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