Fresnel Parking Lens - Budget Alternative Parktronic and Rear View Camera? Calculation of Lens Fresnel Fire using Fresnel Lenzel Video

27.08.2020 Analyzes

The words were printed with large letters completely insignificant, and everything was essentially depicted in the smallest font.
M.E. Saltykov-Shchedrin

Whenever rereading Mikhail Evgrafovich, amazed by the insightness of the Tver Vice-Governor. That's where he learned about cheese products, beer drinks And others who pretend to eat food, with tiny letters on packages?! Yes, let it see in 20 years without a problem. But youth is a parable, which goes by itself. And if your eyes still allow microtectors to read the pink pink, your old men can be very useful.

In principle, they are naming such pieces (called Fresnel lens) is not difficult. Thing to make suitable. I feared much worse. But with the quality clearly lucky.

Pre-test

On the package of hieroglyphs, a "magnifying glass of high definition in business card format" is written. He took the first flyer. By the way, you can roughly estimate the increase.


We see that the image is not as in a good lens - in the direction from the center to the periphery, the clarity drops a bit. But it remains quite decent. In the lower part, where the lens is attached to the frame - distortion. But rainbow divorces (chromatic aberration) and distortion (transformation of the square in the pillow or barrel) is not noticeable

Illustrations about aberration

Distortia

Chromatic aberration

And example

Like Fresnel Lens is arranged

Additional Information

Fresnel Lens from the exposition of the Museum of Lighthouses in Point Arena, California


Usually, for understanding the idea of \u200b\u200bFresnel lenses, these pictures lead.


. "... Let's cut the flat-convex lens on the rings and lay them to the plane." Of course, this is only a simplified model. First, in this variant, different zones will not gather the light at one point, it will be a shift along the optical axis. Secondly, the lens worked for inclined beams, the transition from the zone to the zone is not with a sheer, but inclined. Thirdly, you have to search for a compromise between narrow and wide rings ... As a result, the calculation is quite complicated. But we, fortunately, do not need :) It is necessary to manufacturer.

Delivery and packaging

Order July 19, 2018, shipment July 22, received August 06. Full track

Transport packaging - Gray PE package. Commercial packaging - transparent PE package. Both do not deserve personal portraits.

Specification

Transparent Magnifier Rimix.
Color: random
Material: PVC.
Size: 85x55x1
Increase: 3 x

Appearance

The lens is equipped with a plastic pocket cover that protects the optical surface from scratches and pollution. Inscription by hieroglyphs on the case "Magnifying glass of high definition in business card format" (Troika map - for scale. Signs in size with a plastic bank card, but does not palette card numbers.


Card sizes (not covered) exactly correspond to the size of plastic cards


An increase in eye I would appreciate two times, so check.

Focal length

Checked characteristics, except sizes only one - 3X Increase
On the household damage, under the increase, they understand the private from dividing the distance of optimal vision (250 mm is accepted, although different eyes - Miscellaneous) and focal length of the lens. Approximately * Measure it easier to build an image from a remote source and measuring the distance from the lens to the image. As a remote source, the sun is ideal for the cloud - an image is appeared on a sheet of paper not only the sun, but also the clouds. The fact that Lens Fresnel built a clear image pleasantly surprised me. This is almost always on the usual lens. Fresnel lenses like our often make coarse and instead of the image of the clouds it turns out fog. Unfortunately, it was not possible to sfat this matter, I did not have enough of the cliquia of the smartphone camera :(

* Approx. For boring

In fact, it is necessary to measure not from the edge of the magnifying glass, but from the so-called. Rear main plane. But with our accuracy, the difference can be neglected. Moreover, the Lenza Fresnel strictly speaking as many pairs of main planes, how many annular zones :)

So, I measured a rude 140 mm focal length. That is, the increase is really about 2x and brow (at 3, remind, promised). And optical force - about 7d. 7 Diopters is a lot of glasses. Characteristic optical power of glasses for pensioners 2-2.5-3 diopters. Although there is a lot more, of course.

In the shop

This is, of course, the main application. Lens found permanent place In my wallet and use daily. Example - type of cheese in the pyater


The terrible word Himosin on the test turned out to be quite a legitimate component - the rennet enzyme (although it is hardly natural). But the salts of cyanistic acid somehow strained me.
E536 - Ferrotian Kalia
The substance itself - the potassium ferrocyanide is very lowly toxic, but when it interacts with water in the reaction process, poisonous gases are distinguished. But their number, as a rule, does not represent serious health hazards. In the interaction of hexacyanoferrate with some acids, a large amount of strong-toxic gas of cyano hydrogen may be allocated. IN food Industry It is used mainly to prevent competent and track, as an additive to the cooking salt. It is also used in the production of sausages, which always immediately reports white flag on the shell product.

Collect sunlight

For children, such a thing can also be a fun toy, first of all burn something with sun rays. The experiments below put in the village on the subwoofers of the materials, do not shoot a pianist. From the black hose immediately goes smoke and stinks. On a check from the thermal printer, it is harder to focus, but it turns out, the TC when heated it is black. But I could only burn a sheet from the school notebook only with the second attempt and only about noon


In the process it turned out that the lenses had a huge coma. In practice, this means that it is necessary to keep it for burning it is quite precisely perpendicular to the direction in the sun. I did not cause any problems, but my daughter had all the time approximately like that. (Attention on the image on the hose)

Children's poems: Gave me dad lupus

Gave me dad pupa
(I'm terribly lucky!)
I will consider everything
In this thick glass.

Increases Lupa
Everything that only sees eyes
I now found out that in the soup
Mom cooks every time.

Cabbage is a terrible look -
Everything, my appetite disappest ...
And the second I ate immediately,
And now I will not fly.

I caught a cat in the kitchen,
To consider the mustache,
And she immediately - in the window,
Although there is no lupus - dogs!

The sun shines in the window brightly,
I fell a ray into my palm ...
Lupu I brought ... how hot!
I began to consider the beam ...

Point burned palm
I involuntarily cried out ... oh! ..
But I shook a little bit
Hiding a magnifying glass under the ottoy.

To mom not scold
Pope, Lupu and me,
This little rank
I love the green and me.

Oll Lukoeva

Advantages and disadvantages

+ Unexpectedly high-quality picture for this type of lenses. Speaks about high-quality material, the right design calculation and compliance with technology.
+ Lung and compact, fits in the wallet and will be at the right time at hand
+ Can be used for educational purposes and as a toy, to wait for solar light
+ On the long side a small ruler

No cheap option. The lenses of this size is also cheaper
- nedodynted multiplicity - 2 with the stated 3
- The cover does not climb into a plastic card office. And without a cover it is impossible, quickly will be in disrepair.

TOTAL

Lens I liked more than I expected. I will clarify again, then full of offers many times cheaper. I strongly doubt that a similar quality. But for the purposes of studying the composition of false cheese in the store, the Rainbow Divorces at the edges are not deadly. So everyone can choose cheaper or better. With optics constantly such a parsley.

The goods are provided for writing a survey shop. The review is published in accordance with paragraph 18 of the site rules.

I plan to buy +22. Add to favourites I liked the review +61 +96

I promised to start talking about studio devices and start with Fresnel lenses. In a conventional photo studio, you are unlikely to be leased. The first reason is that it is quite expensive, and the second is most of those who come to such studios about the Frennel lens do not know anything.
And the vicious idea is: "If you do not know why you need it - you don't need it," makes her business. Sometimes you just need to try.

left: Fresnel Lens, Right: Normal Lens

So, Fresnel lens performed initially two functions:

1) reduced the weight of the lenses. If the lens do a standard form, then, for example, a lens for a lighthouse can weigh a couple of tons.

2) collected all the light into the beam, keeping the soft borders of the light beam. It was also used on the beacons, as it allowed to shine very brightly.

In the future, both of these properties were successfully used by cinema, including Hollywood. And since Hollywood became famous for all the world with his films, then the light became known as Hollywood.

Illustration of a book "HOLLYWOOD PORTRAITS". Extreme, by the way, useful book. It describes the ideology of working with sources equipped with Fresnel lenses (reference at the end of the article). It is also accepted to call them by sobs, because They give a stain.

Work with light spots is the professional work of the photographer. Spots with gently rustic borders smoothly flow into each other, allowing you to maintain a natural image of a black and white pattern.

here are two stains of light: orange and blue, which gently flow into each other, almost no hacking each other

on the picture: In the background of 11 spots that form the letter P (most likely from Paramount). This is possible only in large film studios.

