User:Epzcaw/holography

For other uses, see User:Epzcaw/holography (disambiguation).

Figure 1: Two photographs of a single hologram taken from different viewpoints

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Holography (from the Greek ὅλος hólos, "whole" + γραφή grafē, "writing, drawing") is a technique that allows the light scattered from an object to be recorded and later reconstructed so that when an imaging system (a camera or an eye) is placed in the reconstructed beam, an image of the object will be seen even when the object is no longer present. The image changes as the position and orientation of the viewing system changes in exactly the same way as if the object were still present, thus making the image appear three-dimensional. This effect can be seen in the figure on the right where the orientation of the mouse is significantly different in the two images and its position relative to other parts of the scene has changed. The holographic recording itself is not an image – it consists of an apparently random structure of either varying intensity, density or profile – an example can be seen in Figure 4 below.

Most holograms produced are of static objects but systems for displaying changing scenes on a holographic volumetric display are now being developed.

Holograms can also be used to store, retrieve, and process information optically.

Overview and history

Holography was invented in 1947 by the Hungarian-British physicist Dennis Gabor (Hungarian name: Gábor Dénes), work for which he received the Nobel Prize in Physics in 1971. Pioneering work in the field of physics by other scientists including Mieczysław Wolfke resolved technical issues that previously had prevented advancement. The discovery was an unexpected result of research into improving electron microscopes at the British Thomson-Houston Company in Rugby, England, and the company filed a patent in December 1947 (patent GB685286). The technique as originally invented is still used in electron microscopy, where it is known as electron holography, but optical holography did not really advance until the development of the laser in 1960.

The first practical optical holograms that recorded 3D objects were made in 1962 by Yuri Denisyuk in the Soviet Union and by Emmett Leith and Juris Upatnieks at University of Michigan, USA. Early holograms used silver halide photographic emulsions as the recording medium. They were not very efficient as the grating produced absorbed much of the incident light. Various methods of converting the variation in transmission to a variation in refractive index (known as "bleaching") were developed which enabled much more efficient holograms to be produced.

Several types of holograms can be made. Transmission holograms, such as those produced by Leith and Upatnieks, are viewed by shining laser light through them and looking at the reconstructed image from the side of the hologram opposite the source. A later refinement, the "rainbow transmission" hologram, allows more convenient illumination by white light rather than by lasers. Rainbow holograms are commonly seen today on credit cards as a security feature and on product packaging.

Another kind of common hologram, the reflection or Denisyuk hologram, can also be viewed using a white-light illumination source on the same side of the hologram as the viewer and is the type of hologram normally seen in holographic displays. They are also capable of multicolour-image reproduction.

Specular holography is a related technique for making three-dimensional images by controlling the motion of specularities on a two-dimensional surface. It works by reflectively or refractively manipulating bundles of light rays, whereas Gabor-style holography works by diffractively reconstructing wavefronts.

In its early days, holography required high-power expensive lasers, but nowadays, mass-producsed low-cost semi-conductor lasers, such as those found in millions of DVD recorders and used in other common applications, can be used to make holograms and have made holography much more accessible to low-budget researchers, artists and dedicated hobbyists.

It was thought that it would be possible to use X-rays to make holograms of molecules and view them using visible light. However, X-ray holograms have not been created to date.

How holography works

Figure 2: Optical arrangement for recording a hologram

Figure 3: Optical arrangement for reconstructing a hologram

Figure 4: Photograph of the recorded interference pattern in an amplitude-modulation hologram

Holographyis a technique which enables a light field, which is generally the product of a light source scattering off objects, to be recorded and later reconstructed when the original light field is no longer present (due to the absence of the original objects). Holography can be thought of as somewhat similar to sound recording, whereby a sound field created by vibrating matter, like musical instruments or vocal chords, is encoded in such a way that it can be reproduced later without the presence of the original vibrating matter.

Holograms are recorded using a flash of light that illuminates a scene and then imprints on a recording medium, much in the way a photograph is recorded. A hologram, however, requires a laser as the light source, since lasers can be precisely controlled and have a fixed wavelength, unlike white light, which contains many different wavelengths.

