Optimum sampling of Fresnel transforms

VanderLugt, A.

doi:10.1364/ao.29.003352

Cited by 25 publications

(9 citation statements)

References 10 publications

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“…Several nonuniform sampling schemes have been suggested based on the observation that the bandwidth of the object remains unchanged as a consequence of the all-pass nature of the linear system that represents the diffraction [186], [187], [188]. Another approach observes that the information of interest in a hologram is carried in the complex envelope of the fringe pattern and not in the carrier ( [189]).…”

Section: ) Sampling Of Optical Signals With Finite Extent In Differementioning

confidence: 99%

A Survey of Signal Processing Problems and Tools in Holographic Three-Dimensional Television

Onural

Gotchev

Özaktaş

et al. 2007

IEEE Trans. Circuits Syst. Video Technol.

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Abstract-Diffraction and holography are fertile areas for application of signal theory and processing. Recent work on 3DTV displays has posed particularly challenging signal processing problems. Various procedures to compute Rayleigh-Sommerfeld, Fresnel and Fraunhofer diffraction exist in the literature. Diffraction between parallel planes and tilted planes can be efficiently computed. Discretization and quantization of diffraction fields yield interesting theoretical and practical results, and allow efficient schemes compared to commonly used Nyquist sampling. The literature on computer-generated holography provides a good resource for holographic 3DTV related issues. Fast algorithms to compute Fourier, Walsh-Hadamard, fractional Fourier, linear canonical, Fresnel, and wavelet transforms, as well as optimization-based techniques such as best orthogonal basis, matching pursuit, basis pursuit etc., are especially relevant signal processing techniques for wave propagation, diffraction, holography, and related problems. Atomic decompositions, multiresolution techniques, Gabor functions, and Wigner distributions are among the signal processing techniques which have or may be applied to problems in optics. Research aimed at solving such problems at the intersection of wave optics and signal processing promises not only to facilitate the development of 3DTV systems, but also to contribute to fundamental advances in optics and signal processing theory.

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Section: ) Sampling Of Optical Signals With Finite Extent In Differementioning

confidence: 99%

A Survey of Signal Processing Problems and Tools in Holographic Three-Dimensional Television

Onural

Gotchev

Özaktaş

et al. 2007

IEEE Trans. Circuits Syst. Video Technol.

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“…The one exception is Ref. 5, wherein Vanderlugt proves that the total number of samples required to represent a Fresnel ͑near-field͒ hologram is exactly the same as the number of samples needed for an equivalent Fourier ͑far-field͒ hologram provided the sample size is varied from place to place.…”

Section: Previous Workmentioning

confidence: 99%

“…Our method relies on a nonuniform sampling technique to represent different regions of the hologram plane. A search of the literature has revealed no previous work in nonuniform sampling approaches of the type discussed in this paper as applied to computational holograms, although a paper by Vanderlugt 5 discusses a related technique of representing holographic fringe patterns.…”

Section: Introductionmentioning

confidence: 99%

Nonuniformly sampled computer‐generated holograms

Pappu

1996

Opt. Eng

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Abstract. An novel algorithm for computing holographic fringe patterns based on nonuniform sampling is described. We show both analytically and via simulation that nonuniform sampling reduces the number of samples required to represent the hologram, in some cases by as much as 30 to 40%. This method of computing compact holograms is information-theoretically lossless. Methods for decompressing the computed fringe pattern are also presented. The algorithm is implemented on the Massachusetts Institute of Technology (MIT) Mark II Holographic Video System and results demonstrating its performance are provided. To the best of the author's knowledge, this is the first time that nonuniform sampling has been used to compress holographic fringe patterns for display purposes. The possibility of using other sophisticated nonuniform sampling approaches emerges from this research. © 1996 Society of Photo-Optical Instrumentation Engineers.

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“…Thus, the light distribution in the crystal plane may be termed the Fresnel transform of o(x, y) [6] of which the Fourier transform is a specific case at (3)…”

Section: Theorymentioning

confidence: 99%