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