What can be done with fresnel lenses. Optics

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

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

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

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

Fresnel lens. History of creation

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

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

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

The sensor lenses are made up of many segments, which are Fresnel lenses. Each segment scans a specific area of ​​the sensor coverage area. The lens shapes of the motion sensors determine the shape of the detection area.

For example, in ceiling devices, the shape of the lenses is a hemisphere, respectively 360 degrees. For devices with cylindrical lenses, it is usually 110-140 degrees. There are also square shapes of detection zones.

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

Unlike prismatic and other diffusers, lenses in lighting fixtures are almost always used for spot lighting. As a rule, optical systems using lenses consist of a reflector (reflector) and one or more lenses.

Converging lenses direct light from a source located at the focal point into a parallel beam of light. As a rule, they are used in lighting structures together with a reflector. The reflector directs the light flux in the form of a beam in the right direction, and the lens concentrates (collects) the light. The distance between the converging lens and the light source is usually variable, allowing the angle to be obtained to be adjusted.

A system of both a light source and a converging lens (left) and a similar system of a source and a Fresnel lens (right). The angle of the light flux can be changed by changing the distance between the lens and the light source.

Fresnel lenses consist of separate concentric ring-shaped segments adjacent to each other. They got their name in honor of the French physicist Augustin Fresnel, who first proposed and put into practice such a design in lighthouse lighting fixtures. The optical effect of such lenses is comparable to that of traditional lenses of similar shape or curvature.

However, Fresnel lenses have a number of advantages due to which they are widely used in lighting designs. In particular, they are much thinner and cheaper to manufacture than converging lenses. Designers Francisco Gomez Paz and Paolo Rizzatto did not fail to take advantage of these features in their work on a bright and magical model range.

Made from lightweight and thin polycarbonate, the "sheets" of Hope, as Gomez Paz calls them, are nothing more than thin and large diffusing Fresnel lenses that create a magical, sparkling and voluminous glow by coating with a polycarbonate film textured with microprisms.

Paolo Rizzatto described the project as follows:
“Why have crystal chandeliers lost their relevance? Because they are too expensive, very difficult to handle and manufacture. We have decomposed the idea itself into components and modernized each of them.”

Here is what a colleague had to say about it:
“A few years ago, the marvelous possibilities of Fresnel lenses caught our attention. Their geometric features make it possible to obtain the same optical properties as conventional lenses, but on a completely flat surface of the petals.

However, the use of Fresnel lenses to create such unique products, combining a great design project with modern technological solutions, is still rare.

Such lenses are widely used in stage lighting with spotlights, where they allow you to create an uneven light spot with soft edges, perfectly blending with the overall light composition. Nowadays, they have also become widespread in architectural lighting schemes, in cases where individual adjustment of the angle of light is required, when the distance between the illuminated object and the lamp can change.

The optical performance of a Fresnel lens is limited by the so-called chromatic aberration that forms at the junctions of its segments. Because of it, a rainbow border appears on the edges of the images of objects. The fact that a seemingly flawed feature of the lens was turned into a virtue once again underlines the power of the authors' innovative thought and their attention to detail.

Lighting design of a lighthouse using Fresnel lenses. The ring structure of the lens is clearly visible in the picture.

Projection systems consist of either an elliptical reflector or a combination of a parabolic reflector and a condenser directing light onto a collimator, which can also be supplemented with optical accessories. After that, the light is projected onto a plane.

Spotlight systems: A uniformly illuminated collimator (1) directs the light through a lens system (2). On the left is a parabolic reflector with a high light output, on the right is a condenser that allows for high resolution.

The size of the image and the angle of light is determined by the features of the collimator. Simple curtains or iris diaphragms form light beams of different sizes. Contour masks can be used to create different contours of the light beam. You can project logos or images using a gobo lens with drawings printed on them.

Different angles of light or image size can be selected depending on the focal length of the lenses. Unlike lighting fixtures using Fresnel lenses, here it is possible to create light beams with clear contours. Soft contours can be achieved by shifting the focus.

Examples of optional accessories (from left to right): a lens to create a wide beam of light, a sculpted lens to give the beam an oval shape, a grooved deflector, and a “honeycomb lens” to reduce glare.

Stepped lenses convert light rays in such a way that they are somewhere between the "flat" light of a Fresnel lens and the "hard" light of a plano-convex lens. The convex surface is preserved in stepped lenses, however, stepped recesses are made on the side of the flat surface, forming concentric circles.

The front parts of the steps (risers) of concentric circles are often opaque (either painted over or have a chipped matte surface), which makes it possible to cut off the scattered radiation of the lamp and form a beam of parallel rays.

Fresnel spotlights form an uneven light spot with soft edges and a slight halo around the spot, making it easy to blend with other light sources to create a natural light pattern. That is why Fresnel spotlights are used in cinema.

Projectors with a plano-convex lens, compared to projectors with a Fresnel lens, form a more uniform spot with a less pronounced transition at the edges of the light spot.

Visit our blog to learn new things about luminaires and lighting design.

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 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 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.

This article will talk about fresnel lens and how to use it to make fire.

