The factor of encircled energy from the optical transfer function
TL;DR: In this paper, a generalized technique for computing the factor of encircled energy (FEE) in a diffraction image from the optical transfer function (OTF) of the imaging system is proposed.
Abstract: This paper proposes a generalized technique for computing the factor of encircled energy (FEE) in a diffraction image from the optical transfer function (OTF) of the imaging system. This technique is applicable to diffraction-limited optical systems as well as to systems suffering from any aberrations, provided the transfer function of the same is known. It is also applicable to any kind of rotationally symmetric or asymmetric apertures. The accuracy of the results depends on the precision with which the OTF of the system can be determined. The FEE values are obtained using this technique for an aberration-free spherical lens as well as for the same having primary spherical aberration. The results are computed for the Gaussian image plane and other observation planes and are compared with the previously reported results. A numerical technique for computing the FEE in a diffraction pattern formed by a conventional lens suffering from off-axis aberrations and that formed by rotationally asymmetric apertures is also depicted.
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TL;DR: In this article, the authors studied the focusing of a singular beam by a lens in the presence of spherical aberration and defocusing by using Fresnel-Kirchhoff diffraction integral for two different values of topological charge.
Abstract: Focusing of a singular beam by a lens in the presence of spherical aberration and defocusing is studied by using Fresnel–Kirchhoff diffraction integral for two different values of topological charge. Results of intensity distribution and encircled energy are plotted for defocused observation planes. Spherical aberration spreads the dark core and reduces the intensity at maxima. The results have been verified by the optical transfer function (OTF) approach.
15 citations
TL;DR: In this article, two different values of topological charge are selected compensation of aberration in the presence of appropriate value of defocusing is investigated Presence of spherical aberration results in an increase in the size of the dark core of the diffraction pattern.
Abstract: Diffraction pattern formed by a lens for a vortex containing truncated beam with Gaussian background, and in the presence of spherical aberration and defocusing has been studied by Fresnel–Kirchhoff diffraction integral For the study, two different values of topological charge are selected Compensation of aberration in the presence of appropriate value of defocusing is investigated Presence of spherical aberration results in an increase in the size of the dark core of the diffraction pattern Results are also presented for the encircled energy Some results are also presented for the influence of truncation parameter of the beam, on the point spread function at different observation planes
15 citations
01 Jan 2008
TL;DR: In this article, the role of amplitude-, phase-, and polarization distribution on the tightly focused structure of the optical beams is reviewed. And some applications in which tight focusing is desired are briefly discussed.
Abstract: Complex amplitude and polarization distribution of an optical beam plays a dominant role in shaping the focused structure of the beam. It is therefore possible to engineer the focal spot using the pupil function manipulation. Helical phase structure arising due to phase singularity in the wave front plays an important role in shaping the focal spot. Tight focusing of an optical beam produces intensity distribution in the focal volume different from the well-known results based on scalar theory, and polarization distribution shows space variant characteristics. In the present paper, roles of the amplitude-, phase-, and polarization distribution on the tightly focused structure of the optical beams are reviewed. Impact of the helical phase structure in the pupil function engineering and subsequently on the focused structure is discussed with special reference to the authors' investigations at IIT Delhi. Certain applications in which tight focusing is desired are briefly discussed. Some miscellaneous investigations are also mentioned.
7 citations
Cites background from "The factor of encircled energy from..."
...…1966, Hunt et al 1976, Gupta et al 1977, 1978 [317-321]), (Gupta and Singh 1978a, b, Yoshida 1982, Biswas and Villeneuve 1985, 1986 [322-326]), (Born and Wolf 1989 [46], Williams and Becklund 1989, Cojocaru et al 1990 [327-328], Mahajan 2001 [51], Sanyal and Ghosh 2002 [329], Goodman 2007 [54])....
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...In a number of papers, researchers have studied the effects of aberrations in terms of optical transfer function (OTF) and/or PSF (Kapany and Burke 1962, Barakat and Houston 1966, Hunt et al 1976, Gupta et al 1977, 1978 [317-321]), (Gupta and Singh 1978a, b, Yoshida 1982, Biswas and Villeneuve 1985, 1986 [322-326]), (Born and Wolf 1989 [46], Williams and Becklund 1989, Cojocaru et al 1990 [327-328], Mahajan 2001 [51], Sanyal and Ghosh 2002 [329], Goodman 2007 [54])....
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TL;DR: In this article, an optical system consisting of an aberration-free birefringent lens sandwiched between two linear polarizers is computed directly from the optical transfer function (OTF) of the system.
Abstract: The factor of encircled energy (FEE) in the diffraction pattern formed by an optical system consisting of an aberration-free birefringent lens sandwiched between two linear polarizers is computed directly from the optical transfer function (OTF) of the system. FEE curves are given showing the variation of image quality of the proposed system at the Gaussian image plane and other observation planes with the birefringent lens parameters and the azimuthal settings of the transmission axes of the polarizers. The performance is compared to that of an ideal conven- tional glass lens. © 2003 Society of Photo-Optical Instrumentation Engineers.
