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(hŏlŏg`rəfē, hō–), method of reproducing a three-dimensional image of an object by means of light wave patterns recorded on a photographic plate or film. Holography is sometimes called lensless photography because no lenses are used to form the image. The plate or film with the recorded wave patterns is called a hologram. The light used to make a hologram must be coherent, i.e. of a single wavelength or frequency and with all the waves in phase. (A coherent beam of light can be produced by a laserlaser
[acronym for light amplification by stimulated emission of radiation], device for the creation, amplification, and transmission of a narrow, intense beam of coherent light. The laser is sometimes referred to as an optical maser.
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.) Before reaching the object, the beam is split into two parts; one (the reference beam) is recorded directly on the photographic plate and the other is reflected from the object to be photographed and is then recorded. Since the two parts of the beam arriving at the photographic plate have traveled by different paths and are no longer necessarily coherent, they create an interferenceinterference,
in physics, the effect produced by the combination or superposition of two systems of waves, in which these waves reinforce, neutralize, or in other ways interfere with each other.
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 pattern, exposing the plate at points where they arrive in phase and leaving the plate unexposed where they arrive out of phase (nullifying each other). The pattern on the plate is a record of the waves as they are reflected from the object, recorded with the aid of the reference beam. When this hologram is later illuminated with coherent light of the same frequency as that used to form it, a three-dimensional image of the object is produced; it can even be photographed from various angles. This technique of image formation is known as wave front reconstruction. Dennis Gabors, a British scientist who in 1948 developed the wave theory of light (itself first suggested by Christopher Huygens in the late 17th cent.) can be viewed as the father of theoretical holography. However, no adequate source of coherent light was available until the invention of the laser in 1960. Holography using laser light was developed during the early 1960s and has had several applications. In research, holography has been combined with microscopy to extend studies of very small objects; it has also been used to study the instantaneous properties of large collections of atmospheric particles. In industry, holography has been applied to stress and vibrational analysis. Color holograms have been developed, formed using three separate exposures with laser beams of each of the primary colors (see colorcolor,
effect produced on the eye and its associated nerves by light waves of different wavelength or frequency. Light transmitted from an object to the eye stimulates the different color cones of the retina, thus making possible perception of various colors in the object.
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). Another new technique is acoustical holography, in which the object is irradiated with a coherent beam of ultrasonic waves (see soundsound,
any disturbance that travels through an elastic medium such as air, ground, or water to be heard by the human ear. When a body vibrates, or moves back and forth (see vibration), the oscillation causes a periodic disturbance of the surrounding air or other medium that
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; ultrasonicsultrasonics,
study and application of the energy of sound waves vibrating at frequencies greater than 20,000 cycles per second, i.e., beyond the range of human hearing. The application of sound energy in the audible range is limited almost entirely to communications, since
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); the resulting interference pattern is recorded by means of microphones to form a hologram, and the photographic plate thus produced is viewed by means of laser light to give a visible three-dimensional image.


See G. W. Stroke, An Introduction to Coherent Optics and Holography (2d ed. 1969); T. Okoshi, Three-Dimensional Imaging Techniques (1976); N. Abramson, The Making and Evaluation of Holograms (1981); J. E. Kasper and S. A. Feller, The Complete Book of Holograms (1987).


A technique for recording, and later reconstructing, the amplitude and phase distributions of a coherent wave disturbance. Invented by Dennis Gabor in 1948, the process was originally envisioned as a possible method for improving the resolution of electron microscopes. While this original application has not proved feasible, the technique is widely used as a method for optical image formation, and in addition has been successfully used with acoustical and radio waves. See Acoustical holography

The technique is accomplished by recording the pattern of interference between the unknown “object” wave of interest and a known “reference” wave (Fig. 1). In general, the object wave is generated by illuminating the (possibly three-dimensional) subject of concern with a highly coherent beam of light, such as supplied by a laser source. The waves reflected from the object strike a light-sensitive recording medium, such as photographic film or plate. Simultaneously a portion of the light is allowed to bypass the object, and is sent directly to the recording plane, typically by means of a mirror placed next to the object. Thus incident on the recording medium is the sum of the light from the object and a mutually coherent “reference” wave. See Laser