Devices for permanent light existed since the beginning of the 20th century, and what about flash? After all, permanent light requires long exposure, heats greatly and it is inconvenient to work with it, using colored gels. Power drops.

Outbreaks have no such disadvantages and many serious manufacturers have released their variants of spot devices. For example, my beloved Broncolor. There are already two such devices.

Broncolor Pulsospot 4.

and, the main device with Fresnel lens ...

Broncolor Flooter.

The device of these devices has not changed the whole century and it is quite simple.

Inside the device Broncolor Pulsospot 4. Two lamps: Pulse flash lamp and a halogen pilot light lamp. Over the lamps there is a varying metal reflector, and the lamps themselves are on the rails and can move closer to Fresnel lens or on. Departure deep into the body of the device, we get a spot of smaller diameter and vice versa. It's all. There is nothing more, except for the fan.
The angle of the light cone from 15 to 40 degrees.

fresnel lens

Broncolor Flooter. - This is generally nozzle on the standard light head. Its advantage in the larger Fresnel lens, which allows you to get a larger spot. Also allows you to use lamps HMI (Permanent light, metal halogen lamp).
The angle of the light cone from 15 to 70 degrees.

The price of the first and second instruments is about 5,000 USD (the devices are not working offline, you need to connect to the studio generator).

The light is soft, and very controlled. And the device is compact. Because it is doubly pleasant to work. I did not shoot him models yet, as I received it recently.

It is a pity that I have it for now and it will not be possible to take a picture completely lit by stains of light from such devices, imitating the Hollywood light. But it is possible to make light from sideways main, and to highlight, say, a portrait plate and a soft diffuser, roughly imitating spot.

Here is such a light studio "insight", and shortness, I hope, supplement the article by snapshots of models.

Book Hollywood Portraits. I am very advised to read. There are also lighting schemes. Link to it below.

Snapshots, with the use of lamps with Fresnel lens, kindly provided by Vadim (Blitzphoto)

Female portrait
Scheme: Figures 650 W, Contercourse 650 W, filling 650 W through an umbrella, background 300 W. Sony A7 camera, lenses everywhere different - SMS PENTAX-M 75-150 / 4, SMS PENTAX-M 100 / 2.8, SMS PENTAX-A 135 / 2.8. Sensitivity 1000 units., Exposure changed around 1/160, 5.6.
Retouch - Pontraiture plugin

Male portrait
There were no retouching - so it can be clearly visible as draws a directed spotlight. The camera is again Sony A7, optics everywhere SMS PENTAX-M 75-150 / 4, aperture 5.6, shutter speed 1/125, sensitivity 500 units. The lighting scheme is similar to the previous shooting, for some exceptions - another lamp is introduced in the scene in the scene, 300 W. In the picture 02, it with another same shines on the background, and in the picture 04 highlights hands.

One of the creators of the wave theory of light, the outstanding French physicist Augusten Jean Frenel was born in a small town near Paris in 1788. He was a painful boy. The teachers considered it to be stupid: in the eight of the age I could not read and hardly remember the lesson. However, in high school, Fresnel showed remarkable abilities to mathematics, especially for geometry. Having received engineering education, he from 1809 participated in the design and construction of roads and bridges in different departments of the country. However, his interests and opportunities were much wider than simple engineering activities in provincial wilderness. Frenel wanted to engage in science; It was especially interested in optics, the theoretical foundations of which were just started to develop. He explored the behavior of light rays, passing through narrow holes, enveling thin threads and edges of the plates. Explaining the features of the paintings arising from this, Frenel 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 XIX century, European maritime states decided to improve the lighthouses - the most important navigation devices of that time. In France, a special commission was created for this purpose, and to work in it because of the rich engineering experience and the deep knowledge of optics was invited to Frenelle.

The lighthouse light should be visible away, so the light lamp is raised to a high tower. And in order to assemble his light into the rays, the lantern must be placed in the focus or a concave mirror, or collecting lens, and quite large. The mirror, of course, can be made any size, but it gives only one beam, and the light of the lighthouse should be visible from everywhere. Therefore, on the beacons, sometimes a century and a half dozen mirrors with a separate lantern in the focus of each mirror. There are several lenses around one lantern around a lantern, but to make them necessary - large - size is almost impossible. In the glass, the massive lens will inevitably be inhomogeneity, it will lose the form under the action of its own severity, and due to uneven heating it can burst.
We needed new ideas, and the Commission, inviting Fresnel, did right choice: In 1819, he proposed the design of the composite lens, deprived of all the shortcomings inherent in the usual lenses. Freniel reasoned, probably. The lens can be represented as a set of prisms that refract parallel light rays - deflect them at such angles, which, after the refraction, they converge at the focus point. So, instead of one large lens, it is possible to assemble the design in the form of thin rings from the individual prisms of the triangular cross section.

