The fresnel lens is large. Optics

Fresnel lens

Creating a parallel beam of light with a Fresnel lens (located in the center).

Fresnel lens- a complex compound lens. It does not consist of a single polished piece of glass with spherical or other surfaces (like ordinary 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 keeps the Fresnel lens thin (and hence light) even at large angular apertures. The sections of the rings near the lens are built 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 annular Fresnel lenses).

Fresnel lenses are ring and belt. Rings direct the light flux in any one direction. Waist lenses send light from a source in all directions in a certain plane.

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

Application

see also

Notes

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See what the "Fresnel lens" is in other dictionaries:

Fresnel lens- stepped lens - [L.G. Sumenko. English Russian Dictionary of Information Technologies. M .: GP TsNIIS, 2003.] Topics information technology in general Synonyms stepped lens EN Fresnel lens ... Technical Translator's Handbook

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

A complex composite lens used in beacons and signal lights. 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 otd. adjacent to each other concentric ... Physical Encyclopedia

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

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

Optical glass used to concentrate the light flux coming from the lamp into a narrow, almost cylindrical beam. For this, the luminous filament of the lamp should be. installed exactly in the focus of L., and the dimensions of the thread may be smaller. L. are smooth and ... ... Technical railway dictionary

Cross section of a Fresnel lens and an ordinary lens The Fresnel lens is a complex composite lens. It does not consist of a single polished piece of glass with spherical or other surfaces, like ordinary lenses, but of separate adjoining ones ... ... Wikipedia

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

Plano-convex lens 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

Not so long ago, I noticed a car on the rear window of which an incomprehensible small lens was pasted, I did not attach any importance to this, but it stuck in my head. Then I saw the same thing again, but on a minivan, and, to my delight, the owner of the table next to his car, my question - what is it, was answered by the Fresnel lens. highly recommend, they say it helps a lot. Let's take a closer look at what kind of device it is and why it can really easily replace parking sensors.

✔ FEATURES

✔ PACKAGING AND COMPLETE SET

Inside of which was a cardboard box.

On the back of which the characteristics are painted and the principle of operation of the lens is schematically displayed.

Inside, so that the lens would not be scratched, the seller carefully wrapped it in a piece of paper.

To do this, let's turn to Wikipedia, which clearly describes what a Fresnel lens is.
The Fresnel lens is a complex composite lens. It is formed by a combination of separate concentric rings of relatively small thickness, adjacent to each other. The section of each of the rings has the shape of a triangle, one of the sides of which is curvilinear, and this section is an element of the section of a continuous spherical lens. Proposed by Augustin Fresnel.

This design provides a small thickness (and hence weight) of the Fresnel lens even with a large angular aperture. The sections of the rings near the lens are built 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 in an almost parallel beam (in the annular Fresnel lenses). #1 is a regular lens, and #2 is a sectioned Fresnel lens.

This effect is clearly visible in this photo. There are small "growths"

The lens itself is made of acrylic, strong enough, I didn’t try to tear it, but it is not afraid of folds and active rubbing of bubbles under it.

At the bottom there is an inscription Rearguard, but on the top TOP, so that they would not be confused during the “stickers” in the car.

The lens size is 20cm x 25cm. There are probably more, but I think it's best option.

✔ OPERATING PRINCIPLE

Vows on the sides of the lens also fall into the focus of the lens.

The lens is completely transparent and does not interfere with the view.

✔ INSTALLATION TO AUTO

Gently wipe the glass inside clean.

We disperse all the pimples with a rag.

This is what the finished version looks like.

Here, 30-40 centimeters from the bumper, there is a small car fire extinguisher. And here there is a gopher and you can see it.

This is what it looks like in the rear view mirror.

✔ FRESNEL LENS TESTS IN AUTO

The lens can be re-glued almost an infinite number of times, we wet, press and expel bubbles.

I drive into the tunnel, the camera does not transmit the photo clearly, but the car can be seen well.

