Gabor hologram registration scheme

In this position (position 1 in Fig. 1.1), the main rays of the object and reference beams propagate in the same direction. The holograms obtained in this way are called axial holograms or Gabor holograms. When recording them, the difference in the path of the object and reference waves within the surface of the plate is minimal compared to all other possible positions, which makes it possible to use it to form a holographic field as radiation sources with a low degree of coherence. The relatively large distance between adjacent maximum surfaces reduces the requirements for the resolution of the recording medium.

Rice. 1.3

A schematic diagram of recording Gabor holograms is shown in Fig. 1.3.1. Here S is a source of coherent radiation, T is a transparency with an image of an object, H is a hologram. In accordance with the above diagram, the total complex amplitude U of light incident on a photosensitive medium in the hologram recording plane can be represented as the sum of the complex amplitude of the background or reference wave that was not diffracted on the structure of the object R and the complex amplitude of the wave that was diffracted on the object - O

U = R + O, (1.3.2)

Hence, the radiation intensity I in the hologram recording plane can be described as follows:

When linearly processing the hologram and restoring it with a reference wave with a complex amplitude R, the field amplitude in the hologram plane, directly behind it - A, can be described up to a proportionality coefficient as follows:

If the amplitude of the reference wave is the same over the entire plane of the hologram, then the first term on the right side of expression (1.3.4.) describes a wave front, the complex amplitude of which is proportional to the amplitude of the original wave U in expression (1.3.2).

Optical scheme for recording Leith-Upatnieks holograms

Interference is observed when two waves are added, when, provided they are coherent, i.e. a constant phase difference between these waves, a characteristic spatial distribution of light intensity arises - an interference pattern. The photographic detector plate records this in the form of alternating light and dark stripes, or an interferogram.

To determine residual stresses, conventional interferometry was also used, but this work could only be carried out in a well-equipped laboratory: special preparation of the surface of the object under study was required, giving it the correct shape, special lighting and equipment.

When the laser was created, i.e. a radiation source with high spatial and temporal coherence, optical holography began to develop - a method of recording and reconstructing light waves scattered by an object and carrying information about its shape (i.e., a three-dimensional image of the object). Some interferometry techniques have become greatly simplified, since the problems of lighting and surface preparation have been eliminated.

The basic optical circuit for recording a hologram according to Leith-Upatnieks is shown in Fig. 1.3.2. The laser beam (1) is expanded by a lens (2) and divided into two parts by a translucent mirror (3). One part - this is the reference beam (RL) - passes through the mirror and immediately falls on the photographic detector plate (5). The second part, reflected from the mirror, illuminates the object (4) and, diffusely scattered by it, passes through the lens (6) and also falls on the detector. This is the object beam (SL).

Rice. 1.4 - Schematic diagram of recording a Leith-Upatnieks hologram: 1 - laser, 2 - lens, 3 - translucent mirror, 4 - object, 5 - photographic plate detector, 6 - lens in magnifying mode, OL - reference beam, PL - object beam

Note that the presence of a lens (6) is not essential for recording holograms, but is necessary for measuring residual stresses. The lens is located at the focal distance from the object and therefore works in magnifier mode: not the entire image of the object is recorded on the photographic plate, but a small part of it, but enlarged by 2-5 times - the surface area with the hole. This helps to consider fairly densely located (especially at the edge of the hole) interferogram stripes.

In this recording scheme, the laser beam is divided by a special device, a divider (in the simplest case, any piece of glass can act as a divider) into two. After this, the rays are expanded using lenses and directed using mirrors to the object and recording medium (for example, a photographic plate). Both waves (object and reference) fall on the plate from one side. With this recording scheme, a transmission hologram is formed, which requires a light source with the same wavelength at which the recording was made, ideally a laser, to be restored.

Holograms obtained on recording media that are relatively thick, in comparison with the period of the maximum intensity of the holographic field, represent a volumetric diffraction grating consisting of a sequence of partially reflecting surfaces.

Such a lattice is known to be selective, i.e. depending on the angle of incidence and wavelength of the reconstruction wave, a response described by Bragg's law. Holograms with such properties are called volumetric or Bragg holograms. If the recording medium, which is thick compared to the period of the maxima of the holographic field, is set to position 3, then the reference and object spherical waves fall on it from different sides. In this case, the distance between the surfaces of the holographic field intensity maxima is approximately half the wavelength of the recording radiation, and these surfaces are close to planes parallel to the surface of the recording medium.

Rice. 1.5

This hologram registration scheme was proposed by Yu.N. Denisyuk and bears his name.

When registering a hologram in such a scheme, a large number of partially reflecting radiation surfaces, called strata, are formed in the volume of the recording medium, acting like a reflective interference filter. Even for recording medium thicknesses of 10 - 12 microns, the number of these strata can be more than 50. The large number of partially reflective surfaces contained in the hologram determines their high spectral selectivity, which makes it possible to restore the image recorded on them in white light. Such holograms are called Yu.N. holograms. Denisyuk or reflective volumetric holograms. It should be noted that Lippmann’s photograph, known from a physics course, is, in essence, a special case of Denisyuk’s hologram.

Holography with an inclined reference beam with a diffuse and non-diffuse object beam.

Obtaining a hologram using a reference wave incident on the plane of the recording medium at an angle different from the angle of incidence of the object wave. Spatial-frequency analysis of this method is based on the concept of a carrier, or reference, wave, the spatial frequency of which is modulated by information about the object. Thus, the expression “carrier frequency hologram” is equivalent to the expression “off-axis hologram”. When using the carrier frequency method, there is no need to obtain a reference wave due to light passing through the object. As a result, when using off-axis holograms, in contrast to Gabor holograms, there is no need to be limited to transparency with large transparent areas. In Fig. 1.3.4. A simple method of dividing the wavefront is shown, which makes it possible to illuminate a transparent transparency with a coherent plane wave and obtain an oblique plane wave from the same source. You can take a halftone transparency as an object. Let O(x, y) be the complex amplitude of the object wave in the hologram plane, R = r exp(2рiоrx) = r exp(ikx sinи) be the complex amplitude of the plane reference wave. From a comparison of these expressions, which states that the phase of the wave is inversely proportional to the optical path traveled, we obtain an expression for the spatial frequency of the reference wave, presented in Fig. 1.3.4.