Recording a hologramenlarge picture
Recording a hologram

The photographic recording obtained is known as a hologram (meaning a “total recording"); this record generally bears no resemblance to the original object, but rather is a collection of many fine fringes which appear in rather irregular patterns. Nonetheless, when this photographic transparency is illuminated by coherent light, one of the transmitted wave components is an exact duplication of the original object wave (Fig. 2). This wave component therefore appears to originate from the object (although the object has long since been removed) and accordingly generates a virtual image of it, which appears to an observer to exist in three-dimensional space behind the transparency. The image is truly three-dimensional in the sense that the observer's eyes must refocus to examine foreground and background, and indeed can “look behind” objects in the foreground simply by moving his or her head laterally.

Obtaining images from a hologramenlarge picture
Obtaining images from a hologram

Holography has been demonstrated to offer the capability of several unique kinds of interferometry. This capability is a consequence of the fact that holographic images are coherent; that is, they have well-defined amplitude and phase distributions. Any use of holography to achieve the superposition of two coherent images will result in a potential method of interferometry. See Interferometry

Optical memories for storing large volumes of binary data in the form of holograms have been developed for commercial use. Such a memory consists of an array of small holograms, each capable of reconstructing a different “page” of binary data. When one of these holograms is illuminated by coherent light, it generates a real image consisting of an array of bright or dark spots, each spot representing a binary digit.

There has been interest in the use of holography for purposes of display of three-dimensional images. Applications have been found in the field of advertising, and there is increased use of holography as a medium for artistic expression.

Microwave holography is microwave imaging by means of coherent continuous-wave electromagnetic radiation in the wavelength range from 1 mm to 1 m. As a long-wavelength imaging modality, it differs from techniques which employ echo timing (for example, conventional radar) by its requirement for phase information. In this respect it resembles optical holography, from which it has departed significantly. The technique usually involves small-scale systems, that is, systems in which the effective data acquisition aperture is of the order of tens or hundreds of wavelengths. Microwave holographic imaging is characterized by high lateral-resolution capability in comparison with images obtained from echo timing. The natural image format of the data it presents to the human observer enhances its diagnostic potential. In particular, it conveniently produces phase imagery which increases further its diagnostic capability.

Microwave holography is useful in applications where images of concealed structure are required. Microwave radiation penetrates a variety of dielectric media to a depth depending on the attenuation of a given wavelength in a particular medium. One such application is the mapping of subsurface pipes and cables. Plastic pipes as well as metal pipes can be imaged. Hence this noninvasive microwave technique has a diagnostic power greater than the normal metal detectors.

The major limitation of the microwave holographic techniques is that the images produced are essentially two-dimensional. The reason is that the microwave wavelength is so long (104–106 times that of light) that the depth of focus of the microwave hologram is prohibitive. This disadvantage is overcome by employing a tomographic mode of imaging which exploits the ability of microwaves to penetrate many materials and thereby characterize their three-dimensional structure more accurately. Microwave holographic tomography requires holograms to be recorded from different views of the object and synthesized.



a method of producing a three-dimensional image of an object based on wave interference. The idea of holography was first expressed by D. Gabor (Great Britain. 1948), but the method was technically extremely complicated, and it did not become widespread. Only with the appearance of lasers have numerous and varied possibilities opened up for the practical use of holography in radio electronics, optics, physics, and various fields of technology.

Principle of holography. A camera, which fixes on a photographic plate the radiation scattered by an object, is ordinarily used to produce a photographic image of the object. Each point of the object in this case is a center for the scattering of the incident light; it sends into space an expanding spherical light wave, which is focused by a lens into a small spot on the light-sensitive surface of the plate. Because the reflecting capacity of the object varies from one point to another, the intensity of the light falling on corresponding parts of the plate also varies, and thus an image of the object appears on the plate. This image consists of images of corresponding points of the object received on each part of the light-sensitive surface. In the process, three-dimensional objects are recorded in the form of two-dimensional images.

In the process of photography, only the distribution of intensity—that is, the amplitude of the light wave reflected from the object—is recorded on the plate (the intensity is proportional to the square of the amplitude). However, when a light wave is reflected from an object, it changes not only its amplitude but also its phase according to the properties of the object at a particular point.