And now pay attention, the car is almost in the blind zone, and it is still fully visible in the lens.

Some panorama.

Pay attention to how much "space" the lens shows behind the car.

"Tavria" is already entering the blind zone, and in the lens it is still fully displayed.

Let's conduct a small test, behind the car I put a small fire extinguisher already known from the photo above, which is not visible, but it can break the bumper.

And this is how it is seen in the lens. In fact, when this happens in motion, it is seen much better, since the object simply begins to move closer, and does not stand still.

Here, for example, from about 3 meters, I’ll clarify in the rear window, I still don’t see it, but through the side mirrors in sunlight, the object is easy to miss, due to its small size.

Well, this is what my yard looked like before installing the lens.

And that's how my horizons expanded thanks to her.

Be in - videos always come out faster!

I did not expect that this piece of plastic would be such a useful car. The blind spots disappeared almost completely, not a single parking sensor sees the column, but here everything is perfectly visible even from 50 centimeters. I highly recommend to owners of minivans and station wagons. Well suited as an original gift to the motorist and yourself. Even the wife already praises and parks almost close to the garage wall, not being afraid to damage the rear bumper. I frankly regret that I didn’t buy this thing a couple of years ago, when I ran into a concrete block with my back, which is stubbornly invisible in the mirrors, a bumper for replacement and painting, and the issue price was not $ 4 ...
And its main value, ease of installation and the complete indifference of thieves, who quite often pick out rear-view cameras.

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. The 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 aptitude for mathematics, especially geometry. Having received an engineering education, since 1809 he participated in the design and construction of roads and bridges in various departments of the country. However, his interests and opportunities were much wider than simple engineering activities in the provincial wilderness. Fresnel wanted to do science; he was especially interested in optics, the theoretical foundations of which had just begun to take shape. He studied the behavior of light rays passing through narrow holes, bending around thin threads and the edges of the plates. Having explained the features of the pictures that arise in this case, Fresnel in 1818-1819 created his theory of optical interference and diffraction - phenomena that arise due to the wave nature of light.

At the beginning of the 19th century, European maritime states decided to work together to 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 in it because of 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 lantern must be placed at the focus of either a concave mirror or a converging lens, and a rather large one at that. The mirror, of course, can be made of any size, but it gives only one beam, and the light of the beacon 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 lamp, but it is almost impossible to make them of the necessary - large - size. In the glass of a massive lens, there will inevitably be 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, inviting Fresnel, made right choice: in 1819 he proposed the design of a compound lens, devoid of all the shortcomings inherent in a conventional lens. Fresnel probably reasoned like this. A lens can be represented as a set of prisms that refract parallel light rays - deflect them at such angles that after refraction they converge at a focal point. This means that instead of one large lens, you can assemble a structure in the form of thin rings from separate triangular prisms.

Fresnel not only calculated the shape of the ring profiles, he also developed the technology and controlled the entire process of their creation, often acting as a simple worker (subordinates turned out to be extremely inexperienced). His efforts have yielded brilliant results. “The brightness of the light that the new device gives 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. Their optical system consisted of eight square Fresnel lenses with a side of 2.5 m, which had a focal length of 920 mm.

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, glasses of various signal lights, car headlights, traffic lights, parts of lecture projectors were made in the form of Fresnel lenses. And just recently, magnifiers appeared in the form of rulers made of transparent plastic with barely noticeable circular grooves. Each such groove is a miniature annular prism; and together they form a converging lens, which can work both as a magnifier, magnifying the object, and as a camera lens, creating an inverted image. Such a lens is able to collect the light of the Sun into a small speck and set fire to a dry board, not to mention a piece of paper (especially black).

