Fresnel lenses, their calculation, modeling and application. Parking Fresnel lens - a budget alternative to parking sensors and a rear view camera? Fresnel magnifier what
Not so long ago, I noticed a car on the rear window of which an incomprehensible small-sized lens was glued, I did not attach any importance to this, but it was deposited in my head. Then I saw the same thing again, but on a minivan, and how to delight the owner of the table next to his car, to my question - what is it, followed by a Fresnel lens. I highly recommend, they say it helps a lot. Let's take a closer look at what this device is and why it really can easily replace the parking sensors.
✔ CHARACTERISTICSDimensions: 200mm x 250mm
Thickness: 1mm
Material: optical acrylic
Negative focal length: -300 mm
Viewing angle: up 13º, sides 25º, down 27º
Application: significantly increases the viewing angle; mounts on the rear window of minibuses, station wagons, SUVs, jeeps, vans; on the side window of trucks.
✔ PACKAGING AND COMPLETE SETArrived in an ordinary cellophane bag.
Inside which was a cardboard package. 
On the back of which the characteristics are written 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, we turn to Wikipedia, which clearly describes what a Fresnel lens is.
Fresnel lens is a complex composite lens. Formed by a set 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 solid spherical lens. Proposed by Augustin Fresnel.
This design provides a low thickness (and hence weight) Fresnel lens even with a large angular aperture. The cross-sections of the rings near the lens 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 in an almost parallel beam (in ring Fresnel lenses). # 1 is a regular lens, and # 2 is a cutaway Fresnel lens. 
This effect is clearly visible in this photo. Small "build-ups" are present 
The lens itself is made of acrylic, strong enough, I have not tried to break it, but it is not afraid of bending and actively rubbing bubbles under it. 
In the lower part there is an inscription Rearguard, but on the upper part there is TOP, so that they would not be confused during the process of "stickers" in the car. 
The lens size is 20cm x 25cm. Most likely there are more, but I think this is the best option. 
✔ OPERATING PRINCIPLEIf the object is in the center of the lens, then it appears smaller and farther than it actually is.
The 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 IN AUTOWe have an ordinary car, a hatchback.
Gently wipe the glass from the inside clean. 
We disperse all the pimples with a cloth. 
This is what the finished version looks like. 
There is a small car fire extinguisher 30-40 centimeters from the bumper. And then there is a gopher and you can see it. 
This is how it looks in the rearview mirror. 
✔ FRENEL LENS TESTS IN AUTONotice how much the billboard is visible in the distance.
The lens can be re-glued almost an infinite number of times, moisten, press and expel bubbles. 
I entered the tunnel, the camera does not clearly transmit the photo, but the car can be seen well. 
Now pay attention, the car is almost in the blind spot, but in the lens you can still see it completely. 
A bit of 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 that's how it can be seen in the lens. In fact, when this happens in motion, it is seen much better, since the object simply starts to move, and does not stand still. 
For example, from about 3 meters, I will clarify in the rear window, I still do not see it, but through the side mirrors in sunlight, the object is easy to miss, due to its small size. 
Well, this is how 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 have disappeared almost completely, not a single parking sensor sees the column, but here everything is perfectly visible even from 50 centimeters. I highly recommend it to owners of minivans and station wagons. Well suited as an original gift for a motorist and yourself. Even the spouse is already praising and parks almost close to the garage wall, not afraid to damage the rear bumper. I frankly regret that I did not buy this thing a couple of years ago, when I ran my backside onto a concrete block that was stubbornly invisible in the mirrors, a bumper for replacement and painting, and the price of the issue was not $ 4 ...
And its main value, ease of installation and complete indifference thieves who quite often pick out rear-view cameras.