Getting fire from the sun with a magnifying glass is a very laborious process, but fascinating. However, you always want something more. For example, in order for the fire to flare up immediately when the beam is focused on an object, without holding shamanic 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's the whole snag: As for the usual glass lens.

1. A large diameter lens is difficult to obtain (buy). (Usually the largest lenses are about 100-120mm in diameter)
2. Such a lens will cost a lot.
3. It will be inconvenient to carry it with you, since the large lens weighs a lot + it is glass and can break.

Fresnel lens.

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 light in weight.

most large lens which I managed to order in local online stores is a lens approximately the size of an A4 sheet. The price is low compared to glass magnifiers.

The magnifying power of this lens was of little interest to me. Let me just say that its multiplicity is 3x.

Fresnel lens. Getting fire from the sun.

Finally getting out into nature, I tested the fresnel lens in action. So, the month of September, the temperature is just below 20 degrees Celsius, the weather is sunny, the time is just over 14 hours.

Let's finally try to set something on fire with the help of a lens.
Without hesitation, I find a rotten stick. I concentrate on it a beam of sunlight. Next, I burn a little in one place.

And the fresnel lens exceeded all my expectations. The stick begins to char, and then a flame erupts in place of the sun's rays!

Let's try to set fire to something else, for example piece of birch bark.
I direct a beam of light onto a birch bark, concentrating all the rays in one place with a lens. I note that the lens is quite large, so catching a sunbeam is a little harder, it is necessary to maintain a perpendicular towards the sun. Thus, the maximum amount of sunlight passes through the lens and then is focused at one point.

We burn out for a very short time and the birch bark also flares up from the sun's rays. The temperature is sufficient for ignition.

Setting fire to the lens is a pleasure. For example easy to set fire to dry foliage, which in the fall, well, a lot. Here, 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 in one place.

The leaves light up, despite the fact that the sun was slightly behind the trees, there was no need to blow!

An even better tinder is dry grass. We collect the dried tops of plants.

It turns out here is such a beam the size of a fist.

Flashes almost instantly! The perfect tinder in this situation. Carefully, don't start a fire!

With the help of a fresnel lens, I managed to make fire even at sunset, when the sun was already hiding behind the trees and it was getting cold, although here it was necessary to inflate the dried grass and rot from the trees.

Fresnel lens as an item in a 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 considered. Since lenses of other sizes have completely different characteristics. A smaller lens is not able to produce fire so effectively, you will have to bother with tinder, 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 purchase it.

So the pros:

Now the cons:

1. Sun, sun. How few sunny days there are in a year. Dependence on the sun is the main and fat minus when making fire from a magnifying glass.
2. The lens is made of plastic, so it can break if you push harder. It is also easy to scratch concentric notches. Therefore, it is better to adapt some kind of cover for the lens, for example, a paper folder, or a plastic bag or file.
3. The lens is still large, matches or a lighter are much smaller.
4. During burning, too bright light blinds the eyes, but not critical. You can wear sunglasses, but I personally don't use them.

I will conclude that the use of a fresnel lens of this size is advisable in autonomous trips when the supply of gas or matches may run out. The longer the autonomous trip, the more practical the use of the lens will be. In places where the sun often shines, a fresnel 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!

A lens made up of concentric rings of small thickness adjacent to each other

Animation

Description

The Fresnel lens is one of the first (if not the first historically) devices based on the diffraction of light. Despite its antiquity, it has not lost its practical significance to this day. The skeletal diagram of the physical idea on which its operation is based is shown in fig. one.

Scheme for constructing Fresnel zones for an infinitely distant observation point (plane wave)

Rice. one

A rigorous consideration of this principle of action requires a rather cumbersome and not quite “transparent” mathematical apparatus for a qualitative understanding. Therefore, in the present short description we will confine ourselves to a qualitative presentation, based on simple geometric “pictures” - which nevertheless makes it easy to understand the basic physical principles of the product. For the same readers who require a more fundamental consideration, we advise you to refer to the cited literature.

Let a point source of optical radiation of wavelength l be located at point O. Naturally, like any point source, it emits a spherical wave, the wave front of which is shown in the figure as a circle. Let's set ourselves a noble goal to somehow "remake" this wave into a flat one, propagating along the dotted axis. Several wavefronts of this “projected” wave, separated by l/2, are shown in Figure 1.

To begin with, we note the following. We want to “construct” a plane wave from an existing spherical wave in free space. Therefore, in accordance with the Huygens-Fresnel principle, only electromagnetic oscillations in the existing one can serve as the “sources” of our projected wave. We are not satisfied with the spatial distribution of the phase of these oscillations, that is, the wave front (spherical) of the original wave. Let's try to fix it.

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

Equivalent phase distribution of secondary radiators in space

Rice. 2

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

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

The first method (amplitude Fresnel lens). And let's just geometrically close these harmful odd zones with opaque rings. This is how it is done in large-sized focusing systems of sea lighthouses. Of course, this will not achieve ideal beam collimation. We see that the remaining, green, part of the secondary emitters, firstly, is not completely flat, and secondly, it is discontinuous (with zero dips in the place of the former odd Fresnel zones). Therefore, the strictly collimated part of the radiation (and its amplitude is nothing more than the zero two-dimensional Fourier component of the spatial distribution of the phase of green emitters along a plane wavefront with zero offset, see Fig. 2) will be accompanied by wide-angle noise (all other Fourier components except for the zero ). Therefore, the Fresnel lens is almost impossible to use for imaging - only for the collimation of radiation. However, the collimated part of the beam will nevertheless be much more powerful than in the absence of the Fresnel lens, since we have at least got rid of the negative contribution to the zero Fourier component from the odd Fresnel zones.

The second method (phase Fresnel lens). Let's now make the rings covering the odd Fresnel zones transparent, with a thickness corresponding to the additional phase shift l /2 . In this case, the wave front of the “red” secondary emitters will shift and become “green”, see fig. 3.

Wave front of secondary emitters behind a phase Fresnel lens

Rice. 3

In other words, we managed to make the initially harmful contribution to the zero Fourier component from the odd Fresnel zones into a useful one by changing its sign due to the half-wave phase shift. This approach is used in smaller Fresnel lenses, in particular in illumination collimation lenses used in standard lecture "transparency" projectors on a screen.

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

Thus, Fresnel lenses make it possible to cope with the collimation of beams with a large transverse aperture, while at the same time being flat parts of low weight and relatively low manufacturing complexity. An equivalent lighthouse glass lens weighs half a ton and costs slightly less than an astronomical telescope lens. The point here is that at such scales of the product, the main difficulty is no longer in the processing of the lens surface, but in obtaining a sufficiently optically homogeneous initial glass casting. Therefore, Fresnel lenses are one of the few examples scientific development, which found an immediate and wide practical use(this is at the beginning of the nineteenth century, then!), And “not withdrawn from service” for 2 centuries now.

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

Constructing an Image of a Point Source with a Fresnel Lens

Rice. four

So, in order for the Fresnel lens to continue to be a Fresnel lens when the source is shifted from position O to position A, it is necessary that the boundaries of the Fresnel zones on it remain the same. And these boundaries are the distances from the axis at which the wave fronts of the incident and “projected” waves intersect. The initially incident one had a front with a radius of curvature F , while the “projected” one was flat (red in Fig. 4). At a distance h from the axis, these fronts intersect, setting the boundary of one of the Fresnel zones, MN=n l /2, n is the number of the zone starting at this distance from the axis.

When the source moved to point A, the radius of the incident wavefront increased and became R 1 (blue in the figure). So, we need to invent a new wavefront surface, such that it intersects with the blue one at the same distance h from the axis, giving the same MN on the axis itself. We suspect that such a surface of the projected wave front can be a sphere with radius R 2 ( green color on the image). Let's prove it.

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

(1)

Here we have neglected the small square of the wavelength compared to the square of the focus, an approximation that is completely analogous to the parabolic approximation in deriving the usual formula thin lens. On the other hand, we want to find a new boundary of the nth Fresnel zone as a result of the intersection of the blue and green wavefronts, let's call it h 1 . Based on the fact that we require the same length of the segment MN :

(2)

Finally, requiring h=h 1 , we get:

This equation is the same as the usual thin lens formula. Moreover, it does not contain the number n of the considered boundary of the Fresnel zones, and therefore it is valid for all Fresnel zones. Thus, we see that the Fresnel lens can not only collimate beams, but also build images. True, it must be borne in mind that the lens is still stepped, and not continuous. Therefore, the image quality will be noticeably degraded by the admixture of the higher Fourier components of the wavefront discussed at the beginning of this section. That is, the Fresnel lens can be used to focus radiation to a given point, but not for precision imaging in microscopic and telescopic devices.

One last note. All of the above referred to monochromatic radiation. However, it can be shown that by careful choice of the diameters of the rings discussed, a reasonable quality of focus can be achieved for natural light as well. The corresponding mathematics is quite complicated, so let's focus on the last verbal statement.

Timing

Initiation time (log to -15 to -13);

Lifetime (log tc 15 to 15);

Degradation time (log td -15 to -13);

Optimal development time (log tk from -1 to -1).

Diagram:

Technical realizations of the effect

Technical implementation of effects

The technical implementation of the effect is quite simple. A spherical wave from a point source (simply a divergent beam of a helium-neon laser after focusing with a lens with a focal length of 3 cm, a point source is a focal beam waist) falls normally on a glass screen, removed at a distance of about 1-2 meters. The circles of the boundaries of the Fresnel zones are marked on the screen (the inner one has a diameter of about 3 mm), and the odd zones are painted over with black ink. In this case, the transmitted beam is collimated into an approximately parallel one.

Applying an effect

Fresnel lenses, both phase and amplitude, are widely used in technology for collimating large aperture light beams, for which the use of conventional spherical lenses and mirrors is difficult. Examples have been discussed above in the content section.

Literature

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

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

3. Physics. Big Encyclopedic Dictionary.- M.: Big Russian Encyclopedia, 1999.- P.90, 460.

Keywords

• interference
• diffraction
• fresnel zone
• Huygens-Fresnel principle
• focal length
• collimation
• image
• wavelength

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