A shutter is required when taking a photograph to limit the time in which the film is exposed ot light. Holography also requires a specific exposure time, and this can be done using a shutter, or by electronic timing of the laser.

This laser beam is generally aimed through a series of elements that change it in different ways - see Figure 2. The first element is a beam splitter, which divides the beam into two identical beams, each aimed in different directions:

• One beam, known as the illumination or object beam, is spread using lenses and directed onto the scene using mirrors, in order to illuminate it. Some of the light scattered (reflected) from this illumination falls onto the recording medium.
• The second beam, known as the reference beam, is also spread through the use of lenses, but is directed so that it doesn't come in contact with the scene, and instead travels directly onto the recording medium.

There are several different materials which can be used as the recording medium. One of the commonest is silver-halide photographic emulsion which uses the same materials as photographic film but with much higher grain density i.e. of much higher resolution. A layer of the recording medium is attached to a transparent substrate which is normally glass, but may be plastic.

On the recording medium, the light waves of the two beams intersect and interfere with each other. It is this interference pattern that is imprinted on the holographic medium. The pattern itself is seemingly random, as this pattern represents the way in which the scene's light interfered with the original light source, but not the original light source itself. The interference pattern can be said to be an encoded version of the scene, requiring a particular key, that is, the original light source, in order to view its contents. This missing key is provided later by shining a laser, identical to the one used to record the hologram, onto the developed film which then recreates a range of the scene's original light.

When the original reference beam illuminates the hologram, it is diffracted by the recorded hologram to produce a light field which is identical to the light field which was originally scattered by the object or objects onto the hologram - see Figure 3. When the object is removed, an observer who looks into the hologram "sees" the same image on his retina as he would have seen when looking at the original scene. This image is known as a virtual image.

Figure 4 is a photograph of a hologram's surface. The object in the hologram is a toy van. It can be seen that it is no more possible to discern the subject of the hologram from this pattern than it is to identify what music has been recorded by looking at the hills and valleys on a vinyl record surface, or the pits on a CD. Also note that the holographic recording is described by the speckle pattern, rather than the "wavy" line pattern; the latter being an incidental result of interference between multiple reflections in the glass plate on which the film is mounted.

Holography vs. photography

Each point in the holographic recording includes light scattered from every point in the scene, whereas each point in a photograph has light scattered only from a single point in the scene which has been focused by a lens onto the film or the digital capture medium.

A hologram differs from a photograph in several ways:

• The hologram allows the recorded scene to be viewed from a wide range of angles whereas the photograph gives only a single view.
• The reproduced range of a hologram adds many of the same depth perception cues that were present in the original scene, which are again recognized by the human brain and translated into the same perception of a three-dimensional image as when the original scene might have been viewed. The photograph is a flat two-dimensional representation.
• The developed hologram surface itself consists of a very fine, seemingly random pattern, which appears to bear no relationship to the scene which it has recorded. A photograph clearly maps out the light field of the original scene.
• When a photograph is cut in two, each part shows only half the scene. When a hologram is cut in two, the whole scene can still be seen in each half. Think of viewing a street outside your house through a 4ft x 4ft window, and then through a 4ft x 2ft window; You can see the same things through the smaller window, but you can see more at once through the 4ft window and you may need to cahnge your viewing position to see everything in the smaller window.
• A photograph can be viewed in a wide range of lighting conditions, whereas holograms can only be viewed with very specific forms of illumination.

Physics of holography

For a better understanding of the process, it is necessary to understand interference and diffraction. Interference occurs when one or more wavefronts are superimposed. Diffraction occurs whenever a wavefront encounters an object. The process of producing a holographic reconstruction is explained below purely in terms of interference and diffraction. It is somewhat simplified but is accurate enough to provide an understanding of how the holographic process works.

For those unfamiliar with these concepts, it is worthwhile to read the respective articles before reading further in this article.

Plane wavefronts

A diffraction grating is a structure with a repeating pattern. A simple example is a metal plate with slits cut at regular intervals. A light wave incident on a grating is split into several waves; the direction of these diffracted waves is determined by the grating spacing and the wavelength of the light.