One of the founders 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 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 talent for mathematics, especially geometry. Having received an engineering education, since 1809 he has been involved 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 had just begun to take shape. He investigated the behavior of light rays passing through narrow openings, enveloping fine filaments and the edges of the plates. Explaining the peculiarities of the paintings 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 jointly improve lighthouses - the most important navigational 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 must be seen far away, so the lighthouse is raised to a high tower. And in order to collect its light into rays, the flashlight must be placed in the focus of either a concave mirror or a collecting lens, which is quite large. 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, at times a half dozen mirrors were placed on the lighthouses with a separate lamp in the focus of each mirror. Several lenses can be mounted around one flashlight, but making them the necessary - large - size is almost impossible. 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, did right choice: In 1819, he proposed a composite lens design, free of all the disadvantages of a conventional lens. Fresnel argued that 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 triangular prisms.
Fresnel not only calculated the shape of the profiles of the rings, he also developed the technology and controlled the entire process of their creation, often performing the duties of a simple worker (the subordinates were extremely inexperienced). His efforts have yielded brilliant results. “The brightness of the light that the new device gives surprised the sailors,” Fresnel wrote to his friends. And even the British - longtime French rivals at sea - admitted that the designs of the French lighthouses were the best. Their optical system consisted of eight square Fresnel lenses with a side of 2.5 m and a focal length of 920 mm.
Since then, 190 years have passed, but the designs proposed by Fresnel remain an unsurpassed technical device, and not only for lighthouses and river beacons. Until recently, glasses of various signal lights, car headlights, traffic lights, and parts of lecture projectors were made in the form of Fresnel lenses. And quite recently, magnifying glasses have 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 collecting lens that can work both as a magnifying glass, magnifying an 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 circular prism-grooves on a piece of transparent plastic in 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 that covers 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, these mirrors are used in telescopes operating in the X-ray range. And stamped in flexible plastic mirrors and lenses for visible light are so easy to manufacture and cheap that they are produced literally kilometers away in the form of ribbons for decorating showcases or curtains for bathrooms.
There have been attempts to use Fresnel lenses to create flat lenses for cameras. But the designers were faced with technical difficulties. White light in a prism is decomposed into a spectrum; the same happens in the miniature Fresnel lens prisms. 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 border is eliminated by installing additional lenses. The same could be done with a Fresnel lens, but then a flat lens will no longer work.
Fresnel lens-ruler focuses the sun's rays no worse, and even better (because it is larger) than usual glass lens... The sunbeams collected by it instantly burn through the 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 of physics of that time - they found the cause of 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 among researchers about the nature of light - whether it is wave or corpuscular - was generally resolved at the end of the 17th century, when Christian 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 enveloping them is a propagating wave front. Huygens' principle solved the problem 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 - diffraction of light (avoiding obstacles) and its interference (wave addition).
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 resulting wave front appears, the real surface on which the wave has a noticeable intensity.
Since all secondary waves are generated by one source, they have the same phases, that is, they are coherent. Fresnel proposed to mentally break 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. The rays emanating from neighboring zones will arrive at point F in antiphase and, when added, will weaken each other until they completely disappear.
Denoting the amplitude of the oscillations of the light wave coming from the zone m as Sm, the total value of the amplitude of the oscillations at point F
S \u003d S0-S1 + S2-S3 + S4 + ... + Sm \u003d S0- (S1-S2) - (S3-S4) -...- (Sm-1-Sm)
Since S0\u003e S1\u003e S2\u003e S3\u003e S4 ... the expressions in parentheses are positive and S is less than S0. But how much less? Calculations of the sum of the alternating series, which were carried out by the American physicist Robert Wood, show that S \u003d S0 / 2 ± Sm / 2. And since the contribution of the far zone is extremely small, the intensity of the light of 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: light from the following zones will get there due to diffraction. By increasing the size of the disc and sequentially covering the following areas, you can ensure that a bright spot remains 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, experiments carried out by Domenic Arago and Fresnel found the stain. Since then it has been called the Poisson 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 bearing ball glued to the glass is used.
Another paradox of the wave properties of light. 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 combined with the light from the central zone, the waves will mutually annihilate. 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 \u200b\u200bthe central zone is less than 1 mm2, it turns out that the luminous flux goes 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 a wave point of view.
A good example illustrating the Fresnel method is the experiment with his zone plate, which works like 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 \u200b\u200bthe central circle. Fill the rings with ink through one, and it doesn't matter whether you leave the central zone light or make it black. The resulting black and white ring structure will be photographed with a large reduction. The negative will produce a Fresnel zone plate. The diameter of its central zone is determined by the formula D \u003d 0.95√λF, where λ is the wavelength of light, F is the focal length of the lens-plate. At λ \u003d 0.64 μm (red light) and F \u003d 1 m, D≈0.8 mm. If the central zone of such a plate is aimed at a bright light bulb, then all of it will begin to glow like a collecting lens. When combined with a weak lens eyepiece, you get a telescope that can give a sharp image of the bulb's filament. And from two zone plates, you can build a telescope according to the Galilean scheme (the lens is a plate with a large focal length, the eyepiece is with a small one). It gives a live image like a theater binocular.
From all of the above, it becomes clear how a small aperture can play the role of a lens called a stenoper or pinhole. It corresponds to the central zone of the Fresnel phase plate. That is why the stenoper does not have any aberrations, except for the chromatic one, as the rays pass through it without distortion.
The light wave passing through the zone plate gives the resulting amplitude S \u003d S0 + S2 + S4 + ... - twice as large as the free wave: the zone plate acts as a converging lens. An even greater effect will be obtained if you do not delay the light of the even zones, but change its phase to the opposite. In this case, 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 zones, so that the difference in the path of the rays in them was λ / 2. He placed the lacquered glass plate on the revolving table. The cutter - it was a gramophone needle - cut off the layers of varnish, for the outer zones one pass of the needle was enough, and on the inner zones the needle moved along a narrow spiral, successively removing several merging grooves. The diameter of the zones and their width were monitored with a microscope.
It would be interesting to try to make such a record using a turntable disc.
Finally, there is 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 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", №5-2009.
Words that were completely insignificant were printed in large letters, and everything significant was depicted in the smallest print.
M.E. Saltykov-Shchedrin
Every time, rereading Mikhail Evgrafovich, one is amazed at the foresight of the Tver vice-governor. That's how he found out about cheese products, beer drinks and other food pretending to be food, with tiny letters on the packages ?! Yes, you can see the letters at the age of 20 without a problem. But youth is a disease that goes away by itself. And if your eyes still allow microtexts to read yellow on pink, your old people can be very useful.
In principle, stamping such things (called a Fresnel lens) is not difficult. Make a thing fit. I feared much worse. But the quality is clearly lucky.
Preliminary test
The package reads "High Definition Magnifying Glass in Business Card Format" in hieroglyphics. I took the first leaflet I came across. By the way, you can roughly estimate the increase.
We see that the image is not like in a good lens - in the direction from the center to the periphery, the clarity drops slightly. But it remains quite decent. At the very bottom, where the lens is attached to the frame, there is distortion. But iridescent streaks (chromatic aberration) and distortion (turning a square into a pillow or barrel) are not noticeable
Illustrations aberration
Distortion 
Chromatic aberration 
And an example 
How the Fresnel lens works
Fresnel lens from the Lighthouse Museum at Point Arena, California 
Usually, to understand the idea of \u200b\u200ba Fresnel lens, similar pictures are given. 
. "... let's cut the plano-convex lens into rings and fold them to a plane." Of course, this is just a simplified model. First, in this case, different zones will not collect light at one point, there will be a shift along the optical axis. Secondly, in order for the lens to work for oblique beams, the transition from zone to zone is made not vertical, but inclined. Thirdly, you have to find a compromise between narrow and wide rings ... As a result, the calculation is quite complicated. But we, fortunately, do not need to count :) We need the manufacturer. 
Shipping and packaging
Order Jul 19, 2018, shipment Jul 22, received Aug 06. Full trackTransport packaging - gray PE bag. Commercial packaging is a transparent PE bag. Both do not deserve personal portraits.