Rice. 1.6

Spatial frequency of the reference wave shown in Fig. 1.3.4. The spatial frequency of the reference wave corresponds to the wave vector of the reference wave directed downward from the z axis, where u is the angle formed by it in the xz plane with the z axis.

The method of illuminating a partially transparent transparency with a plane wave, which we considered earlier, has a number of disadvantages, including:

* the difficulty of observing the reconstructed virtual image, which consists in the need to scan the entire plane of the hologram with the observer’s pupil;

* strong unevenness of the intensity of the object wave in the hologram registration plane, making it difficult to select the intensity of the reference wave.

These disadvantages can be eliminated by using diffuse illumination of the holographic transparency. To do this, a diffuse screen, such as frosted glass, is usually placed between the laser source and the transparency. Since the diffuse screen scatters light over a wide solid angle, the observer no longer needs to scan the entire surface of the hologram with his pupil in order to see the entire image of the transparency. Although the phase of light scattered by a diffuse screen and transmitted through an object is a rapidly changing spatial function of coordinates in the hologram plane, light in this plane can retain coherent properties. This happens if:

* the initial wave illuminating the diffuse screen is spatially coherent over the entire area of ​​the screen;

* the maximum light path length from the source to the hologram through the diffuse screen differs from the reference beam path length by no more than the coherence length;

* the screen remains motionless.

A hologram obtained under diffuse illumination has a number of remarkable properties. The fact is that a diffuse screen has a wider range of spatial frequencies than a holographic transparency; it scatters light over a wide solid angle so that each point of the hologram aperture receives light from all points of the transparency. As a result, at the reconstruction stage, the entire virtual image of the object can be observed through any part of the hologram. When the viewing direction is shifted, the image is visible from the other side. If we have a hologram of a two-dimensional transparency and want to observe its image, we will be able to restore it entirely, even if the hologram was broken or damaged, so that only a small area was preserved. Of course, the resolution in the image is worse, the smaller the area of ​​the remaining part of the hologram. Note that diffuse illumination of an object, in addition to the advantages listed above, also has a number of significant disadvantages. Among them is the grainy, speckle structure of images reconstructed using such holograms. Thanks to it, the reconstructed images consist of individual light spots separated by absolutely dark spaces. The size of the spots is at the limit of the resolution of the hologram, and their contrast (visibility) - V, defined as the ratio of the difference between the maximum and minimum intensities of image elements to their sum, is equal to 1.

The reason for the appearance of speckles lies in the impossibility of recording the entire field scattered by the diffuser. The loss and non-registration of part of the object’s field on the hologram leads to a redistribution of the intensity of the reconstructed image, which has the appearance of a spotty structure. The presence of speckles limits the practical use of holograms with diffuse illumination of an object. For example, in photolithography, speckles are unacceptable because they lead to rupture of the imaged structures. To this day, no radical method of combating speckle has been invented. The only thing that is proposed to be done in this direction is to use the accumulation method, i.e. a method of sequential registration of multiple implementations of the same reconstructed image, characterized by different speckle patterns. This method is practically implemented by installing a rotating diffuser in the restoring beam of rays. The presence of a rotating diffuser makes it possible to average over time different realizations of speckle patterns and reduce them to noise that is constant along the image plane. At the same time, the scatterer causes a change in the structure of the reconstruction beam and, thereby, leads to a decrease in the resolution in the reconstructed image. We will talk about this in more detail later.

Materials for recording holograms

Currently, most volumetric holograms are recorded using photopolymers. Of these, photopolymers from Du Pont are the most widespread and famous. They are produced on an industrial scale and are widely used for the production of security holographic tags, such as holograms on credit cards, banknotes, etc. Photopolymers can be sensed in almost any range of the visible spectrum. Their resolution also exceeds 3000 mm-1, which makes it possible to use these media for recording reflection holograms according to Yu.N. Denisyuk. Their photosensitivity is tens of mJ/cm2. The main advantages of photopolymers include low noise levels and ease of post-exposure processing. The disadvantage of these media is the difficulty of applying them to a substrate in the form of an equal-thickness film.

The most common and widely used method of recording images of objects is photography. In photography, the intensity distribution of light waves is recorded in a two-dimensional projection of the image of an object on the plane of the photograph.

Therefore, no matter what angle we look at the photograph from, we do not see new angles. We also cannot see objects located in the background and hidden by those in front. Perspective in a photograph is visible only by changes in the relative sizes of objects and the clarity of their image.

Holography is one of the remarkable achievements of modern science and technology. The name comes from the Greek words holos - complete and grapho - write, which means a complete recording of an image.

Holography is fundamentally different from conventional photography in that the photosensitive material records not only the intensity, but also the phase of light waves scattered by an object and carrying complete information about its three-dimensional structure. As a means of displaying reality, a hologram has a unique property: unlike photography, which creates a flat image, a holographic image can reproduce an exact three-dimensional copy of the original object. Modern holograms are observed when illuminated by conventional light sources, and full volumetricity in combination with high accuracy of surface texture rendering provides a full effect of presence.

Holography is based on two physical phenomena - diffraction and interference of light waves.

The physical idea is that when two light beams are superimposed, under certain conditions, an interference pattern appears, that is, maxima and minima of light intensity appear in space. In order for this interference pattern to be stable over the time required for observation and to be recorded, the two light waves must be coordinated in space and time. Such consistent waves are called coherent.

The resulting addition of two coherent waves will always be a standing wave. That is, the interference pattern will be stable over time. This phenomenon underlies the production and reconstruction of holograms.

Conventional light sources do not have a sufficient degree of coherence for use in holography. Therefore, the invention in 1960 of an optical quantum generator or laser was crucial for its development - an amazing source of radiation that has the necessary degree of coherence and can emit strictly one wavelength.

Dennis Gabor, while studying the problem of image recording, came up with a great idea. The essence of its implementation is as follows. If a beam of coherent light is divided into two and the recorded object is illuminated with only one part of the beam, directing the second part to a photographic plate, then the rays reflected from the object will interfere with the rays falling directly on the plate from the light source. The beam of light incident on the plate is called supporting, and the beam reflected or passed through the object subject. Considering that these beams are obtained from the same radiation source, you can be sure that they are coherent. A photographic recording of the interference pattern of an object wave and a reference wave has the property of restoring the image of an object if the reference wave is directed at such a recording again. Those. When the picture recorded on the plate is illuminated by the reference beam, the image of the object will be restored, which visually cannot be distinguished from the real one. If you look through the plate from different angles, you can see a perspective image of the object from different sides. Of course, a photographic plate obtained in such a miraculous way cannot be called a photograph. This is a hologram.

In 1962, I. Leith and J. Upatnieks obtained the first transmitting holograms of volumetric objects made using a laser. A beam of coherent laser radiation is directed to a translucent mirror, with the help of which two beams are obtained - an object beam and a reference beam. The reference beam is directed directly to the photographic plate. The object beam illuminates the object, the hologram of which is recorded. The light beam reflected from the object - the object beam - hits the photographic plate. In the plane of the plate, two beams - the object and the reference beams - form a complex interference pattern, which, due to the coherence of the two beams of light, remains unchanged in time and is an image of a standing wave. All that remains is to register it in the usual photographic way. The resulting interference pattern is a coded image that describes the object as it is visible from all points of the photographic plate. This image stores information about both the amplitude and phase of the waves reflected from the object.

If a hologram is recorded in a certain volumetric medium, then the resulting standing wave model unambiguously reproduces not only the amplitude and phase, but also the spectral composition of the radiation recorded on it. This circumstance was the basis for the creation of three-dimensional (volume) holograms. The operation of volumetric holograms is based on the Bragg diffraction effect: as a result of the interference of waves propagating in a thick-layer emulsion, planes are formed that are illuminated with light of higher intensity.

After the hologram is developed, layers of blackening form on the exposed planes. As a result of this, so-called Bragg planes are created, which have the property of partially reflecting light.

Those. a three-dimensional interference pattern is created in the emulsion.

Such a thick-layer hologram provides effective reconstruction of the object wave, provided that the angle of incidence of the reference beam remains unchanged during recording and reconstruction. It is also not allowed to change the wavelength of light during restoration. This selectivity of a volumetric transmission hologram makes it possible to record up to several tens of images on a plate, changing the angle of incidence of the reference beam during recording and reconstruction, respectively.

When reconstructing a volumetric hologram, in contrast to flat transmission holograms, only one image is formed due to reflection of the reconstruction beam from the hologram in only one direction, determined by the Bragg angle.

Reflective volumetric holograms are recorded using a different scheme. The idea of ​​creating these holograms belongs to Yu.N. Denisyuk. Therefore, holograms of this type are known by the name of their creator.

The reference and object light beams are formed using a splitter and directed through a mirror onto the plate from both sides. The object wave illuminates the photographic plate from the side of the emulsion layer, and the reference wave illuminates the photographic plate from the side of the glass substrate. Under such recording conditions, the Bragg planes are located almost parallel to the plane of the photographic plate. Thus, the thickness of the photolayer can be relatively small.

9.4. Elements of integrated circuits.

Beginning of the form

INTEGRATED CIRCUIT(IC), a microelectronic circuit formed on a tiny wafer (crystal or "chip") of semiconductor material, usually silicon, that is used to control and amplify electrical current. A typical IC consists of many interconnected microelectronic components, such as transistors, resistors, capacitors and diodes, fabricated at the surface layer of the chip. The sizes of silicon crystals range from approximately 1.3 x 1.3 mm to 13 x 13 mm. Advances in integrated circuits have led to the development of large-scale and very large-scale integrated circuits (LSI and VLSI) technologies. These technologies make it possible to produce ICs, each of which contains many thousands of circuits: a single chip can have more than 1 million components. Integrated circuits have a number of advantages over their predecessors - circuits that were assembled from individual components mounted on a chassis. ICs are smaller, faster and more reliable; They are also cheaper and less susceptible to failure caused by vibration, moisture and aging. The miniaturization of electronic circuits was made possible due to the special properties of semiconductors. A semiconductor is a material that has much greater electrical conductivity (conductivity) than a dielectric such as glass, but significantly less than conductors such as copper. The crystal lattice of a semiconductor material such as silicon has too few free electrons at room temperature to provide significant conductivity. Therefore, pure semiconductors have low conductivity. However, introducing an appropriate impurity into silicon increases its electrical conductivity. Dopants are introduced into silicon using two methods. For heavy doping or in cases where precise control of the amount of introduced impurity is not necessary, the diffusion method is usually used. Diffusion of phosphorus or boron is usually carried out in an atmosphere of a dopant at temperatures between 1000 and 1150 C for from half an hour to several hours. In ion implantation, silicon is bombarded with high-velocity dopant ions. The amount of implanted impurity can be adjusted with an accuracy of several percent; accuracy in some cases is important, since the gain of the transistor depends on the number of impurity atoms implanted per 1 cm 2 of base.

Which coincide with a very high degree of accuracy, a standing electromagnetic wave arises. When a hologram is recorded, two waves are added in a certain region of space: one of them comes directly from the source (reference wave), and the other is reflected from the recording object (object wave). In the region of a standing electromagnetic wave (or other recording material) is placed, as a result, a complex pattern of darkening bands appears on this plate, which correspond to the distribution of electromagnetic energy (pattern) in this region of space. If now this plate is illuminated by a wave close to the reference one, then it will convert this wave into a wave close to the object one. Thus, we will see (with varying degrees of accuracy) the same light that would be reflected from the recording object.

Sources of light

When recording a hologram, it is extremely important that the lengths (frequencies) of the object and reference waves coincide with each other with maximum accuracy and do not change during the entire recording time (otherwise a clear picture will not be recorded on the plate). This can only be achieved if two conditions are met:

1. both waves were initially emitted by the same source
2. this source emits a wave with a very stable wavelength (radiation)

The only light source that satisfies the second condition well is . Before the invention of lasers, holography practically did not develop. Today, holography places one of the most stringent requirements on laser coherence.

Most often, coherence is usually characterized by the coherence length - that difference in the optical paths of two waves, at which the clarity of the interference pattern drops by half compared to the interference pattern produced by waves that have traveled the same distance from the source. For various lasers, the coherence length can range from several millimeters (high-power lasers intended for welding, cutting and other applications that do not require this parameter) to tens of meters (special, so-called single-frequency lasers for applications that require coherence).

