processing capability of the Vander Lugt filter. To produce powerful
yet practical CGH filters, the space-bandwidth product and dynamic
range of the hologram must be understood and minimized within design
criteria.
One key to reducing the space-bandwidth product of the CGH is to
recognize that much of the spectrum is not useful information. The
terms in Figure 3.5 are described as the convolution of f and g, the
baseband terms ffti and the correlation of f and g. Only the
correlation term is useful for our purposes in the Vander Lugt filter,
but the other terms arrive as a by-product of the square law nature of
the film. The two heterodyned terms which result in the convolution
and correlation of f and g must come as a pair. That is, when the real
part of the heterodyned information is recorded, the plus and minus
frequencies exist. The real part, cos e, can be written as
exp(je)+exp(-je) using Euler's formula. The plus and minus exponents
give rise to the plus and minus frequency terms which become the
convolution and correlation terms. The convolution and correlation
terms are always present in a spatially modulated hologram.
A more efficient hologram is produced using equation 3.5. This
hologram consists of a D.C. term sufficiently large to produce only
non-negative values and the heterodyned terms.
H(u,v) = A2 + F(u,v)ej2'av + F*(u,v)e-j27av (3.17)
The output (shown in Figure 3.9) of the Vander Lugt filter using this
hologram is
O(u,v) = A2G(u,v) + F(u,v)G(u,v)ej2Tav + F*(u,v)G(u,v)e-j2rav (3.18)