of light. Fresnel's work formed the basis of modern optics. Along the way, he predicted and explained several paradoxical optical phenomena, which, nevertheless, are easy to verify even now.

A long-standing dispute between researchers about the nature of light - whether it is wave or corpuscular - was generally resolved at the end of the 17th century, when Christiaan Huygens published his Treatise on Light (1690). Huygens believed that every point in space (in his description - ether) through which a light wave passes becomes a source of secondary waves. The surface surrounding them is a propagating wave front. Huygens' principle solved the problems of reflection and refraction of light, but could not explain a well-known phenomenon - its rectilinear propagation. Paradoxically, the reason for this was that Huygens did not consider deviations from straightness - the diffraction of light (bending around obstacles) and its interference (the addition of waves).

This deficiency was filled in 1818-1819 by Augustin Fresnel, an engineer by training and a physicist by interest. He supplemented Huygens' principle with the process of interference of secondary waves (introduced by Huygens purely formally, that is, for the convenience of calculations, without physical content). Due to their addition, the front of the resulting wave appears, a real surface on which the wave has noticeable intensity.

Since all secondary waves are generated by the same source, they have the same phases, that is, they are coherent. Fresnel proposed to mentally divide the surface of a spherical wave coming from one point O into zones of such a size that the difference in distances from the edges of neighboring zones to a certain selected point F would be equal to λ/2. Rays emanating from neighboring zones will arrive at point F in antiphase and, when added, will weaken each other until they completely disappear.

Having designated the amplitude of oscillations of a light wave coming from zone m as Sm, the total value of the amplitude of oscillations at point F

S = S0-S1+S2-S3+S4+...+Sm=S0-(S1-S2)-(S3-S4)-...-(Sm-1-Sm)

Since S0>S1>S2>S3>S4... the expressions in parentheses are positive and S is less than S0. But how much less? Calculations of the sum of an alternating series carried out by the American physicist Robert Wood show that S=S0/2±Sm/2. And since the contribution of the far zone is extremely small, the intensity of light from the far zones, arriving in antiphase, reduces the effect of the central zone by half.
Therefore, if the central zone is covered with a small disk, the illumination in the center of the shadow will not change: due to diffraction, light from the following zones will get there. By increasing the size of the disk and sequentially covering the following zones, you can make sure that a bright spot will remain in the center of the shadow. This was theoretically proven in 1818 by Simeon Denis Poisson and considered it evidence of the fallacy of Fresnel’s theory. However, experiments carried out by Domenic Arago and Fresnel discovered the spot. Since then it has been called Poisson's spot.

For the experiment to be successful, it is necessary that the edges of the disk exactly coincide with the boundaries of the zones. Therefore, in practice, a miniature ball from a bearing is used, glued to glass.

Another paradox of the wave properties of light. Let's place a screen with a small hole in the path of the beam. If its size is equal to the diameter of the central Fresnel zone, the illumination behind the screen will be greater than without it. But if the size of the hole covers the second zone, the light from it will come in antiphase, and when added to the light from the central zone, the waves will cancel each other out. By increasing the diameter of the hole, you can reduce the illumination behind it to zero!

So, the total amplitude of the entire spherical wave is less than the amplitude created by one central zone. And since the area of the central zone is less than 1 mm2, it turns out that the light flux comes in the form of a very narrow beam, that is, in a straight line. Thus, from a wave point of view, Fresnel's theory explained the law of rectilinear propagation of light.

A good example illustrating Fresnel's method is the experiment with his zone plate, which works as a collecting lens.

On a large sheet of paper, draw a series of concentric circles with radii proportional to the square roots of the natural numbers (1, 2, 3, 4...). In this case, the areas of all the resulting rings will be equal to the area of the central circle. Let's fill the rings through one with ink, and it doesn't matter whether we leave the central zone light or make it black. Let's photograph the resulting black and white ring structure with a large reduction. The negative will produce a Fresnel zone plate. The diameter of its central zone is determined by the formula D=0.95√λF, where λ is the wavelength of light, F is the focal length of the lens-plate. At λ=0.64 µm (red light) and F=1 m D≈0.8 mm. If the central zone of such a plate is pointed at a bright light bulb, then the entire area will begin to glow like a converging lens. When combined with a weak lens eyepiece, the result is a telescope capable of producing a sharp image of the filament of a light bulb. And from two zone plates you can build a telescope according to Galileo’s scheme (the lens is a plate with a large focal length, the eyepiece is a short one). It gives a direct image, like theater binoculars.

From all of the above, it becomes clear how a small hole can play the role of a lens, called a stenope or pinhole. It corresponds to the central zone of the Fresnel phase plate. That is why stenope does not have any aberrations, except for chromatic ones, because rays pass through it without distortion.

A light wave passing through a zone plate gives a resulting amplitude S=S0+S2+S4+... - twice as large as a free wave: the zone plate works as a collecting lens. An even greater effect will be obtained if you do not delay the light of even-numbered zones, but change its phase to the opposite one. The light intensity increases fourfold.

