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Journal ArticleDOI

Walsh Functions in Lens Optimization: II. Evaluation of the Diffraction-based OTF for On-axis Imagery

01 Mar 1981-Journal of Modern Optics-Vol. 28, Iss: 3, pp 389-396
About: This article is published in Journal of Modern Optics.The article was published on 1981-03-01. It has received 2 citation(s) till now. The article focuses on the topic(s): Lens (optics).

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Topics: Lens (optics) (66%)
Citations
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Journal ArticleDOI
Lakshminarayan Hazra1, A. Guha1Institutions (1)
Abstract: Radial Walsh functions form a closed set of orthogonal functions over a given finite interval, each function taking merely one constant value (either +1 or −1) in each of a finite number of subintervals into which the entire interval is divided. This set provides a remarkable set of orthogonal radial filters for the pupil of an imaging system. We report analytical expressions for members of the set and their Hankel transforms of order zero. Far-field diffraction characteristics, namely, the far-field amplitude distribution and the optical transfer functions, are presented for the first eight members of the set.

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22 citations


Journal ArticleDOI
L. N. Hazra1Institutions (1)
15 Aug 1988-Applied Optics
TL;DR: A new quadrature technique is presented that obviates the need for knowledge of derivatives of the argument of the exponential integrand in the calculation of image assessment critiera.

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Abstract: The calculation of image assessment critiera, eg, the Strehl ratio, the point spread function, or the optical transfer function, involves the evaluation of an integral where the integrand is highly oscillatory over a large range of integration Prefaced with a brief description of the well-known numerical quadrature methods adopted for the purpose, this paper presents a new quadrature technique that obviates the need for knowledge of derivatives of the argument of the exponential integrand Some illustrative numerical results are presented

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4 citations


References
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Journal ArticleDOI
H. H. Hopkins1Institutions (1)
01 May 1962-
Abstract: A resume of the treatment of image formation from the standpoint of the theory of passive linear systems is given, it being shown that image formation for an incoherent object satisfies the basic postulates of superposition and stationarity. It then follows that the spatial frequency response of an optical system will be given by the Fourier transform of its impulse response, this latter being simply the distribution of intensity in the image of a narrow self-luminous line. There follows an account of work done in the author's image-assessment group at Imperial College. This includes the diffraction theory of optical frequency response, aberration tolerance theory and the numerical evaluation of frequency response and diffraction integrals together with examples of the response curves for particular cases. A number of methods for the measurement of frequency response are described, and the theory of these methods and results showing the comparison of theoretical and measured response curves are discussed. The final section describes methods for the measurement of the Fourier spectra of photographic images, and their application to the study of the influence of the detector properties on recorded images.

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72 citations


Journal ArticleDOI
Eric C. Kintner1, R.M. Sillitto1Institutions (1)
Abstract: Using a series expansion in Zernike polynomials to express the pupil function of an optical system, a means for computing the Optical Transfer Function has been found which avoids explicit numerica...

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45 citations


Journal ArticleDOI
TL;DR: In previous OTF computer programs, various geometrical optical aspects of image formation appear often to have been ignored, leading to considerable errors in the computed values of the transfer function, particularly for high-aperture or wide-angle systems.

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Abstract: In previous OTF computer programs, various geometrical optical aspects of image formation appear often to have been ignored. The neglect of factors associated with anamorphotic imagery, pupil aberrations and vignetting, and a shift of focal plane can lead to considerable errors in the computed values of the transfer function, particularly for high-aperture or wide-angle systems. In addition, the numerical integration processes employed have not always been entirely satisfactory in terms of efficiency, generality, and convenience.

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36 citations


Journal ArticleDOI
M. De1, Lakshminarayan Hazra1Institutions (1)
TL;DR: A reformulation of Walsh functions in polar coordinates facilitates the analysis which is presented, along with a restatement of the basic properties of these functions pertinent to the purpose.

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Abstract: Walsh functions provide a viable and interesting tool in the treatment of problems of optical imagery. A reformulation of Walsh functions in polar coordinates facilitates the analysis which is presented, along with a restatement of the basic properties of these functions pertinent to the purpose. Some numerical results of aberrational diffraction images are cited to illustrate the compatibility of the proposed approach.

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25 citations


Journal ArticleDOI
Abstract: A program for the calculation of the optical transfer function, using Gaussian quadrature, is described. The program uses considerations of symmetry to save computer time, and several means of checking intermediate results are described. The program may be used to calculate either monochromatic or heterochromatic values of the OTF.

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13 citations


Performance
Metrics
No. of citations received by the Paper in previous years
YearCitations
19881
19861