Fresnel not only calculated the shape of the rings profiles, he also developed the technology and controlled the entire process of their creation, often fulfilling the obligations of a simple worker (subordinates turned out to be extremely inexperienced). His efforts gave a brilliant result. "The brightness of the light, which gives a new device, surprised the sailors," wrote Frenel to friends. And even the British - the long-standing competitors of the French at sea - recognized that the designs of French beacons were the best. Their optical system consisted of eight square lenses of Fresnel with a side of 2.5 m, which had a focal length of 920 mm.

Since then, 190 years has passed, but the designs proposed by Frenels remain unsurpassed technical device, and not only for lighthouses and river buoy. In the form of Fresnel lenses, until recently, they made a glass of various signal lamps, automotive headlights, traffic lights, details of lecture projectors. And quite recently there were magnifiers in the form of lines from transparent plastic with barely notable circular grooves. Each such groove is a miniature ring prism; And together, they form a collecting lens, which can work and like a magnifier, increasing the subject, and as a camera lens, creating an outbound image. Such a lens can collect the light of the sun in a small speck and set fire to the dry board, not to mention the piece of paper (especially black).

Fresnel lens can be not only collecting (positive), but also scattering (negative) - for this you need an annular groove groove on a piece of transparent plastic to make another form. Moreover, the negative Fresnel lens with a very short focal length has a wide field of view, a piece of landscape is placed in a reduced form in a reduced form, two to three times greater than covers the naked eye. Such "minus" lenses plates are used instead of panoramic rear-view mirrors in large cars such as minibuses and universal.

The facets of miniature promenos can be covered with a mirror layer - say, sputtering aluminum. Then Fresnel lens turns into a mirror, convex or concave. Made using nanotechnology, such mirrors are used in telescopes operating in the X-ray range. And settled in flexible plastic mirrors and lenses for visible light are so simple in the manufacture and cheaps that they are literally produced by kilometers in the form of tapes for the design of the showcase or curtains for bathrooms.
There were attempts to use Fresnel lenses when creating flat lenses for cameras. But on the path of the designers, a technical difficulty stood. White light in the prism decomposes into the spectrum; The same happens in the miniature promences of Fresnel lenses. Therefore, it has a significant drawback - the so-called chromatic aberration. Because of it at the edges of the images of items, a rainbow kime appears. In good lens, Kaima eliminate, put additional lenses. It could also be done with the Frenelly lenses, but the flat lens will not succeed then.

Freshelevskaya lens-line focuses the sun's rays is no worse, but even better (because it is more) the usual glass lenses. The sun rays, collected by her, instantly burn a dry pine board.

Augusten Frenel entered the history of science and technology not only and not so much thanks to the invention of his lens. His studies and based on them the theory finally confirmed the wave nature of the light and allowed the most important problem of physics of that time - they found the reason for the straight-line propagation of light. Fresnel works formed the basis of modern optics. Along the way, he predicted and explained several paradoxical optical phenomena, which nevertheless to check and now.

The longtime dispute of researchers about the nature of light is a wave or corpuscular - in general devils were resolved at the end of the XVII century, when Christians Guigens issued his "light treatise" (1690). Guygens believed that each point of space (in its description - ether) through which the light wave passes, becomes the source of secondary waves. The surface, the envelope, is a propagating wave front. The Guigens principle solved the tasks of reflection and refraction of light, but could not explain the well-known phenomenon - its rectilinear distribution. A paradoxically, the reason for this was that Guygens did not consider the retreat from straightness - the diffraction of light (overtakening of obstacles) and its interference (addition of waves).

