Carrier fringes and a non-conventional rotational shear in a triangular cyclic-path interferometer
TL;DR: In this article, a method for generating carrier fringes and a nonconventional rotational shear in a triangular cyclic-path interferometer, while simultaneously suppressing the presence of typical lateral and radial shearing, is presented.
Abstract: This work presents a method for generating carrier fringes and a nonconventional rotational shear in a triangular cyclic-path interferometer, while simultaneously suppressing the presence of typical lateral and radial shearing. To carry out this method, a 4f optical system is implemented into the cyclic interferometer. The most important contributions of this paper are its demonstration of the linear dependence of the movable mirror displacement with the carrier frequency introduced, and the realization of a nonconventional rotational shearing interferometer. Additionally, we think that one of its possible potential applications is the observation of the angular derivative of parallel projections of a phase object placed at the output plane, generating a great advantage in edge-enhancement optical tomography. In this paper, we develop a theoretical model and show experimental results.
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Journal Article•
TL;DR: In this article, a fast Fourier transform method of topography and interferometry is proposed to discriminate between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour generation techniques.
Abstract: A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.
3,742 citations
TL;DR: The proposed Gram-Schmidt orthogonalization method can effectively alleviate the ill-conditioning of the problem, and is numerically stable compared with the classic least-squares method, especially for non-circular apertures and in the presence of noise.
Abstract: Wavefront reconstruction in radial shearing interferometry with general aperture shapes is challenging because the problem may be ill-conditioned. Here we propose a Gram-Schmidt orthogonalization method to cope with off-axis wavefront reconstruction with any aperture type. The proposed method constructs a set of orthogonal basis functions and computes the corresponding expansion coefficients, which are converted into another set of expansion coefficients to reproduce the original wavefront. The method can effectively alleviate the ill-conditioning of the problem, and is numerically stable compared with the classic least-squares method, especially for non-circular apertures and in the presence of noise. Computer simulation and experimental results are presented to demonstrate the performance of the algorithm.
18 citations
TL;DR: Experimental results presented in this Letter could provide an insight into the momentum change associated with the energy redistribution in the fundamental phenomenon of optical interference.
Abstract: A scheme to study the effect of residual phase gradients in an optical interference between two out-of-phase Gaussian beams is proposed. In a Sagnac interferometer configured to provide a null output, a variable linear phase swept across the null point unfolds an optical field rotation due to an apparently negligible residual phase gradient present orthogonal to the linear phase sweep. As the optical beam that rotates around its propagation axis carries orbital angular momentum, the experimental results presented in this Letter could provide an insight into the momentum change associated with the energy redistribution in the fundamental phenomenon of optical interference.
5 citations
30 Aug 2017
TL;DR: The differential shearing interferometer (DSI) as mentioned in this paper incorporates a set of Risley prisms in a Sagnac interferometric configuration, which deviates the beam in both propagation directions.
Abstract: We present a novel interferometer that we call the differential shearing interferometer (DSI). It incorporates a set of Risley prisms in a Sagnac interferometric configuration. The Risley prisms deviates the beam in both propagation directions. This interferometer interferes two beams displaced in the same direction, but with different magnitudes. The resultant interferogram is the directional derivative of the wavefront. The interferometer sensitivity depends on the difference between the beam deviations. This deviation is controlled by the position of the Risley prisms inside the beam path and their angular orientations. The advantages of quasi-common-path configuration include its low sensitivity to vibrations.
3 citations
01 Dec 2015
TL;DR: In this paper, a scheme to sense the residual phase gradients in an optical interference of two out-of-phase Gaussian beams is proposed, which is implemented using a Sagnac interferometer configured to provide a null output.
Abstract: A scheme to sense the residual phase gradients in an optical interference of two out-of-phase Gaussian beams is proposed. Its implementation by detecting the residual phase gradient as an optical field rotation in a Sagnac interferometer, configured to provide a null output is presented.
3 citations
References
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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
Journal Article•
TL;DR: In this article, a fast Fourier transform method of topography and interferometry is proposed to discriminate between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour generation techniques.
Abstract: A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.
3,742 citations
TL;DR: In this paper, a fast Fourier transform method of topography and interferometry is proposed to discriminate between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour generation techniques.
Abstract: A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.
3,650 citations
"Carrier fringes and a non-conventio..." refers methods in this paper
...The procedure for measuring 0 experimentally consists in applying the Fourier‐transform method for phase extraction introduced by Takeda et al [27], but without centring the filtered lobule of the interferogram spectrum....
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...In summary, this displacement produces two important effects simultaneously: in the first place, it introduces a linear phase with high reliability, which is appropriate for fringe analysis by applying the Fourier-transform method [27]....
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TL;DR: A cyclic interferometers can be used for both lateral and radial shearing, and the working of a polarization phase shifting cyclic shear interferometer is demonstrated.
Abstract: A cyclic interferometer can be used for both lateral and radial shearing. Being common-path this interferometer is quite stable. The use of a cyclic shear interferometer for phase shifting interferometry is discussed. The phase shifting is provided here by polarization techniques. Some useful cyclic phase shifting interferometer arrangements are discussed, and the working of a polarization phase shifting cyclic shear interferometer is demonstrated.
112 citations