Page 471 - Introduction to Information Optics

456 8. Information Storage with Optics

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

2
2
2
2
2
\O + R\ R = \0 R + (K| R + 0\R + 0*R . (8.10)
The third term is of particular interest. If R represents a plane wave, Rf is
constant across the photographic plate, and the third term is proportional to
the complex amplitude 0 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

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 advantage-
ous 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