as possible to one. That is, the quantity z f.gi-112, is minimized

where f is the SDF and the gi's are the images in the training set.

 A constraint on the number of images in the training occurs when

the dynamic range is limited. To illustrate this, note that if the

medium on which the SDF will be reproduced has limited dynamic range,

small values can not be recorded on the same medium as the large

values. The images with larger weights will appear in the SDF of

limited dynamic range, while the images with smaller weights will be

lost in the noise. As more and more images are combined into the SDF,

the sums will become large but the small details in any one image will

be too small to appear in the recorded SDF image. This problem is

greatly simplified by leaving the SDF in the computer where the

dynamic range is not practically limited. That is, to create the

hologram pattern on the computer rather than producing the hologram

optically. As was shown in chapter 3, the dynamic range can be

reduced by eliminating unnecessary terms from the hologram. However,

when producing the hologram optically, the SDF image must be displayed

on a device with a definite limit to its dynamic range. This

restriction is quite severe and frequently prevents the use of SDFs in

optically-generated holographic matched filters. This can be somewhat

eliminated by the judicious choice of weights to reduce the dynamic

range to a minimum while maintaining adequate performance.