Holography makes it possible to obtain more complete information about an object, since it is a process for recording on a photographic plate not only the amplitude but also the phase of the light wave scattered by the object. In order to do this it is necessary, simultaneously with the wave scattered by the object (a signal wave), to direct an auxiliary wave at the plate from the same light source (a laser), with fixed amplitude and phase (a reference wave; see Figure 1).

Figure 1. Production of a hologram with interference of two plane light waves (reference and incident); Θ is the angle between the directions of diffusion of the reference and signal waves, and d is the distance between adjacent dark bands of the interference pattern

The interference pattern (the alternation of dark and light bands or spots) appearing as a result of the interaction of the signal and reference waves contains complete information on the amplitude and phase of the signal wave—that is, about the object. The interference pattern fixed on the light-sensitive surface after developing is called a hologram. If a hologram is viewed through a microscope, in the simplest case, a system of alternating light and dark bands is seen. The interference pattern of real objects is more complex.

In order to see (reconstruct) the image of an object it is necessary to illuminate the hologram with the same reference wave as that used to produce it. In the simplest case—the interference of two plane waves (two parallel beams of light)—the hologram is an ordinary diffraction grating. A plane wave incident on such a hologram passes partly through it and continues in its original direction and is partly transformed by diffraction into two secondary plane waves propagating at an angle Θ (Figure 2). The angle Θ depends on the period d of the grating and the wavelength λ of the light according to the formula

sin Θ = ±(λ/d)

As can be seen from Figure 2, the wave that is headed “downward” appears to be a continuation of the signal wave used to photograph the hologram (Figure 1). Therefore, it in no way differs from a wave coming from the object when viewed directly. As a result, when light is beamed through the hologram, exactly the same wave that came from the object is reconstructed. Consequently, an observer looking through the hologram sees a virtual image of the object in the place where the object was when it was photographed. The wave that is going “upward” (Figure 2) also contains information about the object and forms its real image.

Figure 2. Reconstruction of Images by means of a hologram

Hologram of a point. Let the light from a laser be incident on a point object A and on a plane reflector, which generates a reference wave (Figure 3). The reference wave and the wave diffused from the point object are incident on a photosensitive layer, on which an interference pattern is recorded. The hologram in this case is formed as a result of the interference of the spherical signal wave and the plane reference wave and consists of a system of concentric dark and light rings. Since the distance between the interference rings is d = λ/sin Θ, the alternation of light and dark rings becomes increasingly frequent toward the lower edge of the hologram (Figure 4).

Figure 3. Production of a hologram of a point object

Figure 4. Real [A”] and virtual (Λ’) images of point A; H is the distance from the object to the hologram

When the hologram is illuminated by the plane reference wave, two spherical waves arise as a result of diffraction. These waves form real and virtual images of point A, which can be observed from different angles (Figure 4). The expanding spherical wave I forms a virtual image A’, and when the observer perceives this wave he sees a virtual image A’ behind the hologram in the same place where the real object A appeared. The second expanding spherical wave II creates a real image A” of the object, located in front of the hologram.

Three-dimensional nature of holographic images. By repeating the arguments given for each of the points of an object consisting, for example, of four points, it is clear that the interference pattern fixed on the hologram will contain complete information about all four points. When the hologram is illuminated by the reference beam, two images appear—the virtual and real images—and both images will be perceived by the observer as three dimensional.

The virtual image is observed if the observer looks through the hologram as if through a window (Figure 5). Indeed, in positions b, c, and d, point 1 is visible, and in positions c, d, and e, point 3 may be seen; in positions c and d the observer sees simultaneously points 1 and 3 and points 2 and 4, which are situated between them—that is, he sees the whole object. If the observer shifts his gaze from point 2 to point 3 (or 4), he must refocus his eyes, and if he changes his position fromc to d. for example, then the perspective of the image will also change. Moreover, in some positions the observer will not see point 4 because it will be blocked out by point 2 of the object, which is situated nearer the observer. Thus, the holographic image is three-dimensional, and the visual perception of this image is in no way different from the perception of the original object. In photographing the virtual image it is possible, depending on where the camera is placed and on its focusing, to record all these features in photographs. Such holograms were first produced experimentally by the American physicists E. Leith and J. Upatnieks in 1962.

