correlation image whose size is the sum of the individual image sizes.

Non-zero correlation values can exist when any points in the two

images overlap. However, the number of points which overlap becomes

very small near the outer edge of the correlation plane. In a

practical system, a threshold is set to determine correlations which

are "targets" (above threshold) or "background" (below background).

When the target fills the reference image and is entirely present in

the test image, the autocorrelation condition exists and the

correlation can be normalized to one. When the target begins to fall

off the edge of the test image, correlations will still occur.

However, the correlation value will fall from unity by the ratio of

the target area present in the test image to the target area in the

reference image. A practical rule of thumb might be to ignore the

correlations when half of the target falls outside the test image in

any direction. This reduces the correlation plane to the size of the

test image, offering some relief to the required hologram size. If

the outer edge of the correlation plane is ignored, it does not matter

if that edge is aliased. This reduces the sampling and heterodyning

requirements in the filter hologram especially when the reference

contains many points. When using the absorption hologram with 50%

aliasing (shown in Figure 3.11), the spatial frequency is


 a = Bg + Bf (3.23)


and the number of points in the hologram in the v direction (SBPv) is


 SBPv = 2Bg + 3/2 Bf. (3.24)


Phase encoding this hologram does not relieve the requirement on the