A simple hologram can be made by superimposing two plane waves from the same light source on a holographic recording medium. The two waves interfere giving a straight line fringe pattern whose intensity varies sinusoidally across the medium. The spacing of the fringe pattern is determined by the angle between the two waves, and on the wavelength of the light.

The recorded light pattern is a diffraction grating. When it is illuminated by only one of the waves used to create it, it can be shown that one of the diffracted waves emerges at the same angle as that at which the second wave was originally incident so that the second wave has been 'reconstructed'. Thus, the recorded light pattern is a holographic recording as defined above.

Point sources

Figure 5: Sinusoidal zone plate

If the recording medium is illuminated with a point source and a normally incident plane wave, the resulting pattern is a sinusoidal zone plate which acts as a negative Fresnel lens whose focal length is equal to the separation of the point source and the recording plane.

When a plane wavefront illuminates a negative lens, it is expanded into a wave which appears to diverge from the focal point of the lens. Thus, when the recorded pattern is illuminated with the original plane wave, some of the light is diffracted into a diverging beam equivalent to the original plane wave; a holographic recording of the point source has been created.

When the plane wave is incident at a non-normal angle, the pattern formed is more complex but still acts as a negative lens provided it is illuminated at the original angle.

Complex objects

To record a hologram of a complex object, a laser beam is first split into two separate beams of light. One beam illuminates the object, which then scatters light onto the recording medium. According to diffraction theory, each point in the object acts as a point source of light so the recording medium can be considered to be illuminated by a set of point sources located at varying distances from the medium.

The second (reference) beam illuminates the recording medium directly. Each point source wave interferes with the reference beam, giving rise to its own sinusoidal zone plate in the recording medium. The resulting pattern is the sum of all these 'zone plates' which combine to produce a random (speckle) pattern as in the photograph above.

When the hologram is illuminated by the original reference beam, each of the individual zone plates reconstructs the object wave which produced it, and these individual wavefronts add together to reconstruct the whole of the object beam. The viewer perceives a wavefront that is identical to the wavefront scattered from the object onto the recording medium, so that it appears to him or her that the object is still in place even if it has been removed. This image is known as a "virtual" image, as it is generated even though the object is no longer there.

Mathematical model

A light wave can be modelled by a complex number U, which represents the electric or magnetic field of the light wave. The amplitude and phase of the light are represented by the absolute value and angle of the complex number. The object and reference waves at any point in the holographic system are given by U_O and U_R. The combined beam is given by U_O + U_R. The energy of the combined beams is proportional to the square of magnitude of the combined waves as:

$|U_{O}+U_{R}|^{2}=U_{O}U_{R}^{*}+|U_{R}|^{2}+|U_{O}|^{2}+U_{O}^{*}U_{R}$

If a photographic plate is exposed to the two beams and then developed, its transmittance, T, is proportional to the light energy that was incident on the plate and is given by

$T=kU_{O}U_{R}^{*}+k|U_{R}|^{2}+k|U_{O}|^{2}+kU_{O}^{*}U_{R}$

where k is a constant.

When the developed plate is illuminated by the reference beam, the light transmitted through the plate, U_H is equal to the transmittance T multiplied by the reference beam amplitude U_R, giving

$U_{H}=TU_{R}=kU_{O}|U_{R}|^{2}+k|U_{R}|^{2}U_{R}+k|U_{O}|^{2}U_{R}+kU_{O}^{*}U_{R}^{2}$

It can be seen that U_H has four terms, each representing a light beam emerging from the hologram. The first of these is proportional to U_O. This is the reconstructed object beam which enables a viewer to 'see' the original object even when it is no longer present in the field of view.

The second and third beams are modified versions of the reference beam. The fourth term is known as the "conjugate object beam". It has the reverse curvature to the object beam itself and forms a real image of the object in the space beyond the holographic plate.

When the reference and object beams are incident on the holographic recording medium at significantly different angles, the virtual, real and reference wavefronts all emerge at different angles, enabling the reconstructed object to be seen clearly.

