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Journal ArticleDOI

A New 'Analytic' Method for Computing the Optical Transfer Function

01 Aug 1976-Journal of Modern Optics (Taylor & Francis Group)-Vol. 23, Iss: 8, pp 607-619

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...
Topics: Pupil function (66%), Zernike polynomials (65%), Optical transfer function (64%), Series expansion (59%)
Citations
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Journal ArticleDOI
Stanislav Budzinskiy1Institutions (1)
Abstract: We elaborate an elliptic averaging procedure to estimate astigmatism and defocus of optical transfer functions that allows to reduce the problem to a simpler one of estimating defocus only. Based on approximate closed-form formulas for the zeros of defocus optical transfer functions, we reparametrise the frequency domain and derive a class of nonlinear transformations that turn elliptic null-curves of astigmatic optical transfer functions into circles. Our results make astigmatic images amenable to restoration.

1 citations


Journal ArticleDOI
TL;DR: This work presents a compact statistical model of the retinal image quality in a large population of human eyes following two objectives: to develop a general modal representation of the optical transfer function (OTF) in terms of orthogonal functions and construct a basis composed of cross-correlations between pairs of complex Zernike polynomials.
Abstract: This work presents a compact statistical model of the retinal image quality in a large population of human eyes following two objectives. The first was to develop a general modal representation of the optical transfer function (OTF) in terms of orthogonal functions and construct a basis composed of cross-correlations between pairs of complex Zernike polynomials. That basis was not orthogonal and highly redundant, requiring the application of singular value decomposition (SVD) to obtain an orthogonal basis with a significantly lower dimensionality. The first mode is the OTF of the perfect system, and hence the modal representation, is highly compact for well-corrected optical systems, and vice-versa. The second objective is to apply this modal representation to the OTFs of a large population of human eyes for a pupil diameter of 5 mm. This permits an initial strong data compression. Next, principal component analysis (PCA) is applied to obtain further data compression, leading to a compact statistical model of the initial population. In this model each OTF is approximated by the sum of the population mean plus a linear combination of orthogonal eigenfunctions (eigen-OTF) accounting for a selected percentage (90%) of the population variance. This type of models can be useful for Monte Carlo simulations among other applications.

Journal ArticleDOI
Noé Alcalá Ochoa1Institutions (1)
Abstract: A unique approximation to the vectorial Rayleigh–Sommerfeld diffraction integrals (RSDI) is developed to study the diffraction properties of apertures illuminated with collimated, converging or diverging polarized waves. The apertures can be bigger or smaller than the wavelength of the illumination light. For circular apertures, it is shown that the approach can be expressed as a simple set of equations containing one-dimensional integrals.

3 citations


OtherDOI
Joseph Braat1, Peter Török2Institutions (2)
01 May 2019

Book ChapterDOI
Joseph Braat1, Peter Török2Institutions (2)
01 May 2019

References
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01 Oct 1999
Abstract: The book is comprised of 15 chapters that discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals. The text covers the elements of the theories of interference, interferometers, and diffraction. The book tackles several behaviors of light, including its diffraction when exposed to ultrasonic waves.

19,501 citations


Journal ArticleDOI
Abstract: The expansion of the aberration function of lens systems in analytic form is considered. The results are used to obtain an expansion of the aberration function of a rotationally symmetric system, with either a circular or annular pupil, in a series of orthogonal polynomials. The significance of this for aberration balancing is discussed, and algorithms for obtaining such an expansion numerically are described.

40 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.
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.

36 citations


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.

72 citations