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