The Fresnel lens can be not only collecting (positive), but also scattering (negative) - for this you need to make ring prisms-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 which a piece of landscape is placed in a reduced form, two to three times larger than it covers the naked eye. Such "minus" plates-lenses 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 - for example, by spraying 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 molded in flexible plastic, mirrors and visible light lenses are so easy and cheap to make that they are produced literally miles in the form of ribbons for window dressing 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 happens in the miniature prisms of a Fresnel lens. Therefore she has significant disadvantage- the so-called chromatic aberration. Because of it, a rainbow border appears on the edges of the images of objects. In good lenses, the border is eliminated by adding additional lenses. The same could be done with a Fresnel lens, but then a flat lens would no longer work.

The Fresnel lens-ruler focuses the sun's rays no worse, and even better (because it is larger) than a conventional glass lens. The sun's rays collected by her 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 their 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.

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

This shortcoming was filled in 1818-1819 by Augustin Fresnel, an engineer by education and a physicist by interest. He supplemented the 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 arises, a real surface on which the wave has a 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 chosen point F were equal to λ/2. The rays emanating from neighboring zones will come to point F in antiphase and, when added, weaken each other until they completely disappear.

Denoting the amplitude of oscillations of the light wave that came from zone m as Sm, the total value of the oscillation amplitude 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 parenthesized expressions are positive and S is less than S0. But how much less? Calculations of the sum of an alternating series, which were 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, acting 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: light from the following zones will get there due to diffraction. By increasing the size of the disk and successively covering the following zones, one can be sure that a bright spot will remain in the center of the shadow. This was theoretically proved in 1818 by Simeon Denis Poisson and considered evidence of the fallacy of Fresnel's theory. However, the experiments done by Domenic Arago and Fresnel found the spot. Since then, it has been called the Poisson spot.

For the success of the experiment, 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 glued to glass is used.

Another paradox of the wave properties of light. Let's put 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 also 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 luminous flux comes in the form of a very narrow beam, that is, in a straight line. This is how Fresnel's theory explained the law of rectilinear propagation of light from the wave point of view.

A good example of Fresnel's method is the experience with his zone plate, which works like a converging lens.

On a large sheet of paper, draw a series of concentric circles with radii proportional to the square roots of the numbers natural series(1, 2, 3, 4...). In this case, the areas of all the resulting rings will be equal to the area of ​​\u200b\u200bthe central circle. Fill the rings with ink through one, and it does not matter whether to leave the central zone light or make it black. The resulting black-and-white ring structure is photographed with a large reduction. On the negative, you get 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 whole of it will begin to glow like a converging lens. When combined with an eyepiece made from a weak lens, you get a telescope that can give a sharp image of the filament of a light bulb. And from two zone plates, you can build a telescope according to the Galileo scheme (the lens is a plate with a large focal length, the eyepiece is with a small one). It gives a direct image, like theatrical binoculars.

From all of the above, it becomes clear how a small hole can play the role of a lens, called a stenop or pinhole. It corresponds to the central zone of the Fresnel phase plate. That is why the stenope has no aberrations, except for chromatic aberrations, because the rays pass through it without distortion.

The light wave passed through the zone plate gives the resulting amplitude S=S0+S2+S4+... - twice as large as the free wave: the zone plate works as a converging lens. An even greater effect will be obtained if the light of the even zones is not delayed, but its phase is reversed. In this case, the light intensity increases four times.

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

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

Finally, one more 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 stenop (or pinhole) lens 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.

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

The Fresnel lens enlarges the portrait of its creator. (Page from the volume "Physics, Part 2" of the Children's Encyclopedia of the "Avanta +" publishing house).

You can collect light into a narrow beam using a concave mirror (a) or a lens (b), placing the light source at the focal point. At a spherical mirror, it lies at a distance of half the radius of curvature of the mirror.

A converging lens can be thought of as a set of prisms that deflect light rays to a single point - the focus. By repeatedly increasing the number of these prisms, respectively reducing their size, we get practically flat lens- Fresnel lens.

The design of the lighthouse lighting system (Fresnel drawing). The light of the burner F is focused by the lenses L and L" reflected by the mirrors M. The light of the burner propagating downward is reflected in the desired direction by a system of mirrors (shown by a dotted line).