Figure 5. Holograms of an object consisting of four points

The real image is also three-dimensional and has all the properties mentioned above; it appears to be suspended in front of the hologram but it is somewhat more difficult to observe.

Properties of holograms. The holographic image of a point is a spot whose diameter δ is δ = 2(λH/D) where D is the size of the hologram, λ is the wavelength, and H is the distance from the object to the hologram. The quantity δ characterizes the resolving power of the holographic image—that is, the distinguishability of two adjacent points of an object. One of the remarkable properties of a hologram is that every part of it contains information about the whole object and therefore makes it possible to reconstruct a complete image of the object (when the size of the hologram D is decreased, only the resolution of the image is diminished). As a result of this, information recorded in the form of a hologram is preserved in a highly reliable manner.

The length λ of the reference wave can be changed when holograms are illuminated. In this case two images are observed, but at the other distance H’ from the hologram, defined by the formula:

H’ =(λ12)

Here H is the distance between the object and the hologram when photographed, λ1, is the length of the reference wave during the photographing, and λ2 is the length when the hologram is viewed. Thus it is possible to visualize images of objects recorded in the form of holograms by means of radio waves or infrared, ultraviolet, or X radiation.

When holograms are viewed it is possible to change not only the length of the reference wave but also its wave front. For example, when a hologram is illuminated by an expanding spherical wave, it is possible to see an enlarged image of the object. The holographic microscope is based on this fact.

The possibilities of holography are radically increased if the hologram is recorded on a thick emulsion, as was first proposed by Iu. N. Denisiuk (USSR, 1962). In this case the interference pattern produced is three-dimensional, so that the hologram acquires new properties. In particular, such a hologram makes it possible to see the image of an object when it is illuminated by nonmonochromatic (white) light.

It is possible to produce a holographic image of an object in color if three monochromatic lasers operating on different wavelengths—for example, blue, yellow, and red beams— are used in preparing the hologram. In this case the hologram can be recorded on an ordinary emulsion, and it will not differ outwardly from an ordinary black-and-white hologram. A color image of the object is seen when the hologram is illuminated simultaneously by three reference waves corresponding to the colors indicated.

Quality of holographic images. The quality of holographic images depends on the monochromatic nature of the light from the lasers and the resolving power of the photographic materials used in preparing the holograms. If the radiation spectrum of the laser is broad, then when the hologram is being photographed, a particular interference pattern will correspond to every wave of a given length in this spectrum, and the resulting interference pattern will be indistinct and blurred. Therefore, in preparing holograms, lasers are used that have a very narrow radiation spectrum line.

The quality of the interference pattern is also determined by the resolving power of the photographic material—that is, by the number of interference lines that can be fixed per millimeter. The greater this number, the better the quality of the reconstructed image. Because of this, photographic materials with high resolution (1.000 lines and more per mm) are used in holography.

Most of the photographic emulsions used are suspensions of light-sensitive grains situated a certain distance apart. The discrete structure of photographic emulsions is such that “fragments” of the interference pattern are recorded on the hologram, rather than a continuous distribution of brightness. This creates a light background, since the light is scattered on the developed grains when the hologram is illuminated. Therefore, extensive searches are under way for grainless photographic materials, which would also make it possible to erase and rerecord information, which is very important for a number of applications of holography. The first holograms on fine-domain magnetic tapes, on photochrome glass and film, on crystals, and on other materials have already been produced.

Photographic conditions also affect the quality of holographic images. When continuous-emission lasers are used, the exposure time varies from fractions of a second to dozens of minutes (depending on the size of the object and the hologram). During this time the object, the photographic plate, and other optical elements of the scheme must not be moved distances comparable to the wavelength λ, or the interference pattern will be blurred. This difficulty is eliminated by using pulsed lasers, which provide strong light radiation over very short time intervals (up to 10∼9 sec). Such a short exposure time makes it possible to produce holograms of objects moving at speeds on the order of 1.000 m/sec (Figure 6).

