or
o(x,y) = A2g(x,y) + f(x,y)@g(x,y)~(x,y+a) + f(-x,-y)g(x,y)@S(x,y-a)
= A2g(x,y) + f(x,y)@g(x,y)@6(x,y+a) + Rfg(x,y)@S(x,y-a) (3.19)
which gives the spectrum shown in Figure 3.9 assuming Bf=Bg=B. Here
the spectrum extends to 5B rather than 7B and considerable space
saving is possible. However, the 5B is not a power of 2 and most
computer systems would still be forced to employ 8B points. The terms
in Figure 3.9 are the convolution term, the image term, and the
correlation term. The image term arises from the product of the D.C.
term with the test image g(x,y). In a normal absorption hologram, it
is not possible to eliminate the D.C. term. The image term takes up
the space from -B to B, forcing the spatial carrier frequency to 3B
and requiring 5B total space. If the absorption hologram is replaced
with a bleached hologram where the phase varies across the hologram,
the D.C. term may be eliminated.
As discussed in Chapter II, film may be bleached to produce a
phase modulation. This is accomplished at the expense of the
amplitude modulation. However, this phase hologram behaves much like
the original amplitude or absorption hologram. One advantage of the
bleaching process and the use of phase modulation is the opportunity
to eliminate the D.C. term (set it to zero) and reduce the space-
bandwidth product. Equation 3.17 is changed to
H(u,v) = F'(u,v)ej2;av + F*'(u,v)e-j2rav (3.20)
where the prime mark (') indicates the function has been modified by
the bleaching process. There is no D.C. term, so the output of the