Specification
RIMIX transparent magnifierColor: Random
Material: PVC
Size: 85x55x1
Magnification: 3 X
Appearance
The lens is equipped with a plastic case-pocket that protects the optical surface from scratches and dirt. The inscription in hieroglyphs on the case "High-definition magnifying glass in the format of a business card" (Troika card - for scale. Corresponds to the size of a plastic bank card, but does not show the card numbers.
The dimensions of the card (not the case) exactly correspond to the dimensions of plastic cards
I would rate the magnification by eye twice, so we'll check it out.
Focal length
Tested characteristics other than dimensions, only one - 3X magnificationIn everyday life, magnification is understood as the quotient of dividing the distance of optimal vision (250 mm is taken, although different eyes are different) and the focal length of the lens. The easiest way to measure it * is to build an image from a distant source and measure the distance from the lens to the image. The sun behind a cloud is ideal as a distant source - an image of not only the sun, but also clouds appears on a sheet of paper. The fact that the Fresnel lens built quite a clear image surprised me pleasantly. This is almost always the case with an ordinary lens. Fresnel lenses like ours are often made coarser and instead of clouds, we get fog. Unfortunately, I didn't manage to take a picture of this case - the brightness range of the smartphone's camera was not enough :(
* Approx. for nerds
In fact, you need to measure not from the edge of the magnifying glass, but from the so-called. rear principal plane. But with our precision, the difference is negligible. Moreover, a Fresnel lens, strictly speaking, has as many pairs of main planes as there are annular zones :)
So, I measured the focal length roughly 140 mm. That is, the increase is actually about 2X (at 3, let me remind you, as promised). And the optical power is about 7D. 7 diopters is a lot by the standards of glasses. The characteristic optical power of glasses for pensioners is 2-2.5-3 diopters. Although there are many more, of course.
In the shop
This is, of course, the main application. The lens has found a permanent place in my wallet and I use it every day. Example - like cheese in Pyaterochka
The terrible word KHIMOZIN for testing turned out to be a completely legal component - rennet (although it is hardly natural). But the salts of cyanic acid somehow strained me.
E536 - Potassium ferrocyanide
The substance itself - potassium ferrocyanide - is very slightly toxic, but when it interacts with water, poisonous gases are released during the reaction. But their number usually does not pose a serious health hazard. When hexacyanoferrate interacts with some acids, a large amount of highly toxic hydrogen cyanide gas can be released. In the food industry it is mainly used to prevent clumping and caking, as an additive to table salt. It is also used in the production of sausages, which is always immediately reported white bloom on the product shell.
Collecting sunlight
For children, such a thing can also be a funny toy, first of all, to burn something with the sun's rays. The experiments below were staged in the village on improvised foot materials, do not shoot the pianist. Smoke immediately comes from the black hose and stinks. It is more difficult to focus on a receipt from a thermal printer, but it turns out that when it heats up it turns black. But I was able to burn through a sheet from a school notebook only on the second attempt and only at about noonIn the process, it turned out that the lens had a huge coma. In practice, this means that to burn it you need to hold it fairly accurately perpendicular to the direction of the sun. This did not cause problems for me, but for my daughter it turned out like this all the time. (attention to the picture on the hose)
Children's poems: Dad gave me a magnifying glass
Dad gave me a magnifying glass
(I'm terribly lucky!)
I will consider everything
This thick glass.
Magnifies the magnifier
Everything that the eye only sees
I have now learned that in the soup
Mom cooks every time.
The cabbage looks terrible -
That's it, my appetite is gone ...
And I ate the second right away,
And now it will not fly into me.
I caught a cat in the kitchen
To examine the mustache
And she immediately - through the window,
Even though a magnifying glass is not worse - dogs!
The sun shines through the windows brightly
A ray fell into my palm ...
I aimed the magnifying glass ... how hot!
I began to examine the beam ...