This is what a modern Fresnel lens looks like. Often it is made from a single piece of glass.

The Fresnel lens-ruler focuses the sun's rays no worse, and even better (because it is larger) than a conventional glass lens. The sun's rays collected by her instantly set fire to a dry pine board.

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. The 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 aptitude for mathematics, especially geometry. Having received an engineering education, since 1809 he participated in the design and construction of roads and bridges in various departments of the country. However, his interests and opportunities were much wider than simple engineering activities in the provincial wilderness. Fresnel wanted to do science; he was especially interested in optics, the theoretical foundations of which had just begun to take shape. He studied the behavior of light rays passing through narrow holes, bending around thin threads and the edges of the plates. Having explained the features of the pictures that arise in this case, Fresnel in 1818-1819 created his theory of optical interference and diffraction - phenomena that arise due to the wave nature of light.

At the beginning of the 19th century, European maritime states decided to work together to 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 in it because of 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 lantern must be placed at the focus of either a concave mirror or a converging lens, and a rather large one at that. The mirror, of course, can be made of any size, but it gives only one beam, and the light of the beacon must be visible from everywhere. Therefore, sometimes one and a half dozen mirrors were placed on lighthouses with a separate lantern at the focus of each mirror (see Science and Life, No. 4, 2009, article). Several lenses can be mounted around one lamp, but it is almost impossible to make them of the necessary - large - size. In the glass of a massive lens, there will inevitably be 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, inviting Fresnel, made the right choice: in 1819, he proposed the construction of a composite lens, devoid of all the shortcomings inherent in a conventional lens. Fresnel probably reasoned like this. A lens can be represented as a set of prisms that refract parallel light rays - deflect them at such angles that after refraction they converge at a focal point. This means that instead of one large lens, you can assemble a structure in the form of thin rings from separate triangular prisms.

Fresnel not only calculated the shape of the ring profiles, he also developed the technology and controlled the entire process of their creation, often acting as a simple worker (subordinates turned out to be extremely inexperienced). His efforts have yielded brilliant results. “The brightness of the light that the new device gives 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. Their optical system consisted of eight square Fresnel lenses with a side of 2.5 m, which had a focal length of 920 mm.

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, glasses of various signal lights, car headlights, traffic lights, parts of lecture projectors were made in the form of Fresnel lenses. And just recently, magnifiers appeared in the form of rulers made of transparent plastic with barely noticeable circular grooves. Each such groove is a miniature annular prism; and together they form a converging lens, which can work both as a magnifier, magnifying the object, and as a camera lens, creating an inverted image. Such a lens is able to collect the light of the Sun into a small speck and set fire to a dry board, not to mention a piece of paper (especially black).

The Fresnel lens can be not only collecting (positive), but also scattering (negative) - for this you need to make ring prisms-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 which a piece of landscape is placed in a reduced form, two to three times larger than it covers the naked eye. Such "minus" plates-lenses 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 - for example, by spraying 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 molded in flexible plastic, mirrors and visible light lenses are so easy and cheap to make that they are produced literally miles in the form of ribbons for window dressing 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 happens in the miniature prisms of a Fresnel lens. Therefore, it has a significant drawback - the so-called chromatic aberration. Because of it, a rainbow border appears on the edges of the images of objects. In good lenses, the border is eliminated by placing additional lenses (see "Science and Life" No. 3, 2009, article). The same could be done with a Fresnel lens, but then a flat lens would no longer work.

FRESNEL LENS

In the previous section, we determined that a Fresnel lens, or "Fresnel", is needed to illuminate our LCD panel. The lens is named after its inventor, the French physicist Augustin Jean Fresnel. Originally used in lighthouses. The main property of fresnel is that it is light, flat and thin, but at the same time it has all the properties of a conventional lens. Fresnel consists of concentric triangular grooves. The pitch of the grooves is comparable to the height of their profile. Thus, it turns out that each groove is, as it were, part of an ordinary lens.

