Vander Lugt filter is

0(u,v) = F'(u,v)G(u,v)ej2rav + F*,(u,v)G(u,v)e-j2rav (3.21)

or

o(x,y) = f'(x,y)g(x,y)6(x,y+a) + f'(-x,-yg(x,y) (x,y-a) (3.22)


 = f'(x,y)g(x,y)@6(x,y+a) + Rf,g(x,y)@(x,y-a)


which gives the spectrum shown in Figure 3.10, assuming Bf=Bg=B.

This phase hologram reduces the number of points to 4B, a power of 2.

This is the smallest possible size in a spatially modulated hologram.

As will be shown later, the phase modulation process may significantly

affect the information, and the correlation obtained may be a poor

approximation to the ideal correlation.

 The Vander Lugt filter is typically used to detect the presence of

a small object in a large scene. This implies that Bf may be much

smaller than B In any case, the least theoretical hologram size

using equation 3.20 is still twice the size of the reference image and

test image combined in the y direction. For example, a large scene

consisting of 1024 by 1024 points is to be searched for an object that

would occupy 32 by 32 points in that scene. The smallest continuous-

tone hologram to perform that correlation would contain 2112 points in

the y direction (at least 1088 in the x direction). For most

practical applications, the absorption hologram illustrated in Figure

3.9 would be used. For the same example consisting of a 1024 by 1024

test scene and a 32 by 32 reference image, a square hologram would be

at least 2144 by 2144.

 Another practical consideration provides some relief in the size

of the correlation plane. The correlation of two images creates a