to provide N unit vectors. The K cells in each component are "opened"
or "closed" to provide the appropriate weights for each component.
The control over the amplitude and phase is not absolute with finite N
and K. The result at each cell is the vector sum of components with
integer length and fixed direction. Figure 3.3 shows that various
combinations of points turned on or off define an array of specific
points addressable in the complex plane. By increasing the number of
points N and K, the amplitude and phase can be more accurately
matched. When the total number of plotter dots is limited and more
subcells used for each cell, fewer cells can exist. Thus, with a
limited number of points, the hologram designer must choose between
space-bandwidth product (number of cells) and quantization noise.
The GBCGH allows more accurate determination of the amplitude and
phase of the cell by using more points. However, the complex sample
to be represented was taken at the center of the aperture. If N, the
number of points in the cell, is large, the outer pixel may have
noticeable error due to the offset in sample location. Allebach12
showed that the Lohmann hologram fell into a class of digital
holograms which sample the object spectrum at the center of each
hologram cell to determine the transmittance of the entire cell. The
Lee hologram fell into a class of digital holograms which sample the
object spectrum at the center of each aperture to determine its size.
He also described a new third class in which the object is sampled at
each resolvable spot to determine the transmittance at that spot.
Although the function to be recorded should be constant over the
entire cell, there is some phase shift across the cell dimensions. By
sampling the object spectrum at the center of each aperture rather