Fourier optics described by operator algebra

Nazarathy, Moshe; Shamir, Joseph

doi:10.1364/josa.70.000150

Cited by 123 publications

(53 citation statements)

References 2 publications

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“…As different authors use slightly different definitions, we decided to adopt the original presentation of [7]. The four basic operations other than the identity are:…”

Section: Appendix: the Operational Calculus Of Fourier Opticsmentioning

confidence: 99%

“…The problem is not new, and in fact we re-derive known results that date at least as far back as Wadsworth's extensive investigation of the effects of the slit aperture on the shape of spectral lines [3] (see also [4,5] and references therein). However, for our treatment of the problem, we adopted the tools of the operational calculus of Fourier optics (e.g., [6,7], and references therein), which lead to a very general and compact description of the optical transfer operator (OTO) of a slit spectrograph, opening the ground for further investigations of the performance of such instruments under different illumination conditions, through both analytic and numerical approaches.…”

Section: Introductionmentioning

confidence: 99%

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On the instrument profile of slit spectrographs

Casini¹,

Wijn²

2014

J. Opt. Soc. Am. A

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We derive an analytic expression for the instrument profile of a slit spectrograph, also known as the line spread function. While this problem is not new, our treatment relies on the operatorial approach to the description of diffractive optical systems, which provides a general framework for the analysis of the performance of slit spectrographs under different illumination conditions. Based on our results, we propose an approximation to the spectral resolution of slit spectrographs, taking into account diffraction effects and sampling by the detector, which improves upon the often adopted approximation based on the root-sumsquare of the individual contributions from the slit, the grating, and the detector pixel.

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“…As different authors use slightly different definitions, we decided to adopt the original presentation of [7]. The four basic operations other than the identity are:…”

Section: Appendix: the Operational Calculus Of Fourier Opticsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the instrument profile of slit spectrographs

Casini¹,

Wijn²

2014

J. Opt. Soc. Am. A

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“…A Special Issue [339] is devoted to the Wigner distribution and phase space in optics. Related topics are sometimes referred to as operator optics [340]- [345].…”

Section: B Transformation Theory and Space-frequency Analysismentioning

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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“…Operator calculus is very useful for analysing the scalar (or non-polarizing) characteristics of optical systems [16][17][18][19] and the propagation through anisotropic, but homogeneous, media [21] . In this section, the operator calculus notation is combined with the Jones calculus to describe the propagation of wavefront aberrations and polarization aberrations .…”

Section: Matrix Operator Representationmentioning

confidence: 99%

“…The wavefront aberration function, which characterizes the optical performance of non-polarizing optical systems is developed, then the Jones calculus is introduced . The wavefront aberration function is written in the notation of the Jones calculus and combined with the scalar operator calculus [17][18][19][20][21] . To describe the polarizing properties of optical systems, the wavefront aberration function is generalized to the polarization aberration function, and a particular expansion of the polarization aberration function into terms analogous to the terms defocus, tilt, and piston of the wavefront aberration expansion is introduced .…”

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confidence: 99%