History of holography

The first hologram was obtained in the year (long before the invention of lasers) during experiments to increase resolution. He also coined the word “holography” itself, with which he emphasized the complete recording of the optical properties of an object. Unfortunately, his holograms were of poor quality. It is impossible to obtain a high-quality hologram without a coherent light source.

Leith-Upatnieks notation scheme

In this recording scheme, the laser beam is divided by a special device, a divider (in the simplest case, any piece of glass can act as a divider) into two. After this, the rays are expanded using lenses and directed to the object and the plate using mirrors. Both waves (object and reference) fall on the plate from one side. With this recording scheme, a transmitting hologram is formed, which requires for its reconstruction a source emitting light in a very small range of wavelengths (monochrome radiation), ideally - .

Denisyuk's recording scheme

In this scheme, the laser beam is expanded and directed towards. Part of the beam passing through it illuminates the object. Light reflected from an object forms an object wave. As can be seen, the object and reference waves fall on the plate from different sides. In this scheme, a reflective hologram is recorded, which independently cuts out a narrow section (sections) from the continuous spectrum and reflects only this. Thanks to this, the hologram image is visible in ordinary white light or a lamp (see the picture at the beginning of the article). Initially, the hologram cuts out the wavelength with which it was recorded (however, during processing and when storing the hologram, it can change its thickness, and the wavelength also changes), which makes it possible to record three holograms of one object on one plate, and with lasers, ultimately obtaining one a color hologram that is almost impossible to distinguish from the object itself.

This scheme is characterized by extreme simplicity and in the case of application (having extremely small dimensions and producing a diverging beam without the use of ) it is reduced to only one laser and some base on which the laser, plate and object are fixed. It is precisely these schemes that are used when recording amateur holograms.

Photo materials

Holography is extremely demanding on the resolution of photographic materials. The distance between the two maxima of the pattern is of the same order of magnitude as the laser wavelength, the latter most often being 633 (helium-neon) or 532 (second harmonic laser) nanometers. Thus, this value is on the order of 0.0005 mm. To obtain a clear image of the interference pattern, photographic plates with from 3000 (Leit-Upatnieks) to 5000 (Denisyuk) lines per millimeter were required.

The main photographic material for recording holograms is special photographic plates based on traditional silver bromide. Thanks to special additives and a special development mechanism, it was possible to achieve a resolution of more than 5000 lines per millimeter, but this comes at the cost of extremely low sensitivity of the plate and a narrow spectral range (precisely matched to the laser radiation). The sensitivity of the plates is so low that they can be exposed to direct sunlight for a few seconds without the risk of flare.

In addition, photographic plates based on bichromated gelatin are sometimes used, which have even greater resolution and allow recording very bright holograms (up to 90% of the incident light is converted into an image), but they are even less sensitive, and they are sensitive only in the short wavelength region (blue and, to a lesser extent, the green portions of the spectrum).

At the moment, there is only one industrial (except for a number of small) production of photographic plates for holography in the world - the Russian Slavich Company.

Some recording schemes make it possible to write on plates with lower resolution, even on ordinary photographic films with a resolution of about 100 lines per millimeter, but these schemes have a lot of limitations and do not provide high image quality.

Amateur holography

As already written above, Denisyuk’s scheme, when using a laser diode as a source of coherent light, turns out to be extremely simple, which made it possible to record such holograms at home without the use of special equipment.

To record a hologram, it is enough to create a certain frame on which a laser, a photographic plate (usually PFG-03M) and a recording object will be fixedly mounted. The only serious requirement imposed on the design is minimal vibration. The installation should be installed on vibration-damping supports; a few minutes before and during the exposure, you must not touch the installation (usually the exposure is measured by opening and closing the laser beam with a screen that is not mechanically connected to the installation; in the simplest case, you can simply hold it in your hand).

Amateur holography uses cheap and readily available semiconductor lasers:

1. laser pointers
2. laser modules
3. separate laser diodes

Laser pointers are the easiest to use and affordable source of coherent light. You can buy them for little money almost anywhere. After unscrewing or sawing off the lens that focuses the beam, the pointer begins to shine like a flashlight (except that its spot is elongated in one direction), allowing it to illuminate the photographic plate and the scene located behind it. You just need to secure the button in some way (for example, with a clothespin) in the on state. The disadvantages of pointers include their unpredictable quality and the need to constantly buy new batteries.

A more advanced source is a laser module, whose focusing lens again needs to be unscrewed or sawed off. Unlike a pointer, the module is not powered by batteries inside it, but by an external source, which can be a stabilized 3V power supply. Such a power supply, like the laser module itself, is usually sold in radio parts stores for relatively little money. The absence of low batteries contributes to stable operation. As a rule, laser modules are made better than pointers, but their coherence is also unpredictable.

Finally, laser individual diodes are the most difficult light sources to operate. Unlike modules and pointers, they do not have a built-in power supply, so you will have to assemble one or buy one (the latter is very expensive). The fact is that laser diodes, as a rule, use a non-standard supply voltage, for example 1.8V, 2.7V, etc. In addition, what is more important for them is not the supply voltage, but the current. The simplest power supply consists of a milliammeter, a variable resistor and a standard 3-5V stabilized power supply. In addition, the laser diode is not capable of cooling itself; it must be installed on a radiator. The thermal power of diodes used for amateur holography does not exceed hundreds of milliwatts, so a minimally sized radiator is sufficient; however, the larger the radiator, the more stable the temperature, and coherence directly depends on temperature stability.

As already written above, the coherence of pointers and modules is completely unpredictable, because this parameter is not important for their normal use. It is quite possible that you will have to buy several modules/pointers before you come across an instance with high coherence. You can understand that coherence is insufficient from the recorded hologram: if it has characteristic stripes that move when it rotates, then the laser generates several wavelengths and its coherence is low.