The dot burned the palm
I involuntarily screamed ... oh! ..
But I cried a little,
Hiding a magnifying glass under the couch.
So that mom does not scold
Daddy, magnifying glass and me
This little wound
I will grease myself with brilliant green.
Olya Lukoeva
Advantages and disadvantages
+ An unexpectedly high quality picture for this type of lens. He talks about high-quality material, correct design calculation and adherence to technology.+ Lightweight and compact, fits in your wallet and will be at the right time at hand
+ Can be used for educational purposes and as a toy, set on fire by sunlight
+ Small ruler on the long side
Not a cheap option. Lenses of this standard size are available and several times cheaper
- Not enough multiplicity - 2 with declared 3
- The case does not fit into the compartment for plastic cards. And without a cover it is impossible, it will quickly become unusable.
Total
I liked the lens more than I expected. I will clarify again, there are a lot of offers many times cheaper. I strongly doubt that it is of the same quality. But for the purpose of studying the composition of fake cheese in a store, rainbow stains around the edges are not fatal. So everyone can choose cheaper or better quality for themselves. With optics, there is always such parsley.The product was provided for writing a review by the store. The review is published in accordance with clause 18 of the Site Rules.
I plan to buy +22 Add to favorites Review liked +61 +96FRESNEL 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. It was originally used in lighthouses. The main property of fresnel is that it is light, flat and thin, but it has all the properties of a conventional lens. Fresnel consists of concentric triangular grooves. The step of the grooves is comparable to the height of their profile. Thus, it turns out that each groove is, as it were, part of a conventional lens.
It should be noted that the projector uses steam instead of one fresnel. If you come across a fresnel from an overhead projector, note that it is smooth on both sides, i.e. actually consists of two fresnel, facing each other with ribbed surfaces and glued around the perimeter.
Why use two fresnel and can you get by with one?
Take a look at the diagram and everything will become clear.
If only one fresnel is used, the lamp needs to be in approximately double focus. The beams from the lamp will also converge at approximately double focus. The minimum focal length for the available fresnel is 220 mm. 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.
By using 2 fresnel, both disadvantages can be eliminated. The light source is located slightly closer to the focal length of the left fresnel, and it forms an "imaginary" source outside the double focal length of the right fresnel. After passing through the right fresnel, the rays will converge between the focus and double focus.
Let's go back to our optical scheme from the previous section (we mean that we have two fresnel, although one is drawn):
Remember when I said that this diagram was simplified? If everything was as drawn, we would not need the lens. Each beam from a light source would pass through a single point on 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 we 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 of the passage of rays will look like this:
1st stage of construction - the left fresnel forms a "ghost image" of the electric arc of the lamp. We need it in order to correctly build the path of the rays through the right fresnel.
2nd stage of construction - we forget about the presence of the left lens and build the ray path for the right lens, as if the "imaginary" image were real.
3rd stage - 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. In this case, the image of the arc 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 fresnel have?
The fresnel facing the lamp is taken as short as possible for a larger angle of coverage. The focal length of the second fresnel should be 10-50% greater 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 the double focus of the lens, depending on the distance from the lens to the screen). In fact, the most common fresnel on the market is with 2 focal lengths: 220 mm and 330 mm.
When choosing the fresnel focal length, you need to pay attention to the fact that, unlike conventional lenses, fresnel are moody to the angle of incidence of light. I will explain in two diagrams:
The caprice lies in the fact that the rays falling 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". In the left diagram, the light source is approximately at the focus of the left lens, so the rays between the lenses go 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 to the focal length, so some of the rays fall on the non-working surfaces of the right lens. The greater the distance from the focus to the source and the larger the lens diameter, the greater this effect.
1. Lenses should be placed with grooved sides to each other, not vice versa.
2. It is desirable to place the light source as close as possible to the focus of the first lens, and as a consequence:
3. The ability to move the light source to adjust the point of convergence of the beam into the lens is limited to only a few centimeters, otherwise it will lose the brightness of the picture at the edges and the appearance of moiré.