7 citations
TL;DR: In this article, a comparison of materials for adhering layers of holographically formed polymer dispersed liquid crystal (H-PDLC) films layered in stacks fabricated on common substrates is presented.
Abstract: We present a comparison of materials for adhering layers of holographically formed polymer dispersed liquid crystal (H-PDLC) films layered in stacks fabricated on common substrates. The results of this study are used in applications that rely on maximization of transmitted light through the layers of H-PDLC. Data is presented by comparing a simulated transmission envelope modeled on the individual H-PDLC cells with the actual stacked transmission spectrum. Additionally, data is presented on the quality of the wavefront of H-PDLC transmission spectrum individually and layered using air and index matching layers.
2 citations
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TL;DR: The second edition of this respected text considerably expands the original and reflects the tremendous advances made in the discipline since 1968 as discussed by the authors, with a special emphasis on applications to diffraction, imaging, optical data processing, and holography.
Abstract: The second edition of this respected text considerably expands the original and reflects the tremendous advances made in the discipline since 1968. All material has been thoroughly updated and several new sections explore recent progress in important areas, such as wavelength modulation, analog information processing, and holography. Fourier analysis is a ubiquitous tool with applications in diverse areas of physics and engineering. This book explores these applications in the field of optics with a special emphasis on applications to diffraction, imaging, optical data processing, and holography. This book can be used as a textbook to satisfy the needs of several different types of courses, and it is directed toward both engineers ad physicists. By varying the emphasis on different topics and specific applications, the book can be used successfully in a wide range of basic Fourier Optics or Optical Signal Processing courses.
12,159 citations
Book•
01 Jan 1968
TL;DR: The second edition of this respected text considerably expands the original and reflects the tremendous advances made in the discipline since 1968 as discussed by the authors, with a special emphasis on applications to diffraction, imaging, optical data processing, and holography.
Abstract: The second edition of this respected text considerably expands the original and reflects the tremendous advances made in the discipline since 1968. All material has been thoroughly updated and several new sections explore recent progress in important areas, such as wavelength modulation, analog information processing, and holography. Fourier analysis is a ubiquitous tool with applications in diverse areas of physics and engineering. This book explores these applications in the field of optics with a special emphasis on applications to diffraction, imaging, optical data processing, and holography. This book can be used as a textbook to satisfy the needs of several different types of courses, and it is directed toward both engineers ad physicists. By varying the emphasis on different topics and specific applications, the book can be used successfully in a wide range of basic Fourier Optics or Optical Signal Processing courses.
9,800 citations
TL;DR: In this paper, the response of a defocused aberration-free optical system to line-frequencies in the object is studied analytically, and curves are given showing the response as a function of line-frequency for a range of values of defect of focus.
Abstract: The response of a defocused aberration-free optical system to line-frequencies in the object is studied analytically. Curves are given showing the response as a function of line-frequency for a range of values of defect of focus. A comparison is made with the results to be expected from geometrical optics. A tolerance for defect of focus is obtained, which accords well with published experimental results. Both circular and rectangular apertures are considered.
489 citations
TL;DR: In this paper, a theoretical study of the possibilities of using an annular aperture to increase the focal depth of a photographic objective is made and it is shown that for a given gain in focal depth the loss in speed is the same for both annular apertures and conventional stopping down.
Abstract: A theoretical study is made of the possibilities of using an annular aperture to increase the focal depth of a photographic objective. It is shown that for a given gain in focal depth the loss in speed is the same for both annular apertures and conventional stopping down. For images of isolated point objects, the definition is improved by using an annular stop. The gain in focal depth is less for off-axis points, but it is found that, for example, a factor of 2.7 in focal depth gained by means of an annular aperture is barely affected at a field angle of 30°.
294 citations
Book•
01 Jan 1950
TL;DR: Carlaw's theory of Fourier's series and integrals as mentioned in this paper is a well-known work on the theory of series and integral analysis, and it is of this work that the present book is the new edition.
Abstract: PROF. CARSLAW'S excellent book is so well known that it needs little general introduction. The first edition, published in 1906, was a work on “Fourier's Series and Integrals and the Mathematical Theory of the Conduction of Heat”. The second edition followed in 1921, in two volumes. The great advances in the theory of Fourier's series had caused the earlier chapters to develop into a self-contained book on analysis, including much matter on sequences and integration in addition to the theory of Fourier's series. It is of this work that the present book is the new edition.Introduction to the Theory of Fourier's Series and Integrals.Prof. H. S. Carslaw. Third edition, revised and enlarged. Pp. xiii + 368. (London: Macmillan and Co., Ltd., 1930.) 20s. net.
254 citations