Holography

Principle of holography

When one Photography a traditional object of way, one records on a Sensitive plate the Luminosité of the various points of this object. In other words, only the power per unit of area of the light waves emitted by this object is taken into account.

One cannot record the phase of the light. No significant surface (Retina, photographic plate, sensor with semiconductor, etc) is sensitive to the phase. In a hologram one circumvents this difficulty while making interfere the light coming from the scene with a standard beam of coherent Lumière with the light illuminant the scene. In such manner, which one records on the photographic plate is an interferometric image formed by more or less luminous zones. The most luminous zones will be those in which the light coming from the scene and that of the standard beam are in phase. This luminosity will also depend on the amplitude of the light coming from the scene.

The hologram thus recorded and treated will be read in the illuminant with a beam of light Monochromatique similar to that used like reference. The hologram will let pass more light to the places where the amplitude of the light coming from the scene was larger is especially where the phase of this light was close to that of the standard beam. The hologram does not record really the phase of the light (it is impossible) but it records the places where the phase " was the bonne". Thus, during the reading, the phase of the light which leaves the hologram is not identical to the phase of the light which recorded it, but it is sufficiently close so that this Information of phase makes it possible to restore the Depth object and to recreate the real image (with the optical direction) of the scene.

The aspect of a hologram is that of a more or less uniform film gray. The details are practically invisible because they are of size comparable with the Wavelength of the light (a half-micrometer for the green).

Recording of a hologram

To record a Hologram, it is necessary to manage to code on a support the amplitude and the phase of the light resulting from the object considered. For that, one makes interfere two beams coherent on a photographic plate. The first beam, called wave of reference , is sent directly on the plate. The second, called wave object, is sent on the object to photograph, which diffuses this light in direction of the photographic plate. The figure of interferences thus formed contains all information concerning the amplitude and the phase of the wave object, i.e. the shape and the position of the object in space.

Since it utilizes a phenomenon of interferences, the holographic recording is not possible that if the light used is coherent, i.e.:

Monochromatic (temporal coherence)
in phase (temporal coherence)
directing (space coherence)

The only source of light which answers these requirements is the Laser.

One mentions since 1973 ( IBM Systems Journal ), and with irregular intervals since, the experimental creation of holograms per computer (Infographie), i.e. the direct realization of a network calculated starting from a digital model of the image to obtain. But this slow and thus not-interactive operation being (for the moment), it did not upset the profession.

Reading of a hologram

After development of the photographic plate, one lights this one with the wave of reference. In practice it can be a question of the laser used during the recording, illuminant the plate with the same angle of incidence. The wave restored by the plate is then a wave identical to the wave object, with the same amplitude and the same phase as during the recording. By looking at a hologram, we have really the impression that the object is located in front of us. However the colors are generally not restored, because of the use of a monochromatic laser source.

Certain holograms can also be looked with a non-cohesive light: the depth of the well restored image is all the more large as this incidental light is more directing and monochromatic. Holograms not too major thus are very suitably restored when they are directly exposed in the light of the Sun, directive only with one near and at all monochromatic half-degree.

Numerical holography

It as should be mentioned as, for a few years, a new branch of holography has developed: numerical holography. Indeed, thanks to progress in the field of the numeric cameras and that of the computers, it is now possible to record a hologram on a numeric camera, and to rebuild the object numerically by simulating the process of illumination of the hologram with a " wave of reference numérique".

This idea was proposed for the first time in 1967 by J.W Goodman and R.W Laurence in the article image formation from electronically detected holograms". They still recorded the hologram on a photographic plate, but they sampled it in a numerical way in order to rebuild the object numerically. Complete numerical holography in the direction of the recording and the rebuilding was carried out first of all by O. Coquoz and Al (O. Coquoz and Al " Numerical rebuilding off images from endoscopic holograms, " off present to 14th Annual International Conference the IEEE - EMBS, Paris, IEEE, p.338-339, 1992.) then by U. Schnars and W. Jüptner in 1994 when they introduced a camera CCC like support of recording (). In 1999, Cuche and Al applied numerical holography to microscopy and showed that, starting from a single numerical hologram, one can measure the quantitative values of the amplitude and phase of a wave, with a side resolution about the micron (similar to traditional microscopy) and especially with an axial resolution about the nanometer (,). Since this date, many groups throughout the world work on the subject of numerical holography.

The advantage of this technique is the possibility of recording holograms at video frequencies and thus of obtaining quantitative sights tridimentionnelle of objects in real-time. Moreover, it was shown that, with the introduction of objectives of microscopes, it is possible quantitatively to represent the shape of microscopic objects like cells (). Lastly, like the process of rebuilding is done numerically, it is possible to apply digital processings to the hologram or in the process in order to improve quality of the images, to change the position of the plan of rebuilding or to compensate for the aberrations.

Brief formalism for the recording and the reading

In a point of the photographic support, illumination $E$ is:

$E= (O+R) (O+R) ^*$

where $O$ is the complex amplitude of the wave object and $R$ that of the wave of reference. This expression of illumination takes account of the interference between the two concerned waves. All the sizes considered depend on the point of the hologram considered, i.e of the variable of space $\ vec r$ .

Let us adopt the simple approach of a hologram functioning in transmission, whose transmittance is simply proportional to illumination:

$t=A*E=A* (OO^*+RR^*+OR^*+RO^*)$

When one comes to read again this hologram with a wave of reading equal to the wave of reference $R$ , we obtain a wave diffracted whose amplitude complexes $U$ is given by:

$U=t*R=A*$ .

Here, one considered waves of unit amplitude, i.e. $OO^*=1$ and $RR^*=1$ .

Let us clarify these three terms:

the first $O$ term is the restitution of the wave object (order +1 of diffraction)
the second $2*R$ term is order 0 of diffraction (transmission of the wave of reading $R$ )
the third term is the combined wave object (order -1 of diffraction)

The perception of the object by the observer is done thanks to the first term.

Types of holograms

3 holographic forms of mediums are distinguished:

mean supports
holograms with modulation of surface, such as the holographic holograms rainbow presenting a mirror effect, or cameras without effect mirror
holograms of volume (in photorefractive materials for example)

One also distinguishes two types of operation of hologram. If the wave of reference and the wave object are same side compared to the holographic support during the recording, one speaks about hologram by transmission. In the contrary case it is about hologram by reflection.

Applications of holography

Holographic imagery

Holograms of rare or fragile objects exposed in the museums
Publicity
Industry of leisures (plays, memories, etc)

Protection

Protection against the counterfeits (bank cards, passports, indentity cards, visas, banknotes, etc)
Monitoring of access (holographic badges)

Storage of Information

The holography of volume for example makes it possible to record a very great number of images in a restricted volume. In theory, such an optical memory would make it possible to store approximately 10¹⁴ bits per cm ³.

Reading

Holography makes it possible for example to replace a screen and to perceive a film or an emission in 3D

Control - Measurement

three-dimensional Positioning of small object (about 10 100 times have the wavelength of refers). This technique is in particular used for the localization of tracer in a jet in mechanics of the fluids. The advantage of this method is that it requires one sensor for a positioning 3D (thus less calibration).
the holographic interferometry allows, by comparing the hologram of an object in a state given to the hologram of this object or the object itself in another state, to measure and detect the defects of structures or endurance. One obtains a result similar to the moire : the difference between the object and the image generates clear and dark fringes.

Sources

TABOURY, Jean. Holography . Course of the University of Optics, 2002.
Museum of Holography: www.museeholographie.com, (4/20/2004), < http://www.museeholographie.com/ >
TPE Holography: http://www.tpe1s2.com http://holographie2.free.fr

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