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

Date

2000-01-15

Author

Ozgen, MT

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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.

Subject Keywords

Cohen's bilinear class of space-frequency representations, Particle-field analysis, In-line Fresnel holograms, Inverse Radon transform, Radon transform, Ambiguity function

URI

https://hdl.handle.net/11511/63886

Journal

OPTICS COMMUNICATIONS

DOI

https://doi.org/10.1016/s0030-4018(99)00571-4

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Department of Electrical and Electronics Engineering, Article

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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: https://hdl.handle.net/11511/63886.