Automatic kernel design procedure for Cohen's bilinear class of representations as applied to in-line Fresnel holograms

Ozgen, MT
Cohen's bilinear class of shift-invariant space-frequency representations provides an automated means for extracting three-dimensional particle locations from in-line Fresnel holograms without any focusing. Choosing kernel parameters of a fixed-kernel representation in order to achieve the trade-off between auto-term sharpness and cross-term suppression while processing a multiple-particle hologram is a tedious task, especially if the hologram considered is crowded. Hence, this paper proposes an automatic kernel design procedure in order to eliminate this parameter selection task altogether and obtain a signal adaptive representation that matches the particular hologram analyzed. An ambiguity function (AF) domain analysis of a two-dimensional (2-D), multiple-particle hologram reveals AF slices of it that carry the auto-term information. By applying the Radon transform (RT) and the inverse RT to moduli of these slices successively, a 2-D discrete AF domain kernel that matches the hologram is obtained in separable form. This procedure is used in our fixed-frequency slice technique recently proposed for 2-D holograms, and also in computing complete space-frequency patterns for one-dimensional holograms, for particle-location analysis of them.


Cohen's bilinear class of shift-invariant space/spatial-frequency signal representations for particle-location analysis of in-line Fresnel holograms
Ozgen, MT; Demirbaş, Kerim (The Optical Society, 1998-08-01)
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...
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Citation Formats
M. Ozgen, “Automatic kernel design procedure for Cohen’s bilinear class of representations as applied to in-line Fresnel holograms,” OPTICS COMMUNICATIONS, pp. 51–67, 2000, Accessed: 00, 2020. [Online]. Available: