## 851 Principle Of Holography

Holography was originally invented by Gabor [37] in 1948 to improve electron microscope images. Holography is a technique to record and to reconstruct wavefronts. Consider that we are in a room looking at an object, such as a flower, through a window. The light from the flower must transmit through the window to form an image on our retinas. If we could record the light at the window plane, then by reproducing the recorded light we would be able to see the flower, although there is no window. This cannot be done by traditional photographic techniques, because the recording medium is sensitive only to energy or light intensity and is not sensitive to phase. The light from the flower at the window plane is represented by its wavefront that has both amplitude and phase. The artificial window can only be made by recording and reconstructing the wavefront at the window plane. The wavefront can be recorded and later reconstructed by recording the interference pattern of the object wavefront and a reference wavefront [37]. Holography has been improved and made practical by Leith and Upatnieks [38], who introduced the concept of carrier frequency in 1962.

The principle of holography can be described briefly as follows. The recorded intensity on a hologram is

where 0 and R are complex amplitudes of object and reference beams, respectively, on the hologram plane. The symbol * indicates a complex conjugate. The amplitude transmittance of the hologram (which is a developed photographic plate) is proportional to the recorded intensity. When the hologram is illuminated by a reconstructing laser beam, which is the same as the reference beam when it was recorded, the wavefront of light transmitted through the hologram is given by

The third term is of particular interest. If R represents a plane wave, |i?|2 is constant across the photographic plate, and the third term is proportional to the complex amplitude O that is the original wavefront of the object on the hologram plane. It is important to note that following the scheme introduced by Leith and Upatnieks [38], propagation directions of the first, second, and fourth terms of Eq. (8.10) are separated from the propagation direction of the wavefront represented by the third term. Thus, in principle, the artificial window discussed previously can be realized using a hologram.

8.5.2, PLANE HOLOGRAPHIC STORAGE

Basic engineering concepts of holographic storage were introduced in the 1960s [39,40,41], following the publication of van Heerden's seminal papers [5,6]. For bit-pattern storage such as conventional high-density microfiche, even a small dust particle on the film can create a missing portion on the record, and the missing information can never be recovered. However, when using holograms for high-density recording, a scratch or dust on the film will not destroy information but merely causes a slight increase in the noise of the reconstructed image, so that no particular portion of the recording is lost [42], Consider that the information to be recorded is a string of bits, this string of bits being first arranged in a 2-D format called page memory. It is advantageous to record the Fourier-transform hologram of the page memory because the minimum space bandwidth is then required and the information about any one bit of the page memory is spread over the hologram plane [43].

In the simplest optical system, the page memory is displayed on a page composer which is a spatial-light modulator. A collimated coherent beam is modulated by the spatial-light modulator. The modulated light then passes through a lens that performs the Fourier transform of the page memory on the focal plane of the lens. A holographic medium records the interference pattern of a reference beam and the Fourier transform of the page memory on the focal plane. If the same reference beam is incident onto the recorded hologram, the Fourier transform of the page memory will be produced. The page memory can be reconstructed by passing its Fourier transform through another lens.

Equation (8.10) shows that only the same reference beam as was employed when the hologram was recorded will reconstruct the object. This characteristic provides multiplexing capability. A number of holograms can be recorded successively with reference beams having different incident angles on the same holographic plate. A specific angular reference beam would reconstruct only the object that was recorded with it at a certain position. Note that other objects are reconstructed at shifted positions. The multiplexing hologram can also be produced with reference beams having specific wavefronts [44], The wavefront is generated by passing a plane wave through a phase-only spattallight modulator. In fact, this phase modulator can also generate a wavefront similar to that of an oblique plane-wave reference beam.

Since the page memory must be displayed on a spatial-light modulator, and the reconstructed image of the page memory must be read by an array detector, the size of the page memory is restricted by the state of the art of the spatial-light modulator and the array detector. The size of the page memory is also restricted by the size of lenses and other optical elements used in the system. Based on today's technology, it should be realistic to construct a page memory that is 1000 x 1000 in size. Assuming the wavelength of light, X, is approximately 1 fim, a page memory in principle could be stored in an area of 1 mm2 either in a bit pattern or holographically.

The capacity of plane holographic storage might be larger than 10b bits, while the string of bits arranged in a page memory has only 106 bits. Consequently, many page memories can be stored in a plane hologram. As mentioned previously, one may apply angular multiplexing technique to superimpose a number of holograms on the same plate. However, larger optics and higher laser power are required to cover the whole holographic plate at one time. It is more practical to record each page memory in a tiny subhologram. Subholograms form an array on the holographic plate. A laser beam deflector is able to select a specific subhologram. In other words, a page memory is retrieved by addressing the read beam to a selected subhologram using the deflector. Figure 8.7 depicts the schematic diagram for plane holographic storage. Needless to say, the object beam in the recording is also deflected accordingly to form the subhologram array on the plate.

The experiment using an erasable magneto-optic MnBi thin film to record a 8 x 8 bit page memory was demonstrated by Rajchman in 1970 [45]. The MnBi thin film modulates the polarization of the read beam based on the Faraday effect and the Kerr effect in the transmissive and reflective modes, respectively. Note that the polarization modulation is actually phase modulation in two polarization directions. Thus, a MnBi thin film acts as a phase hologram and no analyzer is required in the reconstruction.

Instead of using beam deflectors, subholograms may be recorded on a moving media [46]. In fact, holographic disks consisting of 1-D subholograms have been experimentally demonstrated. The prototypes of a WORM holographic disk using a photographic plate and an erasable holographic disk using

Reconstructed

Fig. 8.7. Reference beam being addressed by a deflector to a subhologram on a holographic plane to retrieve a page memory.

a photorefractive layer were built by Kubota et al. in 1980 [47] and Mikaelian et al. in 1992 [48], respectively.

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