This disadvantage replenished in 1818-1819 by Augusten Frennel, education engineer and interest physicist. He completed the Guigens principle of the interference of secondary waves (introduced by Guigens purely formally, that is, for the convenience of calculations, without physical content). Due to their addition and the front arises the resulting wave, 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, coherent. Fresnel proposed to mentally split the surface of a spherical wave coming from one point O, the zones of this size so that the difference of distances from the edges of the adjacent zones to a certain selected point F was equal to λ / 2. Rays emanating from adjacent zones, to the point f come in antiphase and, when adding, weaken each other until a complete disappearance.

Designating the amplitude of the oscillations of the light wave, which came from the M zone as SM, the total value of the amplitude of the oscillations at the 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 ... expressions in brackets are positive and s less than S0. But how less? Calculations of the amount of the alternate series, which conducted 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 light of the distant zones, entering the antiphase, reduces the action of the central zone twice.
Therefore, if the central zone is closed with a small disk, the illumination in the center of the shade will not change: there is a light from the following zones at the expense of the diffraction. By increasing the size of the disk and consistently closing the following zones, you can make sure that the shadow will remain a bright stain. This theoretically proved in 1818 Simeon Denis Poisson and considered evidence of the fallacy of Fresnel theory. However, the experiments who were trained by Domenic Arago and Frenel, discovered. Since then, it is called Poisson's stain.

For the success of experience, it is necessary that the edges of the disk exactly coincide with the boundaries of the zones. Therefore, in practice, a miniature ball from the bearing pastened to the glass is used.

Another paradox of the wave properties of light. We put the screen with a small hole on the side of the beam. If its size is equal to the diameter of the center of Fresnel, the illumination behind the screen will be greater than without it. But if the size of the opening is covered and the second zone, the light from it will come in antiphase, and when adding with light from the central wave zone, the waves are mutually destroyed. 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 light stream goes in the form of a very narrow beam, that is, straightly. So the theory of Fresnel with a wave point of view explained the law of rectilinear light propagation.

A good example illustrating the Fresnel method is experience with its zone plate, which works as a collecting lens.

On a large sheet of paper, we draw a number of concentric circles with radii, proportional to roots square from the numbers of natural rows (1, 2, 3, 4 ...). At the same time, the area of \u200b\u200ball the resulting rings will be equal to the area of \u200b\u200bthe central circle. The ring of the rings through one thing, and it does not matter whether to leave the central zone with light or make it black. The resulting black and white ring structure is photographing with a large decrease. The negative will be the zone plate of Fresnel. The diameter of its central zone determines the formula d \u003d 0.95 √λf, where λ is the wavelength of the 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 visited on a bright light, then it will start glowing like a collecting lens. If it is combined with an eyepiece from a weak lens, a pickle pipe will be able to give a sharp image of the filament of the incandescent bulb. And from two zone plates, you can build a telescope according to the Galilee scheme (lens - plate with a large focal length, eyepiece - small). It gives a direct image like theatrical binoculars.

It becomes clear from all the outlined, as a small hole can play the role of the lenses called by wallpaper or pinhole. It corresponds to the central zone of Fresnel phase plate. That is why the wallop does not have any aberrations, except chromatic, because through her rays pass without distortion.

The light wave passing through the zone plate gives the resulting amplitude S \u003d S0 + S2 + S4 + ... - twice as large than a free wave: the zone plate works as a collecting lens. An even greater effect will turn out if you do not delay the light zones, but to change its phase to the opposite. The intensity of light at the same time increases four times.

Such a record in 1898 made Robert Wood covering the glass layer of varnish and removing it from odd zones, so the difference between the rays in them was λ / 2. Glass plate, covered with varnish, he placed on a rotating table. Cutter - they served a gramophone needle - cut off layers of varnish, for the external zones there were enough needle passage, and on the inner needle moved along a narrow spiral, consistently removing several merging grooves. The diameter of the zones and their width were controlled in the microscope.

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

Finally, another paradox of wave optics. As already mentioned, it is completely unimportant, the central zone is transparent or not. This means that the role of the wall-wall (or pinhole) can play not only a small hole, but also a tiny ball, the diameter of which is equal to the size of the center zone of Fresnel.

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

Despite the variety of infrared motion sensors, almost all of them are equally equal in their structure. The main element in them is a pyrribronyon, or a porgettor, which includes two sensitive elements.

The detection zone of the pyrribronyon is two narrow rectangles. To increase the detection zone from one ray of rectangular shape to the maximum possible value
and increase its sensitivity, collecting lenses are used.

