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Berge Tatian

Bio: Berge Tatian is an academic researcher. The author has contributed to research in topics: Rectangular function & Orthogonal polynomials. The author has an hindex of 4, co-authored 5 publications receiving 158 citations.

Papers
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Journal ArticleDOI
TL;DR: In this paper, the transfer function is expressed as a trigonometric series whose coefficients are proportional to the sampled values of the edge response function, and the series may be modified by means of added terms to take into account the known asymptotic behavior of the EDF.
Abstract: The transfer function is expressed as a trigonometric series whose coefficients are proportional to the sampled values of the edge response function. The series may be modified by means of added terms to take into account the known asymptotic behavior of the edge response function. Numerical results are given for pure defocusing.

104 citations

Journal ArticleDOI
TL;DR: In this article, the authors considered the expansion of the aberration function of a rotationally symmetric system in analytic form, with either a circular or annular pupil, in a series of orthogonal polynomials.
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.

45 citations

Journal ArticleDOI
TL;DR: In this paper, the sampling theorem from the edge-, line-, and point-spread functions produced by a lens with a circular aperture is used to correct the error due to truncation in calculating the transfer function using the sampling theory.
Abstract: Formulas are derived for correcting the error due to truncation in calculating the transfer function using the sampling theorem from the edge-, line-, and point-spread functions produced by a lens with a circular aperture. Numerical results are given for several cases of defocusing and one case of spherical aberration.

13 citations


Cited by
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Journal ArticleDOI
TL;DR: The edge method provides a convenient measurement of the presampled MTF for digital radiographic systems with good response at low frequencies.
Abstract: The modulation transfer function (MTF) of radiographic systems is frequently evaluated by measuring the system's line spread function (LSF) using narrow slits. The slit method requires precise fabrication and alignment of a slit and high radiation exposure. An alternative method for determining the MTF uses a sharp, attenuating edge device. We have constructed an edge device from a 250-microm-thick lead foil laminated between two thin slabs of acrylic. The device is placed near the detector and aligned with the aid of a laser beam and a holder such that a polished edge is parallel to the x-ray beam. A digital image of the edge is processed to obtain the presampled MTF. The image processing includes automated determination of the edge angle, reprojection, sub-binning, smoothing of the edge spread function (ESF), and spectral estimation. This edge method has been compared to the slit method using measurements on standard and high-resolution imaging plates of a digital storage phosphor (DSP) radiography system. The experimental results for both methods agree with a mean MTF difference of 0.008. The edge method provides a convenient measurement of the presampled MTF for digital radiographic systems with good response at low frequencies.

701 citations

Journal ArticleDOI
TL;DR: A simple method for accurately estimating the optical transfer function of digital image acquisition devices based on the traditional knife-edge technique but explicitly deals with fundamental sampled system considerations: insufficient and anisotropic sampling.
Abstract: Despite the popularity of digital imaging devices (e.g., CCD array cameras) the problem of accurately characterizing the spatial frequency response of such systems has been largely neglected in the literature. This paper describes a simple method for accurately estimating the optical transfer function of digital image acquisition devices. The method is based on the traditional knife-edge technique but explicitly deals with fundamental sampled system considerations: insufficient and anisotropic sampling. Results for both simulated and real imaging systems demonstrate the accuracy of the method.

267 citations

Journal ArticleDOI
TL;DR: The Zernike annular polynomials as mentioned in this paper describe how a higher order classical aberration of a power-series expansion is balanced with one or more lower-order classical aberrations to minimize its variance.
Abstract: The aberrations of imaging systems with uniformly illuminated annular pupils are discussed in terms of a complete set of polynomials that are orthogonal over an annular region. These polynomials, which we call Zernike annular polynomials, are similar to the Zernike circle polynomials and reduce to them as the annulus approaches the full circle. The Zernike-polynomial expansion of an aberration function is compared with its power-series expansion. The orthogonal aberrations given by Zernike annular polynomials describe how a higher-order classical aberration of a power-series expansion is balanced with one or more lower-order classical aberrations to minimize its variance. It is shown that as the obscuration ratio increases, the standard deviation of an orthogonal as well as a classical primary aberration decreases in the case of spherical aberration and field curvature and increases in the case of coma, astigmatism, and distortion. The only exception is the case of orthogonal coma, for which the standard deviation first increases and then decreases. The orthogonal aberrations for nonuniformly illuminated annular pupils are also considered, and, as an example, Gaussian illumination is discussed. It is shown that the standard deviation of an orthogonal primary aberration for a given amount of the corresponding classical aberration is somewhat smaller for a Gaussian pupil than that for a uniformly illuminated pupil.

173 citations

Journal ArticleDOI
20 Feb 2021
TL;DR: This article begins with a brief history of freeform optics, focusing on imaging systems, including marketplace emergence, and describes fabrication methods, emphasizing deterministic computer numerical control grinding, polishing, and diamond machining.
Abstract: In the last 10 years, freeform optics has enabled compact and high-performance imaging systems. This article begins with a brief history of freeform optics, focusing on imaging systems, including marketplace emergence. The development of this technology is motivated by the clear opportunity to enable science across a wide range of applications, spanning from extreme ultraviolet lithography to space optics. Next, we define freeform optics and discuss concurrent engineering that brings together design, fabrication, testing, and assembly into one process. We then lay out the foundations of the aberration theory for freeform optics and emerging design methodologies. We describe fabrication methods, emphasizing deterministic computer numerical control grinding, polishing, and diamond machining. Next, we consider mid-spatial frequency errors that inherently result from freeform fabrication techniques. We realize that metrologies of freeform optics are simultaneously sparse in their existence but diverse in their potential. Thus, we focus on metrology techniques demonstrated for the measurement of freeform optics. We conclude this review with an outlook on the future of freeform optics.

123 citations

Journal ArticleDOI
TL;DR: In this article, the mathematical properties of Zernike polynomials were investigated and the results showed that the polynomial can be expressed as a function of the number of vertices.
Abstract: (1976). On the Mathematical Properties of the Zernike Polynomials. Optica Acta: International Journal of Optics: Vol. 23, No. 8, pp. 679-680.

111 citations