Uses. Pulse holography makes it possible to arrest and analyze rapidly occurring processes. The study of particle tracks in bubble chambers is of great interest in nuclear physics and the physics of elementary particles. Stereoscopic photography is being used for this purpose at present, but holographic methods are proving very effective, since they make it possible to record information about the entire volume of the chamber. When reconstructed, the image can be observed in various cross sections of the chamber, making it easy to distinguish the tracks corresponding to different particles. The number of particles registered on a hologram can be very large (on the order of 1.000). Analogously, it is possible to study the dynamics of the distribution of in-homogeneities in vapors, liquids, and other transparent mediums.

Pulse holography is promising in the field of interferome-try. Two holograms of an object under study are recorded on the same photographic plate at different moments in time. Upon reconstruction, both waves, which contain information on the object, are superimposed on each other. If any changes have occurred in the object between exposures, a system of interference bands will appear on the reconstructed image. By deciphering the interference pattern obtained, it is possible to determine what changes have occurred. This method makes it possible to measure very small deformations (on the order of fractions of a micron) of objects with complex surface shape caused by vibration, heating, and so on. It can also be used for nondestructive testing of products, to study explosions, gas flows in a supersonic nozzle, plasma, or the shock waves formed, for example, by the path of a bullet.

In principle, holography has opened up the possibility of three-dimensional color television. Indeed, the hologram of an object can be fixed on the light-sensitive surface of a television camera tube, and it can then be transmitted over a radio or optical channel. On the receiving end, the hologram can be reconstructed by recording on light-sensitive film. This will make it possible to observe a three-dimensional image of the object. Even for special purposes, such a system still involves great technical difficulties (the resolving power of television transmission tubes is very low, which complicates the reconstruction of three-dimensional images; sufficiently powerful lasers in the visible spectrum, for producing holograms of real objects, have not yet been developed).

The methods of holography offer prospects for creating new memory systems, which are of great interest in the advancement of computer technology. Holography permits a recording density on the order of 107— 108 bits of information per sq cm of light-sensitive surface, which is several orders higher than in existing memory systems. In addition, holographic recording is highly reliable; the breakdown of small sections of a hologram leads only to a certain decrease in the quality of reproduction. High-capacity holographic memory devices were proposed in 1966 by A. L. Mikaelian and V. I. Bobrinev (USSR) based on the recording of a large number of holograms on the same surface (or volume) of photographic material. In order to keep the images from overlapping one another, the angle at which the reference wave falls on the light-sensitive layer is changed for each image (Figure 6). Before falling on the hologram, the reference beam passes through a deflection system, which establishes the direction of the reference beam according to the address fed into it. To each address corresponds a particular direction of the reference beam. The signal beam is divided into n channels, to each of which is connected a modulator M. When a control voltage is present, the modulator passes a laser beam, but when it is not present, the modulator becomes opaque. At the output of the modulators a combination of n beams arises, and they are recorded together with the reference beam in the form of a hologram. When information is accumulated in the memory device, all addresses are fed to the address input in sequence, and the corresponding numbers are fed to the signal input.

Figure 6. Holographic memory: M1,M2.....M3, are modulators

During readout of information, the deflection system establishes the angle of incidence of the readout reference beam corresponding to the assigned address, and the hologram creates an image in the form of a system of bright spots whose number and distribution are determined by the combination of modulators plugged in during recording. This image is projected onto a system of photographic receivers at whose output the signals give the number that has been read out. The sequential recording of up to 1,000 holograms of 32-order numbers over a surface with a diameter of about 2 mm has already been achieved.

Another type of holographic memory makes it possible to enter large quantities of numbers that are transformed in advance into transparent matrices. Each matrix is recorded in the form of a hologram on a small area of photographic film (of the order of 1–2 mm). The beam of light is switched from one hologram to another by a two-coordinate deflection system, where for any angles of deflection the reference and signal beams are joined on the hologram. When information is read out, each hologram is illuminated by the reference beam, which reconstructs the image of the corresponding matrix. This image falls on a mosaic of photodiodes linked in such a way that it is possible to select any digit from the reconstructed matrix. The time required for readout of an arbitrary number is determined by the capacity of the laser and the sensitivity of the photodiodes, and it can be made very small (10−7−10−8 sec). The capacity of a holographic memory with random access to information at high speed can reach 109 bits.