How big should the fresnel be?
What material should fresnel be made of?
The most available at the moment are fresnel made of optical acrylic (plexiglass, in other words). They have excellent transparency and are slightly elastic. For our purpose, this is sufficient, given that the quality of the fresnel DOES NOT AFFECTLY affect the sharpness and geometry of the picture (only the brightness).
How to handle fresnel?
1. Do not leave fingerprints on the grooved side of the fresnel. Wash hands thoroughly with soap and water before any fresnel operations. It is best to wrap the fresnel with plastic wrap for packaging products from the moment of purchase until the end of the experiments.
2. If prints do appear on the grooved side, DO NOT try to erase them. No detergents (including ammonia-based window cleaners) help, because do not penetrate deep enough. At the same time, the outer edges of the grooves are slightly rounded, and particles from the napkin / cotton used for wiping are clogged between the grooves. As a result, the fresnel begins to scatter the rays. Better left with prints. You can wipe the smooth side, as long as you are sure that the detergent does not get on the grooved side.
3. Watch the temperature regime. Do not let the fresnel heat up above 70 degrees. At 90 degrees, the lenses begin to float and the light beam loses its shape. Personally, I screwed up one set of lenses because of this. Use a thermocouple tester to monitor the temperature. Sold in 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 choose, we need to know 4 main characteristics:
Number of lenses
In principle, one lens can also serve as a lens, for example a magnifying glass. However, the further from the center of the picture, the worse its quality will be. Spherical distortions (aberrations), chromatic aberrations (due to different angles of refraction of rays of different wavelengths, a white point, for example, turns into a piece of a rainbow), loss of sharpness will appear. Therefore, achromatic lenses of 3 or more lenses are used to achieve maximum picture quality. These were used in epidascopes, old cameras, aerial photography equipment, etc. Overhead projectors also use three-lens lenses, but these projectors are more expensive than single-lens models.
Focal length
The focal length of the lens determines at what distance from the original object (matrix) it should be placed and what size the image on the screen you will receive. The longer the focal length, the smaller the screen size, the further from the screen you can place the projector, the longer the projector body. And vice versa.
Vision angle
Shows how big the original image can be covered by the lens while maintaining acceptable brightness, sharpness (resolution), etc. "Acceptable" is a loose concept. If an angle of view is indicated in the passport for an aerial lens, for example, 30 degrees, this may mean that in reality it will cover 50 degrees, but the sharpness at the edges for aerial photography is no longer suitable, but for our projector, where a high resolution is not needed, it is quite suitable ...
Aperture ratio and relative aperture
Relative aperture, if simplified - the ratio of the lens diameter to its focal length. It is designated as a fraction, for example 1: 5.6, where 5.6 is the "f-number". If we have a lens with an inner 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 the f-number), the more the lens aperture - the ability to convey the brightness of the subject - and the worse the sharpness / resolution usually.
What should be the relative aperture?
The aperture can be found by knowing the lens diameter and focal length. With regard to our optical scheme, we can say that the diameter of the objective lenses should not be smaller images of the lamp arc formed by fresnel. Otherwise, some of the lamp light will be lost.
Now it's time to make one more refinement to our optical scheme.
It is obvious that the matrix scatters the rays passing through it. Those. each ray falling on the matrix leaves 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 "fuzzy 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 nothing 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.
F lens \u003d L * (d / (d + D)), where
L-distance to screen
d-diagonal of the matrix
D-screen diagonal
Here is a calculator (grabbed from www.opsci.com, slightly adapted and translated into plain language)
This article will focus on fresnel lens and how to make fire with it.
Getting fire from the sun using a magnifying glass is a laborious but exciting process. However, you always want something more. For example, so that the fire flares up immediately when focusing the beam on an object, without conducting shamanistic rites and rituals, that is, without much effort. But for this you need to collect as much sunlight as possible in a beam, that is, you need a lens large diameter... But here is the whole catch: As for the usual glass lens.