In the case of laser diodes the situation is noticeably better. First, if the diode exhibits a poor emission spectrum (i.e., low coherence) in its normal operating mode, then by slightly lowering or increasing the current through it, you can try to obtain a good spectrum. Secondly, some diodes are manufactured by the manufacturer taking into account the requirements of high coherence. These are lasers with a single longitudinal mode (Single longitudinal mode) or single-frequency lasers. Their coherence length significantly exceeds a meter, which greatly exceeds the needs of amateur holography. Moreover, the price of such lasers starts from several tens of dollars, which is quite affordable for most amateurs. In particular, such laser diodes are produced by Opnext together with Hitachi.

Red semiconductor lasers with a wavelength of 650 nm are most widely used in a wide variety of applications. These same lasers are most widely used in amateur holography. They are distinguished by their low price, fairly high power, and the sensitivity of the eye (and the PFG-03M photographic plates used to record Denisyuk holograms) to this wavelength is quite high. Less common in holography are lasers with wavelengths of 655-665 nm. The sensitivity of the photographic plate (and the eye) to this range is noticeably (about 2 times) less than to 650 nm, but such lasers have many times more power at a similar price. 635nm lasers are even less widespread. Their spectrum is extremely close to the spectrum of the red He-Ne laser (633 nm), for which photographic plates are sharpened, which ensures maximum sensitivity (the sensitivity of the eye is also significantly, twice as high as at 650 nm). However, these lasers have a high price, low efficiency and rarely have high power. In addition, the polarization of these lasers is perpendicular to the polarization of longer wavelength lasers, but this is neither an advantage nor a disadvantage, it just needs to be taken into account when installing the laser to ensure minimal reflection of light from the glass of the photographic plate.

Links

• Holography - Virtual Gallery- the largest website dedicated to holography in the CIS

The hologram recording scheme is shown in Figure 1. Denisyuk recorded a hologram in a three-dimensional environment, thus combining Gabor's idea with Lippmann's color photography. Then the sections of the hologram with maximum light transmission will correspond to those sections of the front of the object wave in which its phase coincides with the phase of the reference wave. Therefore, when the hologram is subsequently illuminated by a reference wave, the same distribution of amplitude and phase is formed in its plane as was the case of the object wave, which ensures restoration...

55. Holography. Scheme for recording and restoring holograms. Recording holograms on thick-layer emulsions. Application of holograms

Holography (from the Greek holos - whole, complete and grapho I write) a method of recording and reconstructing a wave field, based on recording the interference pattern, which is formed by a wave reflected by an object illuminated by a light source S (object wave), and a coherent wave coming directly from the source (reference wave). The recorded interference pattern is called hologram . The hologram recording scheme is shown in Figure 1.

The foundations of holography were laid in 1948 by physicist D. Gabor (Great Britain). Wanting to improve the electron microscope, Gabor proposed recording information not only about the amplitudes, but also about the phases of electronic waves by superimposing a coherent reference wave on the object wave. However, due to the lack of powerful sources of coherent light, he was unable to obtain high-quality holographic images. Holography experienced its rebirth in 1962–1963, when American physicists E. Leith and J. Upatnieks used a laser as a light source and developed a scheme with an inclined reference beam, and Yu.N. Denisyuk recorded a hologram in a three-dimensional environment, thus combining Gabor's idea with Lippmann's color photography. By 1965 1966 The theoretical and experimental foundations of holography were created. In subsequent years, the development of holography proceeded mainly along the path of improving its applications.

Let the interference structure formed by the reference and object waves be recorded by positive photographic material. Then the sections of the hologram with maximum light transmission will correspond to those sections of the front of the object wave in which its phase coincides with the phase of the reference wave. These areas will be more transparent, the greater the intensity of the object wave. Therefore, when the hologram is subsequently illuminated by a reference wave, the same distribution of amplitude and phase is formed in its plane as was the case of the object wave, which ensures the restoration of the latter.

Recovery object wave, the hologram is illuminated by a source creating a copy supporting waves. As a result of light diffraction on the interference structure of the hologram in a diffraction beam first order a copy of the object wave is restored, forming undistorted virtual imageobject, located in the place where the object was during holography. If the hologram is two-dimensional, the conjugate wave is simultaneously reconstructedminus of the first order, forming distorted real imagesubject (Figure 2).

The angles at which diffraction beams of zero and first orders propagate are determined by the angles of incidence of the object and reference waves on the photographic plate. In the Gabor scheme, the reference wave source and the object were located on the hologram axis ( axial diagram ). In this case, all three waves propagated behind the hologram in the same direction, creating mutual interference. In the Leith and Upatnieks scheme, such interference was eliminated by tilting the reference wave ( off-axis scheme).

Interference structurecan be recorded by a photosensitive material in one of the following ways:

1. in the form of variations in light transmittance or reflection. Such holograms, when reconstructing the wavefront, modulate the amplitude of the illuminating wave and are called amplitude;
2. in the form of variations in refractive index or thickness (relief). Such holograms, when reconstructing the wavefront, modulate the phase of the illuminating wave and are therefore called phase.

Often phase and amplitude modulation are performed simultaneously. For example, a conventional photographic plate records the interference structure in the form of variations in blackening, refractive index and relief. After bleaching the hologram, only phase modulation remains.

Interference structure recorded on a photographic plate usually lasts for a long time, that isthe recording process is separated from the recovery process (stationary holograms). However, there are photosensitive media (some dyes, crystals, metal vapors) that almost instantly respond with phase or amplitude characteristics to illumination. In this case, the hologram exists during the influence of the object and reference waves on the medium, and the restoration of the wave front is carried out simultaneously with the recording, as a result of the interaction of the reference and object waves with the interference structure formed by them (dynamic holograms). On principles dynamic holographypermanent and random access memory systems, laser radiation correctors, image intensifiers, laser radiation control devices, and wavefront inversion devices can be created.

If the thickness of the photosensitive layer is significantly greater than the distance between adjacent surfaces of the interference maxima, then the hologram should be considered as volumetric . If the interference structure is recorded on the surface of the layer, or if the layer thickness is comparable to the distance d between adjacent elements of the structure, then holograms are called flat. Criterion for the transition from two-dimensional holograms to three-dimensional ones: .