Recording a hologram

Items required

Figure 6: An optical table being used to make a hologram

To make a hologram, the following are required:

• a suitable object or set of objects
• a suitable laser beam
• optical components which enable the laser beam to be split into two, with one beam (the object beam) directed onto the object, and the other beam (the reference beam) directed onto the recording medium, enabling an interference pattern between the object beam and the reference beam to be created
• a recording medium which converts this interference pattern into an optical element which which modifies either the amplitude or the phase of an incident light beam according to the intensity of the interference pattern.
• an environment which provides sufficient mechanical and thermal stability that the interference pattern is stable during the time in which the interference pattern is recorded

These requirements are inter-related, and it is essential to understand the nature of optical interference to see this. Interference is the variation in intensity which can occur when two light waves are superimposed. The intensity of the maxima exceeds the sum of the individual intensities of the two beams, and the intensity at the minima is less than this and may be zero. The interference pattern maps the relative phase between the two waves, and any change in the relative phases causes the interference pattern to move across the field of view. If the relative phase of the two waves changes by one cycle, then the pattern drifts by one whole fringe. One phase cycle corresponds to a change in the relative distances travelled by the two beams of one wavelength. Since the wavelength of light is of the order of 0.5μm, it can be seen that very small changes in the optical paths travelled by either of the beams in the holographic recording system lead to movement of the interference pattern which is the holographic recording. Such changes can be caused by relative movements of any of the optical components, and also by local changes in air-temperature. It is essential that any such changes are significantly less than the wavelength of light if a clear well-defined recording of the interference is to be created.

The exposure time required to record the hologram depends on the laser power available, on the particular medium used and on the size and nature of the object(s) to be recorded, just as in conventional photography. This determines the stability requirements. Exposure times of several minutes are typical when using quite powerful gas lasers and silver halide emulsions. All the elements within the optical system have to be stable to fractions of a μm over that period. It is possible to make holograms of much less stable objects by using a pulsed laser which produces a large amount of energy in a very short time (μs or less). These systems have been used to produce holograms of live people. A holographic portrait of Dennis Gabor was produced in 1971 using a pulsed ruby laser.

Thus, the laser power, recording medium sensitivity, recording time and mechanical and thermal stability requirements are all interlinked.

Another very important laser parameter is its coherence. This be envisaged by considering a laser to produce a sine wave whose frequency drifts over time; the coherence length can then be considered to be the distance over which it maintains a single frequency. This is important because two waves of different frequencies do not produce a stable interference pattern. The coherence length of the laser determines the depth of field which can be recorded in the scene. A good holography laser will typically have a coherence length of several meters, ample for a deep hologram.

The objects that form the scene must, in general, have optically rough surfaces so that they scatter light over a wide range of angles. A specularly reflecting (or shiny) surface reflects the light in only one direction at each point on its surface, so in general, most of the light will not be incident on the recording medium. Holograms of flat shiny objects have been made by locating it very close to the recording plate.

Hologram classifications

There are three important properties of a hologram which are defined in this section. A given hologram will have one or other of each of these three properties, e.g. we can have an amplitude modulated thin transmission hologram, or a phase modulated, volume reflection hologram.

Amplitude and phase modulation holograms

An amplitude modulation hologram is one where the amplitude of light diffracted by the hologram is proportional to the intensity of the recorded light. A straightforward example of this is photographic emulsion on a transparent substrate. The emulsion is exposed to the interference pattern, and is subsequently developed giving a transmittance which varies with the intensity of the pattern - the more light that fell on the plate at a given point, the darker the developed plate at that point.

A phase hologram is made by changing either the thickness or the refractive index of the material in proportion to the intensity of the holographic interference pattern. This is a phase grating and it can be shown that when such a plate is illuminated by the original reference beam, it reconstructs the original object wavefront. The efficiency (i.e. the fraction of the illuminated beam which is converted to reconstructed object beam) is greater for phase then for amplitude modulated holograms.

Thin holograms and thick (volume) holograms

A thin hologram is one where the thickness of the recording medium is much less than the spacing of the interference fringes which make up the holographic recording.

A thick or volume hologram is one where the thickness of the recording medium is greater than the spacing of the interference pattern. The recorded hologram is now a three dimensional structure, and it can be shown that incident light is diffracted by the grating only at a particular angle, known as the Bragg angle. If the hologram is illuminated with a light source incident at the original reference beam angle but a broad spectrum of wavelengths, reconstruction occurs only at the wavelength of the original laser used. If the angle of illumination is changed, reconstruction will occur at a different wavelength and the colour of the re-consturcted scene changes. A volume hologram effectively acgts as a colour filter.

