## Abstract

The Cohen bilinear class of shift-invariant space-frequency representations provides an automated means for extracting three-dimensional particle locations from in-line holograms without any focusing. For two-dimensional holograms a fixed-frequency slice technique, based on examining, concurrently, the zero-frequency slice and a nonzero-frequency slice of the two-dimensional representation used, is developed for particle-location analysis. The trade-off between auto-term sharpness and cross-term suppression for a multiple-particle hologram is achieved by relating kernel parameters of the representation to the smallest planar interparticle distance determined from the hologram by visual inspection with simple rules that result from an ambiguity-function-domain analysis. In addition, one-dimensional Cohen class representations are used to obtain complete space-frequency patterns that display object-location information and illustrate the cross-term suppression, for multiple-object one-dimensional holograms. The proposed techniques are implemented digitally, and the results are presented.

© 1998 Optical Society of America

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