Volume hologramsare three-dimensional structures in which the surfaces of nodes and antinodes are recorded as variations in the refractive index or reflectance of the medium. The surfaces of nodes and antinodes are directed along the bisector of the angle that constitutes the object and reference beams. Such multilayer structures, when illuminated by a reference wave, act like three-dimensional diffraction gratings. Light specularly reflected from the layers restores the object wave.

Beams reflected from different layers reinforce each other if they are in phase, that is, the path difference between them is equal to (LippmannBragg condition). The condition is automatically satisfied only for the wavelength in the light of which the hologram was recorded. This determines the selectivity of the hologram with respect to the wavelength of the source, in the light of which the wavefront is restored. It becomes possible to restore an image using a continuous spectrum source (Sun, incandescent lamp). If the exposure was carried out with light containing several spectral lines (red, blue, green), then for each wavelength its own three-dimensional interference structure is formed. The corresponding wavelengths will be separated from the continuous spectrum when the hologram is illuminated, which will lead to the restoration of not only the structure of the wave, but also its spectral composition, that is, obtaining a color image. Three-dimensional holograms simultaneously form only one image (imaginary or real) and do not produce zero-order waves.

Properties of holograms.

A) The main property of holograms, which distinguishes it from a photograph, is that in the photograph only the distribution of the amplitude of the object wave incident on it is recorded, while in the hologram, in addition, the distribution of the phase of the object wave relative to the phase of the reference wave is also recorded. Information about the amplitude of the object wave is recorded on the hologram in the form of the contrast of the interference relief, and information about the phase in the form of the shape and frequency of the interference fringes. As a result, the hologram, when illuminated by a reference wave, restores a copy of the object wave.

B) The properties of a hologram, usually recorded on negative photographic material, remain the same as in the case of positive recording: light areas of the object correspond to light areas of the reconstructed image, and dark areas correspond to dark areas. This is easy to understand, taking into account that information about the amplitude of the object wave is contained in the contrast of the interference structure, the distribution of which on the hologram does not change when replacing a positive process with a negative one. With such a replacement, it only shifts to the phase of the restored object wave. This is not noticeable by visual observation, but sometimes appears in holographic interferometry.

IN) If, when recording a hologram, light from each point of an object hits the entire surface of the hologram, each small section of the latter is capable of reconstructing the entire image of the object. However, a smaller section of the hologram will reconstruct a smaller section of the wave front carrying information about the object. If this area is very small, the quality of the reconstructed image will deteriorate.

In the case of focused image holograms, each point of the object sends light to its corresponding small area of ​​the hologram. Therefore, a fragment of such a hologram restores only the corresponding section of the object.

G) The total brightness range transmitted by a photographic plate, as a rule, does not exceed one or two orders of magnitude, while real objects often have significantly larger brightness differences. A hologram with focusing properties uses all the light falling on its entire surface to construct the brightest areas of the image, and it is capable of conveying gradations of brightness up to five and six orders of magnitude.

D) If, when reconstructing the wave front, the hologram is illuminated with a reference source located relative to the hologram in the same way as during its exposure, then the reconstructed virtual image coincides in shape and position with the object itself. When the position of the reconstruction source changes, when its wavelength or the orientation of the hologram and its size changes, the correspondence is violated. As a rule, such changes are accompanied by aberrations in the reconstructed image.

E) The minimum distance between two adjacent points of an object that can still be seen separately when observing an image of an object using a hologram is calledhologram resolution. It grows with increasing size of the hologram. Angular resolution of round (diameter D ) of a hologram is determined by the formula: . Angular resolution of a square hologram with a square side equal to L , is determined by the formula: .

In most holographic schemes, the maximum size of the hologram is limited by the resolution of the recording photographic material. This is due to the fact that an increase in the size of the hologram is associated with an increase in the angle between the object and reference beams and the spatial frequency. An exception is the scheme of lensless Fourier holography, in which it does not increase with increasing size of the hologram.

AND) The brightness of the reconstructed image is determineddiffraction efficiency, which is defined as the ratio of the luminous flux in the reconstructed wave to the luminous flux incident on the hologram during reconstruction. It is determined by the type of hologram, the conditions of its recording, as well as the properties of the recording material.

The maximum achievable diffraction efficiency of holograms is:

For two-dimensional transmitting holograms

amplitude 6.25%,

phase 33.9 5;

For two-dimensional reflective6.25 and 100%, respectively;

For three-dimensional transmittingholograms 3.7 and 100%;

for three-dimensional reflective 7.2 and 100%.

Applications of Holography. When restoring holograms, a complete illusion of the existence of an object is created, indistinguishable from the original. This property of holograms is used in lecture demonstrations, when creating three-dimensional copies of works of art, and holographic portraits. Three-dimensional holographic images are used to study moving particles, raindrops or fog, and tracks of nuclear particles in bubble and spark chambers.

Using holographic devices, various wave transformations are carried out, including wavefront reversal in order to eliminate optical aberrations. One of the first applications of holography was related to the study of mechanical stress. Holography is used to store and process information. This ensures high recording density and recording reliability.

The three-dimensionality of the image makes the creation of holographic cinema and television promising. The main difficulty in this case is the creation of huge holograms that could be viewed simultaneously by a large number of viewers. In addition, the hologram must be dynamic. To create holographic television, it is necessary to overcome the difficulty caused by the need to expand the frequency band by several orders of magnitude in order to transmit three-dimensional moving images.

A hologram can be produced not only by the optical method, but also designed on a computer (digital hologram). Machine holograms are used to obtain three-dimensional images of objects that do not yet exist. Machine holograms of complex optical surfaces are used as standards for interference testing of product surfaces.

Acoustic holography is also known, which can be combined with methods for visualizing acoustic fields.

Additional material

When the reference and object waves meet in space, a system of standing waves is formed. The maxima of the amplitude of standing waves correspond to zones in which the interfering waves are in the same phase, and the minima correspond to zones in which the interfering waves are in antiphase. For a point reference source O 1 and a point object O 2 the surfaces of maxima and minima represent a system of hyperboloids of revolution. The spatial frequency of the interference structure (the reciprocal of its period) is determined by the angle at which light rays emanating from the reference source and emanating from the object converge at a given point: , where is the wavelength. Planes tangent to the surface of nodes and antinodes at each point in space bisect the angle. In the Gabor scheme, the reference source and object are located on the hologram axis, the angle is close to zero and the spatial frequency is minimal. Axial holograms are also called single beam , since one beam of light is used, one part of which is scattered by an object and forms an object wave, and the other part, which passes through the object without distortion, is a reference wave.