It should be noted that the projector uses a pair instead of a single fresnel. If you come across a fresnel from an overhead projector, pay attention that it is smooth on both sides, i.e. in fact, it consists of two fresnels, facing each other with ribbed surfaces and glued along the perimeter.

Why use two fresnels and can you get by with one?

Look at the diagram and everything will become clear.

If only one fresnel is used, the lamp needs to be approximately double focus. The rays from the lamp will also converge at approximately double focus. The minimum focal length for available fresnels is 220mm. This means that the structure will have to be greatly lengthened. But the most important thing is that at such a distance from the lamp to the fresnel, the effective solid angle of the lamp turns out to be very small.

When using 2 fresnels, both disadvantages can be eliminated. The light source is located slightly closer than the focal length of the left fresnel, and it forms an "imaginary" source beyond twice the focal length of the right fresnel. After passing the right fresnel, the beams will converge between focus and double focus.

Let's return to our optical scheme from the previous section (we mean that we have two fresnels, although one is drawn):

Remember I said that this scheme is simplified? If everything was as drawn, we would not need a lens. Each ray from the light source would pass through a single point of the fresnel, then through a single point on the matrix and fly further until it hits the screen and forms a point of the desired color on it. For a point source and an ideal matrix, this would be true. Now add realism - non-point source.

In view of the fact that we use a lamp as a light source, i.e. a luminous body of quite definite, finite dimensions, the real scheme for the passage of rays will look like this:

1st stage of construction - the left fresnel forms a "virtual image" of the electric arc of the lamp. We need it in order to correctly construct the course of rays through the right fresnel.

2nd stage of construction - we forget about the presence of the left lens and build the path of rays for the right lens, as if the "imaginary" image were real.

Stage 3 - we discard all unnecessary and combine the two schemes.

It is easy to guess that it is at the point where the image of the lamp arc is formed that we need to install the lens. The image of the arc in this case carries information about the color of each pixel of the matrix through which the light passed (not shown in the figure).

What focal length should fresnels have?

The fresnel facing the lamp is taken as short as possible for a larger coverage angle. The focal length of the second fresnel should be 10-50% longer than the focal length of the lens (1-2 cm distance from the fresnel to the matrix, the matrix itself is between the focus and double focus of the lens, depending on the distance from the lens to the screen). In fact, fresnels with 2 focal lengths are the most common on the market: 220 mm and 330 mm.

When choosing the focal length of fresnels, you need to pay attention to the fact that, unlike ordinary lenses, fresnels are capricious to the angle of incidence of light. Let me explain with two diagrams:

The whim lies in the fact that the rays incident on the corrugated surface of the fresnel must be parallel to the optical axis (or have a minimum deviation from it). Otherwise, these rays "fly away to nowhere." In the left diagram, the light source is located approximately at the focus of the left lens, so the rays between the lenses run almost parallel to the optical axis and eventually converge at approximately the focus of the second lens. In the right diagram, the light source is located much closer than the focal length, so some of the rays fall on the non-working surfaces of the right lens. This effect is the greater, the greater the distance from the focus to the source and the larger the lens diameter.

1. Lenses should be placed with the ribbed sides facing each other, not the other way around.

2. It is desirable to place the light source as close as possible to the focus of the first lens, and as a result:

3. Opportunities for moving the light source to adjust the point of convergence of the beam into the lens are limited to only a few centimeters, otherwise the image brightness will be lost at the edges and moire will appear.

What size should the fresnels be?

What material should fresnels be made of?

The most available at the moment are fresnels made of optical acrylic (plexiglass, in other words). They have excellent transparency and are slightly elastic. For our purpose, this is enough, given that the quality of the fresnels ABSOLUTELY DOES NOT AFFECT the sharpness and geometry of the picture (only the brightness).

How to deal with fresnels?