Transmission and reflection holograms

A transmission hologram is one where the object and reference beams are incident on the recording medium from the same side. An optical arrangement for making a transmission hologram is shown in Figure 2. In practice, several more mirrors may be used to direct the beams in the required directions.

Normally, transmission holograms can only be reconstructed using a laser or a quasi-monochromatic source, but a particular type of transmission hologram, known as a rainbow hologram, can be viewed with white light.

In a reflection hologram, the object and reference beams are incident on the plate from opposite sides of the plate. The reconstructed object is then viewed from the same side of the plate as that at which the re-constructing beam is incident.

Only volume holograms can be used to make reflection holograms, as only a very low intensity diffracted beam would be reflected by a thin hologram.

Holographic recording media

The recording medium has to convert the original interference pattern into an optical element that modifies either the amplitude or the phase of an incident light beam in proportion to the intensity of the original light field.

The recording medium should be able to resolve fully all the fringes arising from interference between object and reference beam. These fringe spacings can range from tens of microns to less than one micron, i.e. spatial frequencies ranging from a few hundred to several thousand cycles/mm, and ideally, the recording medium should have a response which is flat over this range. If the response of the medium to these spatial frequencies is low, the diffraction efficiency of the hologram will be poor,and a dim image will be obtained. It should be noted that standard photographic film has a very low, or even zero, response at the frequencies involved and cannot be used to make a hologram - see, for example, Kodak's professional black and white film whose resolution starts falling off at 20 lines/mm and it is unlikely than any reconstructed beam would be obtained using this film.

If the response is not flat over the range of spatial frequencies in the interference pattern, then the resolution of the reconstructed image may also be degraded.

The table below shows the principal materials used for holographic recording. Note that these do not include the materials used in the mass replication of an existing hologram which are discussed in the next section. The resolution limit given in the table indicates the maximal number of interference lines/mm of the gratings. The required exposure is for a long exposure. Short exposure times (less than 1/1000 of a second, such as with a pulsed laser) require a higher exposure due to reciprocity failure.

General properties of recording materials for holography. Source:

Material	Reusable	Processing	Type of hologram	Theoretical maximum efficiency	Required exposure [mJ/cm2]	Resolution limit [mm−1]
Photographic emulsions	No	Wet	Amplitude	6%	1.5	5000
			Phase (bleached)	60%
Dichromated gelatin	No	Wet	Phase	100%	100	10,000
Photoresists	No	Wet	Phase	30%	100	3,000
Photothermoplastics	Yes	Charge and heat	Phase	33%	0.1	500–1,200
Photopolymers	No	Post exposure	Phase	100%	10000	5,000
Photorefractives	Yes	None	Phase	100%	10	10,000

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Embossing and mass production

An existing hologram can be replicated, either optically, similar to holographic recording or in the case of surface relief holograms, by embossing. Surface relief holograms are recorded in photoresists or photothermoplastics and allow cheap mass reproduction. Such embossed holograms are now widely used, for instance, as security features on credit cards or quality merchandise. The Royal Canadian Mint even produces holographic gold and silver coinage through a complex stamping process. The first book to feature a hologram on the front cover was The Skook (Warner Books, 1984) by JP Miller, featuring an illustration by Miller. That same year, "Telstar" by Ad Infinitum became the first record with a hologram cover and National Geographic published the first magazine with a hologram cover.

The first step in the embossing process is to make a stamper by electrodeposition of nickel on the relief image recorded on the photoresist or photothermoplastic. When the nickel layer is thick enough, it is separated from the master hologram and mounted on a metal backing plate. The material used to make embossed copies consists of a polyester base film, a resin separation layer and a thermoplastic film constituting the holographic layer.

The embossing process can be carried out with a simple heated press. The bottom layer of the duplicating film (the thermoplastic layer) is heated above its softening point and pressed against the stamper, so that it takes up its shape. This shape is retained when the film is cooled and removed from the press. In order to permit the viewing of embossed holograms in reflection, an additional reflecting layer of aluminum is usually added on the hologram recording layer. Embossed holograms are used widely on credit cards, banknotes, and high value products.