In the Leith and Upatnieks scheme, a coherent inclined reference beam is formed separately (double beam hologram). For double-beam holograms, the spatial frequency is higher than for single-beam holograms. Therefore, recording double-beam holograms requires photographic materials with a higher spatial resolution.

If the reference and object beams fall on the photosensitive layer from different sides (~ 180 0 ), then it is maximum and close to 2/ (holograms in colliding beams). Interference maxima are located along the surface of the material in its thickness. This scheme was first proposed by Denisyuk. Since when such a hologram is illuminated by a reference beam, the reconstructed object wave propagates towards the illuminating beam, such holograms are sometimes called reflective.

Types of holograms. The structure of the hologram depends on the method of generating the object and reference waves and on the method of recording the interference pattern. Depending on the relative position of the object and the plate, as well as on the presence of optical elements between them, the relationship between the amplitude-phase distributions of the object wave in the planes of the hologram and the object is different. If the object lies in the plane of the hologram or is focused on it, then the amplitude-phase distribution on the hologram will be the same as in the plane of the object (focused image hologram; Figure 3).

When the object is far enough from the plate, or at the focus of the lens L, then each point of the object sends a parallel beam of light to the plate. In this case, the connection between the amplitude-phase distributions of the object wave in the hologram plane and in the object plane is given by the Fourier transform (the complex amplitude of the object wave on the plate is the so-called Fourier image of the object). The hologram in this case is calledFraunhofer hologram(Figure 4).

If the complex amplitudes of the object and reference waves are Fourier images of the object and reference source, then the hologram is calledFourier hologram. When recording a Fourier hologram, the object and the reference source are usually located in the focal plane of the lens (Figure 5).

In the case of a lensless Fourier hologram, the reference source is located in the plane of the object (Figure 6). In this case, the front of the reference wave and the fronts of elementary waves scattered by individual points of the object have the same curvature. As a result, the structure and properties of the hologram are almost the same as those of the Fourier transform hologram.

Fresnel hologramsare formed when each point of an object sends a spherical wave to the plate. As the distance between the object and the plate increases, Fresnel holograms turn into Fraunhofer holograms, and as this distance decreases, into focused image holograms.

S

Real Image

Virtual image

Figure 6 Scheme of lensless recording of a Fourier hologram

Hologram

Figure 5 Fourier hologram recording scheme

Reference source

Support beam

L

Support beam

Figure 4 Fraunhofer hologram recording diagram

Figure 3 Scheme of recording a focused image hologram

Figure 1 Schematic of hologram recording

Figure 2 Recovery scheme

holographic image of an object

Support beam

Hologram

Holography- a set of technologies for accurately recording, reproducing and reshaping the wave fields of optical electromagnetic radiation, a special photographic method in which, using a laser, images of three-dimensional objects are recorded and then reconstructed, highly similar to real ones.

This method was proposed in 1947 by Dennis Gabor, who also coined the term hologram and received the Nobel Prize in Physics in 1971 “for the invention and development of the holographic principle.”

History of holography

The first hologram was received in 1947 (long before the invention of lasers) by Dennis Gabor during experiments to increase the resolution of the electron microscope. He also coined the word “holography” itself, with which he emphasized the complete recording of the optical properties of an object. Unfortunately, his holograms were of poor quality. It is impossible to obtain a high-quality hologram without a coherent light source.

Features of the scheme:

After creation in 1960 year of red ruby ​​(wavelength 694 nm, operates in pulsed mode) and helium-neon (wavelength 633 nm, operates continuously) lasers, holography began to develop intensively.

In 1962 year, a classic scheme for recording holograms by Emmett Leight and Juris Upatnieks from the Michigan Institute of Technology (Leith-Upatnieks holograms) was created, in which transmission holograms are recorded (when restoring a hologram, light is passed through a photographic plate, although in practice some of the light is reflected from it and also creates an image , visible from the opposite side).

Leith-Upatnieks scheme

In this recording scheme, the laser beam is divided by a special device, a divider (in the simplest case, any piece of glass can act as a divider) into two. After this, the rays are expanded using lenses and directed using mirrors to the object and recording medium (for example, a photographic plate). Both waves (object and reference) fall on the plate from one side. With this recording scheme, a transmission hologram is formed, which requires a light source with the same wavelength at which the recording was made, ideally a laser, to be restored.

In 1967 The first holographic portrait was recorded with a ruby ​​laser.

As a result of long work in 1968 year, Yuri Nikolaevich Denisyuk received high-quality (until that time the lack of necessary photographic materials prevented obtaining high quality) holograms that restored the image by reflecting white light. To do this, he developed his own hologram recording scheme. This scheme is called the Denisyuk scheme, and the holograms obtained with its help are called Denisyuk holograms.

Features of the scheme:

• observing images in white light;
• insensitivity to vibrations of the “object-RS” element;
• high resolution recording medium.

In 1977 Lloyd Cross created the so-called multiplex hologram. It is fundamentally different from all other holograms in that it consists of many (from tens to hundreds) individual flat views, visible from different angles. Such a hologram, naturally, does not contain complete information about the object; in addition, it, as a rule, does not have vertical parallax (that is, you cannot look at the object from above and below), but the dimensions of the recorded object are not limited by the laser coherence length (which rarely exceeds several meters, and most often only a few tens of centimeters) and the size of a photographic plate.

Moreover, you can create a multiplex hologram of an object that does not exist at all, for example, by drawing a fictitious object from many different angles. Multiplex holography is superior in quality to all other methods of creating three-dimensional images based on individual angles (for example, lens rasters), but it is still far from traditional holography methods in terms of realism.

In 1986 Abraham Secke put forward the idea of ​​creating a source of coherent radiation in the near-surface region of a material by irradiating it with X-rays. Since spatial resolution in holography depends on the size of the source of coherent radiation and its distance from the object, it turned out to be possible to reconstruct the atoms surrounding the emitter in real space.

Unlike optical holography, in all electron holography schemes proposed to date, the restoration of an object’s image is carried out using numerical methods on a computer.