1. Do not leave fingerprints on the grooved side of the fresnel. Wash your hands thoroughly with soap and water before any operation on fresnels. It is best to wrap the fresnels with plastic wrap for product packaging from the moment of purchase until the end of the experiments.

2. If prints do appear on the ribbed side, DO NOT attempt to erase them. No detergents (including ammonia-based window cleaners) help, because. do not penetrate deep enough. In this case, the outer edges of the grooves are slightly rounded, and particles from the napkin / cotton wool used for wiping are clogged between the grooves. As a result, the fresnel begins to scatter the rays. Better to leave with prints. You can wipe the smooth side, but only being sure that detergent will not fall on the grooved side.

3. Watch the temperature regime. Do not allow fresnels to heat above 70 degrees. At 90 degrees, the lenses begin to float and the beam of light loses its shape. Personally, I ruined one set of lenses because of this. Use a thermocouple tester to check the temperature. Sold at any radio store.

LENS

What is a lens and why is it needed, I think you understand. The most important thing is to choose it correctly, and, having chosen, find where to buy :) To select, we need to know 4 main characteristics:

Number of lenses

In principle, one lens, such as a magnifying glass, can also serve as an objective. However, the farther from the center of the picture, the worse its quality will be. Spherical distortions (abberations), chromatic aberrations will appear (due to different angles of refraction of rays of different wavelengths white dot, for example, turns into a piece of a rainbow), loss of sharpness. Therefore, to achieve maximum image quality, achromatic lenses with 3 or more lenses are used. These were used in epidiascopes, old cameras, aerial photography apparatus, etc. Overhead projectors also use three-lens lenses, but these projector models are more expensive than models with single-lens lenses.

Focal length

It depends on the focal length of the lens at what distance from the original object (matrix) it needs to be positioned and what size of the image on the screen you get. The larger the focal length, the smaller the screen size, the farther from the screen you can place the projector, the longer the projector body. And vice versa.

Vision angle

Indicates how large the original image can be captured by the lens while maintaining acceptable brightness, sharpness (resolution), etc. "Acceptable" is a loose concept. If the angle of view is indicated for an aerial photograph in the passport, for example, 30 degrees, this may mean that in reality it will cover even 50 degrees, but sharpness at the edges for aerial photography is no longer suitable, but for our projector, where high resolution is not needed, it is quite suitable .

Aperture and Relative Aperture

Relative aperture, if simplified - the ratio of the diameter of the lens to its focal length. It is indicated as a fraction, for example 1:5.6, where 5.6 is the "aperture number". If we have a lens with an internal lens diameter of 60 mm and a focal length of 320 mm, its aperture ratio will be 1:5.3. The larger the relative aperture (smaller f-number), the greater the aperture ratio of the lens - the ability to convey the brightness of the object - and the worse the sharpness / resolution is usually.

What should be the aperture ratio?

The relative aperture can be found by knowing the diameter of the lenses and the focal length. With regard to our optical scheme, we can say that the diameter of the objective lenses must be no less than the size of the image of the lamp arc formed by the fresnels. Otherwise, part of the lamp's light will be lost.

Here it is time to make one more clarification to our optical scheme.

Obviously, the matrix scatters the rays passing through it. Those. each ray that hits the matrix exits it already in the form of a beam of rays with different angular deviations. As a result, the image of the lamp arc in the plane of the lens turns out to be "blurry", increases in size, but continues to carry information about the colors of the matrix pixels.

Our task is to collect this "blurry image of the arc" with the lens completely.

Hence the conclusion: the relative aperture of the lens should be such as to collect the image of the lamp, but no more.

What should be the focal length and angle of view?

These parameters are determined by the size of the original image (matrix), the distance from the lens to the screen, and the size of the desired image on the screen.

Lens F=L*(d/(d+D)), where

L-distance to the screen

d-diagonal of a matrix

D-diagonal screen

Here is a calculator for calculations (torn from www.opsci.com, slightly adapted and translated into understandable language)