The collecting lens in the form is convex, it directs the optical rays falling on it at one point F is the main focus of the lenses. If you use several such lenses, the detection zone will increase.

The use of spherical convex lenses weights and increases the design of the device. Therefore, in infrared motion sensors and presence uses Fresnel lens.

Fresnel lens. History of creation

French physicist Auguste Frenel in 1819 offered his lenses design for the lighthouse.

Fresnel lens is formed from spherical lenses. The latter was divided into a variety of rings, reduced in thickness. So it turned out a flat lens.

Thanks to this form, the lenses began to produce from a thin plastic plate, which made it possible to apply them in lighting devices and motion sensors and presence.

The lenses of the sensor consist of a variety of segments that are Fresnel lenses. Each segment scans a certain area of \u200b\u200bthe sensor coverage area. Forms of lenses of motion sensors determine the form of detection zone.

For example, the ceiling devices are a form of lenses - hemisphere, respectively 360 degrees. In devices with a cylindrical form of lenses, it is usually 110-140 degrees. There is I. square forms Detection zones.

The line of infrared motion sensors and the presence of B.E.G has high-quality Fresnel lenses that provide excellent detection parameters.

FRESNEL LENS

In the previous section, we decided that for the lighting of our LCD panel, Fresnel lens, or "Fresnel" needed. The lens is named by her inventor, French physics Ogusten Jean Fresnel. Originally used in lighthouses. The main property of Freshers is that it is light, flat and thin, but at the same time has all the properties of the usual lens. Fresnel consists of the concentric grooves of the triangular profile. Step grooves are comparable to their profile height. Thus, it turns out that each groove is like a part of the usual lens.

It should be noted that in the projector instead of one fries used steam. If Frenel is coming from the Overhead projector, pay attention that it is smooth on both sides, i.e. In fact, it consists of two fries facing ribbed surfaces to each other and glued around the perimeter.

Why use two fries and is it possible to do one?

Look at the scheme and everything will become clear.

If you use only one Fresnel, it is necessary that the lamp is approximately in a double focus. Rays from the lamp will also converge in a double focus. The minimum focal length of the available frames is 220 mm. This means that the design will have to extend much. But most importantly - with this distance from the lamp to the Fresnel, the effective body angle of the lamp turns out to be very small.

When using 2 freshers from both drawbacks, it is possible to get rid of. The light source is slightly closer to the focal length from the left Fresnel, and it forms a "imaginary" source outside the double focal length of the right Fresnel. After passing the right Freshelie, the rays will be converged between the focus and double focus.

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

Do you remember, I said that this scheme is simplified? If everything was as painted, we would not need a lens. Each beam from the light source passed through the only Prentel point, then through a single point on the matrix and flew further until it hubs the screen and does not form a point of the right color on it. For a point source and an ideal matrix it would be true. Now add realism - consumer source.

In view of the fact that we use a lamp as a light source, i.e. The luminous body of well-defined, final sizes, the real waume passing scheme will look like this:

The 1st stage of construction - Left Fresnel forms an "imaginary image" of the electric arc of the lamp. It needs us to properly build the course of the rays through the right Frennel.

The 2nd stage of construction - forget about the presence of the left lenses and build the course of the rays for the right lens, as if the "imaginary" image was real.

The 3rd stage - we discard everything too much and combine two schemes.

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

What kind of focal length should be the freshers?

Fresnel facing the lamp is taken as short as possible for a larger coverage angle. The focal length of the second Freshelie should be 10-50% more than the focal length of the lens (1-2 cm. Distance from 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, fresnels with 2 values \u200b\u200bof focal distances are most common on the market: 220 mm and 330 mm.

When choosing a focal length of the Freshers, you need to pay attention to the fact that, unlike conventional lenses, Freshers capricious to the angle of falling light. I will explain with two schemes:

Caprice is that the rays falling on the corrugated surface of Fresnels should be parallel to the optical axis (or have a minimal deviation from it). Otherwise, these rays "fly away the ENIOD". On the left scheme, the light source is approximately in the focus of the left lens, so the rays between the lenses go almost parallel to the optical axis and eventually converge in approximately the focus of the second lens. On the right scheme, the light source is located much closer to the focal length, so part of the rays falls on a non-working surface of the right lens. This effect is the greater, the greater the distance from the focus to the source and the larger the diameter of the lens.