In 1988 Barton proposed such a method for reconstructing a three-dimensional image, based on the use of Fourier-like integrals, and demonstrated its effectiveness using the example of a theoretically calculated hologram for a cluster of a known structure. The first reconstruction of a three-dimensional image of atoms in real space from experimental data was carried out for the Cu(001) surface by Harp in 1990.

Physical principles

Basic law of holography

If a photosensitive material on which a pattern of interference of several light waves is recorded is placed in the position in which it was during the recording process and illuminated again with some of these waves, then the rest will be restored. This feature is explained by the fact that not only the intensity is recorded on the hologram, as on a regular photographic plate, but also the phase of the light emanating from the object. It is information about the phase of the wave that is necessary for the formation of three-dimensional space during reconstruction, rather than the two-dimensional one provided by ordinary photography. Thus, holography is based on wavefront reconstruction.

The holographic process consists of two stages - recording and recovery.

• The wave from the object interferes with the “reference” wave, and the resulting pattern is recorded.
• The second stage is the formation of a new wave front and obtaining an image of the original object.

Recording information about the phase of a wave coming from an object can only be done with a light source with stable phase characteristics. Ideal for this purpose is laser- coherent light source of high intensity and high monochromaticity.

Superposition principle

Everyday experience shows that the illuminance produced by two or more ordinary incoherent light sources is the simple sum of the illuminances produced by each of them separately. This phenomenon is called superposition principle.

Huygens also wrote in his Treatise: “One of the most wonderful properties of light is that when it comes from different directions, its rays produce an effect, passing through one another without any interference.” The reason for this is that each source, consisting of many atoms and molecules, simultaneously emits a huge number of waves that are out of phase. The phase difference changes quickly and randomly, and, despite the fact that interference occurs between some waves, the interference patterns change with such frequency that the eye does not have time to notice the changes in illumination. Therefore, the intensity of the resulting oscillation is perceived as the sum of the components of the original oscillations, and the radiation of the source is "White light, i.e. not monochromatic, but consisting of different wavelengths. For the same reason, this light is unpolarized, but natural, that is, it does not have a predominant plane of vibration.

Coherent oscillations

Under special conditions, the principle of superposition is not observed. This is observed when the phase difference between light waves remains constant for a long enough time to be observed. The waves seem to “sound in time.” Such oscillations are called coherent.

The main feature of coherence is the possibility of interference. This means that when two waves meet, they interact, forming a new wave. As a result of this interaction, the resulting intensity will differ from the sum of the intensities of the individual oscillations - depending on the phase difference, either a darker or lighter field is formed, or instead of a uniform field, alternating bands of different intensities are formed, interference fringes.

Monochromatic waves are always coherent, However, light filters, often called monochromatic, in reality never produce strictly monochromatic radiation, but only narrow the spectral range and, of course, do not transform ordinary radiation into coherent radiation.

Obtaining coherent radiation

Previously, only one way of producing coherent radiation was known - using a special device - interferometer. The radiation from a conventional light source was divided into two beams, coherent with each other. These beams could interfere. Another method is now known, using stimulated radiation. Lasers are based on this principle.

Diffraction in holography

The main physical phenomenon on which holography is based is diffraction- deviation from its original direction of light passing near the edges of opaque bodies or through narrow slits. If not one, but several slits are applied to the screen, then an interference pattern appears, consisting of a series of alternating light and dark stripes, brighter and narrower than with a single slit. In the middle there is the brightest band of “zero order”, on both sides of it there are bands of gradually decreasing intensity of the first, second and other orders. As the number of slits on the screen increases, the stripes become narrower and brighter. A screen with a large number of thin parallel slits, the number of which is often increased to 10,000, is called a diffraction grating.

The grating, which is a hologram, is characterized primarily by the fact that diffraction occurs not at the slit, but at the circle. The diffraction pattern from a round opaque object is a bright central circle surrounded by gradually weakening rings. If, instead of an opaque disk, a disk with rings surrounding it is placed in the path of the wave, the circle in the image will become brighter and the stripes will become paler. If the transparency from a dark to a light area does not change abruptly, but gradually, according to a sinusoidal law, then such a grating forms only stripes of the zero and first orders, and interference in the form of stripes of higher orders does not appear. This property is very important when recording a hologram. If the transition from a dark ring to a light one is carried out strictly according to a sinusoidal law, then the rings in the image will disappear and the image will be a small bright circle, almost a dot. Thus, a circular sinusoidal grating will form from a parallel beam of rays (a plane wave) the same image as a collecting lens.

This lattice, called zone lattice(Soret plate, Fresnel plate), sometimes used instead of a lens. For example, it is used in glasses, replacing heavy high-refraction spectacle lenses. Obtaining zone gratings is possible in various ways, both mechanical and optical, interference. The use of these gratings, obtained by interference, forms the basis of holography.

Hologram recording

To record a hologram of a complex non-self-luminous object, it is illuminated with laser radiation. A coherent reference wave is directed onto the same plate onto which the scattered light reflected by the object falls. This wave is separated from the laser radiation using mirrors.

The light reflected by each point of the object interferes with the reference wave and forms a hologram of that point. Since any object is a collection of light-scattering points, many elementary holograms are superimposed on the photographic plate - points that together give a complex interference picture of the object.

The developed hologram is placed in the place where it was during recording, and the laser is turned on. Just as when restoring a hologram of a point, when the hologram is illuminated by a beam of light from a laser involved in recording, the light waves emanating from the object during recording are restored. Where the object was located during recording, a virtual image is visible. The real image associated with it is formed on the other side of the hologram, on the observer’s side. It is usually invisible, but unlike the imaginary one, it can be obtained on the screen.

Yu. N. Denisyuk (1962) developed a method in which three-dimensional media are used instead of a thin-layer emulsion to register a hologram. In such a thick hologram, standing waves arise, which significantly expanded the capabilities of the method. A three-dimensional diffraction grating, in addition to the previously described properties of a hologram, has a number of important features. The most interesting is the possibility of image restoration using a conventional continuous spectrum source - an incandescent lamp, the sun and other emitters. In addition, in a three-dimensional hologram there are no zero-order waves and a real image, and therefore interference is reduced.