The possibility of using the principles of holography to create special computer devices in which various mathematical operations can be performed on information recorded in the form of a hologram is promising. In this connection, the greatest amount of attention is being devoted to the creation of devices for finding an assigned bit of information and recognizing images. The term “recognition” denotes comparison of the images of two objects and the establishment of correspondences between them. Such devices can be used for the automatic readout of information, for classifying various objects, or for deciphering complex images. The possibility of object recognition is based on the ability of holograms to reconstruct the image of an object only if the reading beam of light coincides in form with the reference beam used in photographing. Let us suppose, for example, that a hologram exists on which is recorded the interference between a point source of light and light that has passed through a transparency with the letter T (Figure 7). If the hologram is then illuminated by the light passing through a transparency on which various letters are recorded, the image of the bright dot will be visible only in the case of the same T. Such a hologram is a unique filter that can be used, for example, to establish the presence of the letter T in any complicated text and rapidly to determine the number of such letters. This method has been tested, in particular, to recognize fingerprints. A holographic filter was made for one of eight similar fingerprints and was used for purposes of recognition in the apparatus examined above. Photographic copies of all the fingerprints were fed into a circuit in sequence, and the image was observed in the recognition plane. A bright dot appeared in only one case, which indicates the high degree of selectivity of the given method. Recognition is sufficiently reliable even if only part of a fingerprint is available. For example, if half a fingerprint is available, the image of the dot will be only 10 percent darker. It has been established experimentally that recognition of natural objects of complex shape, such as fingerprints, is much more reliable than recognition of symbols, letters, or simple figures. For example, errors are possible in recognizing letters with similar shapes (O and C, F and E, and so on).

The use of holography to codify information is closely related to its use in recognizing images. In this case, when a hologram is photographed, a special element, such as a diffusion glass, is placed in the channel of the reference beam to create a complex wave front. In order to see the reconstructed image it is necessary to use exactly the same reference wave. This is possible only if the same specimen of diffusion glass is used as was used when the hologram was photographed. A high degree of coding is associated with the fact that the reference beam that has passed through the diffusion glass is converted into an extended monochromatic light source, which appears as a set of a large number of point radiators having a particular relationship of amplitudes and phases. For this reason, the probability that different specimens of diffusion glass will be the same in the sense indicated is extremely small.

Figure 7. Holographic recognition of images

The use of holography to form specific wave fronts is of great interest. It is known, for example, that optical lenses cannot be made ideal but that they always cause distortions in the images formed by them. It is possible to prepare for every lens a hologram that will correct these distortions. The perfection of holographic techniques will make possible the development of special “holographic lenses,” which will be composed of an array of holograms prepared in advance and taking the place of lenses. They will be free of the aberrations of optical systems.

The holographic method is also applicable in cases of sonic and ultrasonic waves. If an object placed in an opaque fluid is acted upon by a sound generator, then it is possible to create a sound hologram on the surface of the fluid (Figure 8). This

Figure 8. Acoustic holography

makes necessary an auxiliary source of sound to create a reference wave. If the sound hologram formed by the interference of the sound waves (reference and signal) is illuminated with a laser, then it is possible to see a three-dimensional image of the object. Acoustic holography is especially important in studying the internal organs of animals and humans.


Leith, E., and J. Upatnieks. “Fotografirovanie s pomoshch’iu lazerov.” Uspekhi fizicheskikh nauk, 1965. vol. 87, issue 3.
Soroko, L. M. “Golografiia i intetferentsionnaia obrabotka informatsii.” Uspekhi fizicheskikh nauk, 1966, vol. 90, issue 1.
Mikaelian, A. L. Golografiia. Moscow, 1968.
Goodman, D. Vvedenie v Fur’e-optiku. Moscow, 1970. (Translated from English.)



A technique for recording, and later reconstructing, the amplitude and phase distributions of a wave disturbance; widely used as a method of three-dimensional optical image formation, and also with acoustical and radio waves; in optical image formation, the technique is accomplished by recording on a photographic plate the pattern of interference between coherent light reflected from the object of interest, and light that comes directly from the same source or is reflected from a mirror.


the science or practice of producing holograms