Gabor representation and aperture theory

Einziger, P.D.; Raz, S.; Shapira, Moshe

doi:10.1364/josaa.3.000508

Cited by 108 publications

(62 citation statements)

References 4 publications

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“…Although Greynolds was not the first author to suggest the use of Gaussian beams as an elementary field for decomposition applications, [22][23][24][25] to the authors' knowledge, his 1985 article 21 was the first to suggest and demonstrate this powerful technique as a routine tool for the detailed optical analysis of diffraction effects in not only standard imaging systems, but also nonimaging concentrators, multimode fibers, interferometers, and synthetic aperture systems. Greynolds was also the chief architect of the first popular commercially available optical analysis ray-trace code that uses the decomposition of arbitrary optical wave fields into a superposition of Gaussian beamlets to accurately model physical optics phenomena.…”

Section: Arbitrary Wave Fields As a Superposition Ofmentioning

confidence: 99%

Modeling physical optics phenomena by complex ray tracing

Harvey¹,

Irvin²,

Pfisterer³

2015

Opt. Eng

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Abstract. Physical optics modeling requires propagating optical wave fields from a specific radiometric source through complex systems of apertures and reflective or refractive optical components, or even complete instruments or devices, usually to a focal plane or sensor. The model must accurately include the interference and diffraction effects allowed by the polarization and coherence characteristics of both the initial optical wave field and the components and media through which it passes. Like a spherical wave and a plane wave, a Gaussian spherical wave (or Gaussian beam) is also a solution to the paraxial wave equation and does not change its fundamental form during propagation. The propagation of a Gaussian beam is well understood and easily characterized by a few simple parameters. Furthermore, a paraxial Gaussian beam can be propagated through optical systems using geometrical ray-trace methods. The decomposition of arbitrary propagating wave fields into a superposition of Gaussian beamlets is, thus, an alternative to the classical methods of propagating optical wave fields. This decomposition into Gaussian beamlets has been exploited to significant advantage in the modeling of a wide range of physical optics phenomena. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

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Section: Arbitrary Wave Fields As a Superposition Ofmentioning

confidence: 99%

Modeling physical optics phenomena by complex ray tracing

Harvey¹,

Irvin²,

Pfisterer³

2015

Opt. Eng

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“…F 1 and F 2 are the actual intersections of the incident and reflected directions with the x axis, respectively. [ [6][7][8][9][10][11][12][13][14] algorithm based on the configurations described above, including off-axis reflector based conventional configuration, astigmatic off-axis reflector based configuration, and off-axis reflector based off-focus configuration. DGBA algorithm has nearly the same calculation efficiency with PO [6].…”

Section: Numerical Simulationsmentioning

confidence: 99%

Deastigmatism and Circularization of an Elliptical Gaussian Beam by Off-Axis Ellipsoid Reflector Based Off-Focus Configuration

Yang¹,

Bai²,

Miao³

2008

PIER B

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Abstract-Off-axis ellipsoid reflector based off-focus configuration for deastigmatism and circularization of an elliptical Gaussian beam is proposed. Mostly used off-axis ellipsoid reflector based conventional configuration is constructed by aligning the incident direction directed to one focus of the ellipsoid, which reflect the output beam to the another focus of the ellipsoid. However, such configuration is unavailable to deastigmatize and circularize an elliptical Gaussian beam. Therefore, the coupling efficiency between the reflected beam and an essentially circular beam is not well satisfied. In this case, an off-axis ellipsoid reflector based off-focus configuration is proposed to obtain better coupling efficiency. Different from the conventional configuration, in the proposed off-focus configuration, the incident beam direction is diverged from one focus of the ellipsoid. As a result, the coupling efficiency of no less than 99.9% (as compared with coupling efficiency of about 94.2% based on conventional configuration) can be obtained, which is verified with numerical calculations.

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“…With these ideas in mind, several authors have expressed the optical signal inside an aperture in terms of a Gabor expansion [ERS86], [EHF87], [Wol89] and have studied the propagation of light in homogeneous and weakly inhomogeneous media [MMTZ86], [ER88], [MF89], [FKLG91], [SHF91c], [SHF91b], [KFLG92], in layered media [MF90], and in the focal region of a parabolic reflector [DA94]. Whereas most of these papers deal with time-harmonic signals, the case of pulsed signals (where the time-pulse has again a Gaussian shape) has been considered, as well [ER87] [SHF91a] [SH91].…”

Section: Gaussian Elementary Signal and Gaussian Beamsmentioning

confidence: 99%

Gabor’s signal expansion in optics

Bastiaans¹

1998

Gabor Analysis and Algorithms

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Gabor representation and aperture theory

Cited by 108 publications

References 4 publications

Modeling physical optics phenomena by complex ray tracing

Modeling physical optics phenomena by complex ray tracing

Deastigmatism and Circularization of an Elliptical Gaussian Beam by Off-Axis Ellipsoid Reflector Based Off-Focus Configuration

Gabor’s signal expansion in optics

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