1. Lenses should be placed by corrugated sides to each other, and not vice versa.

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

3. Opportunities for moving the source of light to adjust the point of convergence of a beam into the lens are limited to just a few centimeters, otherwise - the brightness of the brightness of the picture along the edges and the appearance of Moire.

What size should Frenelle be?

What material should Fresheli be?

The most available at the moment of Freshers from the optical acrylic (plexiglas, in other words). They have excellent transparency and a little elastic. For our purpose, this is enough, given that the quality of the freshers absolutely does not affect the sharpness and geometry of the picture (only on brightness).

How to handle Fresnels?

1. Do not leave fingerprints on the corrugated side of Fresnels. Carefully my hands with soap in front of any operations over Fresnels. It is best from the moment of purchase and before the end of the experiments wrapped the fries with a polyethylene film for packaging products.

2. If the prints on the corrugated side still appeared, do not try to erase them. No detergents (incl. Means for washing windows based on the ammonia) do not help, because Do not penetrate enough deeply. The outer ribs of the grooves at the same time are slightly curled, and the particles from the napkin / wool used for wipes are clogged between the grooves. As a result, Frenel begins to disperse rays. It is better to leave with prints. You can wipe the smooth side, but only being confident that the detergent will not fall on the corrugated side.

3. Stone for temperature regime. Do not allow the heating of the fares above 70 degrees. At 90 degrees, the lenses begin to swim, and the light beam loses the shape. Personally, I stop one set of lenses because of this. To control the temperature, use a tester with a thermocouple. Sold in any radio car.

LENS

What is a lens and why he need, I think you understand. The most important thing is to choose it correctly, but by choosing, finding where to buy :) For selection, we need to know 4 main characteristics:

Number of lenses

In principle, a lens can also serve one lens, such as a magnifying glass. However, the farther from the center of the picture, the worse there will be its quality. Spherical distortions (abberations) appear, chromatic abberats (due to different angles of refraction of rays of various wavelengths white point, for example, turns into a slice of rainbow), loss of sharpness. Therefore, for achieving the maximum quality of the picture, achromatic lenses of 3 or more lenses are used. Such were used in epidias, old cameras, aerial photography devices, etc. In Overhead projectors, three-lift lenses are also used, but such projector models are more expensive than models with single-zone lenses.

Focal length

From the focal length of the lens depends on what distance from the source object (matrix) it must be positioned and what size image on the screen you will receive. The greater the focal length, the smaller the screen size, the farthest from the screen you can place the projector, the longer the projector case. And vice versa.

Vision angle

Shows what size the original image can cover the lens, while maintaining an acceptable brightness, sharpness (resolving ability), etc. "Acceptable" - the concept of tensile. If an angle of view is specified for an aerial view in the passport, for example, 30 degrees, it may mean that it is actually covered by 50 degrees, but the sharpness on the edges for aerial photography is no longer suitable, but for our projector, where it does not need a large allowing ability, it is quite suitable .

Light and relative hole

The relative hole, if it is simplified - the ratio of the diameter of the lens to its focal length. It is indicated in the form of a fraction, for example 1: 5.6, where 5.6 is a "diaphragm number". If we have a lens with an internal lens diameter of 60 mm and a focal length of 320 mm, its relative hole will be 1: 5.3. The greater the relative hole (less a diaphragm number), the greater the lens torque - the ability to transmit the brightness of the object - and the ultimately worse sharpness / resolution.

What should be the relative hole?

The relative hole can be found, knowing the diameter of the lenses and the focal length. With regard to our optical scheme, it can be said that the diameter of the lens lens should be at least the size of the image of the arc lamp formed by Fresnels. Otherwise, part of the light lamp will be lost.

There is time to make another refinement to our optical scheme.

Obviously, the matrix dispels the rays passing through it. Those. Each beam falling on the matrix leaves it already in the form of a beam of rays with different angular deviation. As a result, the image of the lens arc in the lens plane turns out to be "blurry", increases in size, but continues to carry information about the colors of the matrix pixels.

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

Hence the conclusion: the relative hole of the lens should be so to collect the image of the lamp, but not more.

What should be the focal length and angle view?

These parameters are determined by the size of the source 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 the screen

d-diagonal matrix

D-diagonal screen

Here is a calculator for calculations (rustled with www.opsci.com, slightly adapted and translated into clear language)