Such a plate was made in 1898 by Robert Wood by covering the glass with a layer of varnish and removing it from the odd-numbered zones, so that the difference in the path of the rays in them was λ/2. He placed the glass plate, coated with varnish, on a rotating table. The cutter - it was a gramophone needle - cut off layers of varnish; for the outer zones, one pass of the needle was enough, and in the inner zones the needle moved in a narrow spiral, successively removing several merging grooves. The diameter of the zones and their width were controlled using a microscope.

It would be interesting to try to make such a record using a player disc.

Finally, another paradox of wave optics. As already mentioned, it does not matter at all whether the central zone is transparent or not. This means that the role of a stenope lens (or pinhole) can be played not only by a small hole, but also by a tiny ball, the diameter of which is equal to the size of the central Fresnel zone.

Sergey Trankovsky.
Journal "Science and Life", No. 5-2009.

Fresnel lens

Creation of a parallel beam of light by a Fresnel lens (located in the center).

Fresnel lens- complex compound lens. It does not consist of a single polished piece of glass with spherical or other surfaces (like conventional lenses), but of separate concentric rings of small thickness adjacent to each other, which in cross-section have the shape of prisms of a special profile. Proposed by Augustin Fresnel.

This design ensures that the Fresnel lens has low thickness (and therefore weight) even with a large angular aperture. The sections of the lens rings are constructed in such a way that the spherical aberration of the Fresnel lens is small, the rays from a point source placed at the focus of the lens, after refraction in the rings, come out almost parallel beam(in ring Fresnel lenses).

Fresnel lenses are circular And waist. Ring ones direct the light flux in any one direction. Belt lenses send light from a source in all directions in a specific plane.

The diameter of a Fresnel lens can range from a few centimeters to several meters.

Application

Notes

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Fresnel lens- stepped lens - [L.G. Sumenko. English-Russian dictionary on information technology. M.: State Enterprise TsNIIS, 2003.] Topics information technology in general Synonyms stepped lens EN Fresnel lens ... Technical Translator's Guide

This term has other meanings, see Lens (meanings). Biconvex lens Lens (German: Linse, from Latin... Wikipedia

A complex composite lens used in lighthouse and signal lanterns. Proposed by O. J. Fresnel. It does not consist of a single polished piece of glass with a spherical shape. or other surfaces, like ordinary lenses, and from the department. adjacent to each other concentric... Physical encyclopedia

FRESNEL- (1) diffraction (see) of a spherical light wave, when considering which the curvature of the surface of the incident and diffracted (or only diffracted) waves cannot be neglected. In the center of the diffraction pattern from a round opaque disk there is always... ... Big Polytechnic Encyclopedia

Areas into which the surface of the light wave front is divided to simplify calculations when determining the wave amplitude at a given point in space. Method F. z. used when considering problems of wave diffraction in accordance with Huygens... ... Physical encyclopedia

Optical glass used to concentrate the light flux emanating from the lamp into a narrow, almost cylindrical beam. For this, the luminous filament of the lamp should be used. is installed exactly at the focal point of the lens, and the dimensions of the thread are as small as possible. L. are smooth and... ... Technical railway dictionary

Cross section of a Fresnel lens and a conventional lens. A Fresnel lens is a complex composite lens. It does not consist of a single ground piece of glass with spherical or other surfaces, like conventional lenses, but of separate ones adjacent to each other... ... Wikipedia

A complex composite lens used in lighthouse and signal lanterns. Proposed by O. J. Fresnel (See Fresnel). It does not consist of a single ground piece of glass with spherical or other surfaces, like conventional lenses, but of individual... ... Great Soviet Encyclopedia

Plano-convex lens A lens (German: Linse, from Latin: lens lentil) is usually a disk of transparent homogeneous material, bounded by two polished surfaces, spherical or flat and spherical. Currently, the so-called ... Wikipedia is increasingly used

Despite the variety of infrared motion sensors, almost all of them are the same in structure. The main element in them is a pyrodetector, or pyrodetector, which includes two sensitive elements.

The detection zone of the pyro receiver is two narrow rectangles. To increase the detection area from one rectangular beam to the maximum possible value
and increase its sensitivity, converging lenses are used.

The converging lens is convex in shape; it directs the optical rays incident on it to one point F - this is the main focus of the lens. If you use several of these lenses, the detection area will increase.

The use of spherical convex lenses makes the design of the device heavier and more expensive. Therefore, infrared motion and presence sensors use a Fresnel lens.

Fresnel lens. History of creation

French physicist Auguste Fresnel proposed his design for a lighthouse lens in 1819.

The Fresnel lens is derived from a spherical lens. The latter was divided into many rings, reduced in thickness. This is how a flat lens turned out.

Thanks to this shape, lenses began to be made from a thin plastic plate, which made it possible to use them in lighting devices and motion and presence sensors.

The sensor lenses are made up of many segments called Fresnel lenses. Each segment scans a specific area of the sensor's coverage area. The shapes of the motion sensor lenses determine the shape of the detection zone.

For example, ceiling devices have a hemispherical lens shape, corresponding to 360 degrees. For devices with cylindrical lenses, it is usually 110-140 degrees. There are also square shapes of detection zones.

B.E.G's line of infrared motion and presence sensors feature high-quality Fresnel lenses that provide excellent detection performance.