- Large diameter lens is difficult to obtain (buy) (Usually the largest lenses are around 100-120mm in diameter)
- Such a lens will not be cheap.
- It will be inconvenient to carry with you, since the large lens weighs a lot + it is glass and can break.
Fresnel lens.
The fresnel lens is plastic transparent plate with concentric notches... All notches give focus in one place. It turns out a kind of composite lens. In this case, the fresnel lens may be large and be lightweight.
The largest lens I have been able to order from local online stores is a lens about the size of an A4 album sheet... The price is low compared to glass magnifiers.
The magnification of this lens was of little interest to me. Let me just say that its multiplicity is 3x.
Fresnel lens. We get fire from the sun.
Finally getting out into nature, I tested the fresnel lens in action. So, September is the month, the temperature is just below 20 degrees Celsius, the weather is sunny, the time is just over 14 hours.
Let's try to finally set fire to something with a lens.
Without hesitation I find a rotten stick. I concentrate a beam of sun rays on it. Then I burn it out a little in one place.
And now the fresnel lens exceeded all my expectations. The stick begins to char, and then a flame breaks out in the place of the sun's rays!
Let's try to set fire to something else, for example a piece of birch bark.
I direct a beam of light onto a birch bark, concentrate all the rays in one place with a lens. I note that the lens is large enough, so it is a little harder to catch a sunbeam, you need to maintain a perpendicular to the sun. Thus, the maximum amount of sunlight passes through the lens and then focuses on one point.
We burn it out for a very short time and the birch bark also flares up from the sun's rays. Sufficient temperature for ignition.
Setting fire to the lens is a pleasure. for instance easy to set fire to dry foliage, which is a lot in the fall. Here you go, we collect a bunch of leaves, put them on an iron sheet from the barbecue, so as not to start a fire here. Then, as usual, we take a fresnel lens, concentrate a beam of sunlight with it and burn it out in one place. 
The leaves light up, despite the fact that the sun was slightly behind the trees, there was no need to blow! 
Even better tinder is dry grass. We collect the dried tops of the plants. 
It turns out here is such a bundle the size of a fist.
Flashes almost instantly! Ideal tinder in this situation. Caution, don't start a fire!
Using a fresnel lens, I managed to get fire even at sunset, when the sun was already hiding behind the trees and it was getting cold, though here it was necessary to fan the dried grass and rot from the trees.
Fresnel lens as an item in your survival kit.
Let's talk about the practicality and usefulness of a fresnel lens. In other words, is it worth taking a fresnel lens with you on a hike or where is it better to use it.
I also note that we are talking about a fresnel lens of exactly the same size as I was considering. Because lenses of other sizes have completely different characteristics. A smaller lens is not capable of producing fire so effectively, you will have to bother with tinder very much, and accordingly, without certain skills, fire may not work at all.
The lens is large, firstly, it is already very bulky (it will no longer fit in a bag), and secondly, it is even more difficult to buy or acquire it.
So the pros: 
Now the cons:
- Sun, sun. How few sunny days there are in the year. Dependence on the sun is the main and fatty minus when extracting fire from a magnifying glass.
- The lens is made of plastic, so it can break if you push harder. Concentric grooves are just as easy to scratch. Therefore, it is better to adapt some kind of cover for the lens, for example, a folder for paper or a plastic bag or file.
- The lens is still large, matches or a lighter are much smaller.
- During burnout, too bright light blinds the eyes, but not critical. You can dress sunglasses, but personally I don't use them.
The conclusion I will make is that the use of a fresnel lens of this size is advisable in autonomous hikes when the supply of gas or matches may run out. The longer the autonomous hike, the more practical the lens will be. In places where the sun often shines, a frennel lens will do just fine. For example, if you go to the Crimea in the mountains for a couple of weeks. 
Thanks to all! I wish you more sunny days!
Fire with a fresnel lens video.
That's all. Leave comments.!