It is possible to print holograms directly into steel using a sheet explosive charge to create the required surface relief.

Reconstructing and viewing the holographic image

When the hologram plate is illuminated by a laser beam identical to the reference beam which was used to record the hologram, an exact reconstruction of the the original object wavefront is obtained. An imaging system (an eye or a camera) located in the reconstructed beam 'sees' exactly the same scene as it would have done when viewing the original. When the lens is moved, the image changes in the same way as it would have done when the object was in place, as illustrated in Figure 1. If several objects were present when the hologram was recorded, the reconstructed objects move relative to one another, i.e. exhibit parallax, in the same way as the original objects would have done. It was very common in the early days of holography to use a chess board as the object and then take photographs at several different angles using the reconstructed light to show how the relative positions of the chess pieces appeared to change.

A holographic image can also be obtained using a different laser beam configuration to the original recordign object beam, but the reconstructed image will not match the original exactly.. When a laser is used to reconstruct the hologram, the image is speckled just as the original image will have been. This can be a major drawback in viewing a hologram.

White light consists of light of a wide range of wavelengths. Normally, if a hologram is illuminated by a white light source, each wavelength can be considered to generate its own holographic reconstruction, and these will vary in size, angle, and distance. These will be superimposed, and the summed image will wipe out any information about the original scene, just as if you superimposed a set of photographs of the same object of different sizes and orientations. However, a holographic image can be obtained using white light in specific circumstances, e.g. with volume holograms and rainbow holograms.The white light source used to view these holograms should always approximate to a point source, i.e. a spot light or the sun. An extended source (e.g. a flourescent lamp) will not reconstruct a hologram since it light is incident at each point at a wide range of angles, giving multiple reconstructions which will "wipe" one another out.

White light reconstructions do not contain speckles.

Volume holograms

A volume hologram can give a reconstructed beam using white light, as the hologram structure effectively filters out colours other than those equal to or very close to the colour of the laser used to make the hologram so that the reconstructed image will appear to be approximately the same colour as the laser light used to create the holographic recording.

Rainbow holograms

Figure 7: Rainbow hologram showing the change in colour in the vertical direction

In this method, parallax in the vertical plane is sacrificed to allow a bright well-defined single colour re-constructed image to be obtained using white light. The rainbow holography recording process uses a horizontal slit to eliminate vertical parallax in the output image. The viewer is then effectively viewing the holographic image through a narrow horizontal slit. Horizontal parallax information is preserved but movement in the vertical direction produces colour rather than different vertical perspectives. Stereopsis and horizontal motion parallax, two relatively powerful cues to depth, are preserved.

The holograms found on credit cards are examples of rainbow holograms. These are technically transmission holograms mounted onto a reflective surface like a metalized polyethylene terephthalate substrate commonly known as PET.

Fidelity of the reconstructed beam

To replicate the original object beam exactly, the reconstructing reference beam must be identical to the original reference beam and the recording medium must be able to fully resolve the interference pattern formed between the object and reference beams. Exact reconstruction is required in holographic interferometry, where the holographically reconstructed wavefront interferes with the wavefront coming from the actual object, giving a null fringe if there has been no movement of the object and mapping out the displacement if the object has moved. This requires very precise relocation of the developed holographic plate.

Any change in the shape, orientation or wavelength of the reference beam gives rise to aberrations in the reconstructed image. For instance, the reconstructed image is magnified if the laser used to reconstruct the hologram has a shorter wavelength than the original laser. Nonetheless, good reconstruction is obtained using a laser of a different wavelength, quasi-monochromatic light or white light, in the right circumstances.

Since each point in the object illuminates all of the hologram, the whole object can be reconstructed from a small part of the hologram. Thus, a hologram can be broken up into small pieces and each one will enable the whole of the original object to be imaged. One does, however, lose information and the spatial resolution gets worse as the size of the hologram is decreased — the image becomes "fuzzier". The field of view is also reduced, and the viewer will have to change position to see different parts of the scene.