than at-the center of each hologram cell, some of the false images in

the reconstruction are removed. By sampling the object spectrum at

the center of each resolvable spot in the hologram, the hologram noise

is further reduced. Allebach described an encoding technique in this

last category known as the Allebach-Keegan (A-K) hologram.13 The A-K

hologram encodes the complex-valued object spectrum by quadrature

components as does the Lee hologram. Unlike the Lee hologram, the A-K

hologram compares subsamples within the aperture to an ordered dither

to determine whether each pixel is on or off. The input image is

padded to provide as many points in the FFT as there are resolvable

points. The FFT is decomposed into components spaced a quarter wave

apart (or more as in the GBCGH). Each point is then compared to a

threshold determined by the threshold matrix. The threshold values

are chosen to quantize the amplitude of each component. The threshold

values divide the range from zero to the spectrum maximum in steps

determined by the Max quantizer.27 The size of the dither matrix and

the corresponding points in the cell can increase as with the GBCGH

but the magnitude and phase are sampled at each pixel.

 Sampling and Space-Bandwidth Requirements

 To represent an image on a computer, the image must be sampled and

quantized into a set of numbers. To sample a continuous image or

function, the value of the function is determined at discrete points.

The values of a function f(x,y) are determined at regular intervals

separated by Ax and Ay. The continuous independent variables x and y

are replaced with discrete sample point denoted by mAx and ny .

Here AX and AY are the fixed sample intervals and m and n are

integers. The sampling rate is u=1/Ax in the x direction and v=1/Ay