PROCLAIM is an active-illumination imaging method that utilizes flood illumination of an opaque object with a frequency-tunable laser [1,2,3]. The reflected radiation at a single frequency will create a speckle pattern in the far-field. The intensity of this far-field speckle pattern is directly detected with an array of detectors and without intervening optics. Typically, the illuminating laser will step through several frequencies so that a separate cross-range speckle intensity pattern is collected for each of multiple frequencies. Properly formatted, these data correspond to the modulus squared of the Fourier transform of the object’s 3-D complex reflectivity function [4]. If the object’s Fourier phase can be retrieved, then the Fourier representation of the object will be complete and a 3-D FFT could be used to recover the object’s 3-D complex reflectivity. Thus, phase-retrieval is an integral element of the PROCLAIM imaging modality. A schematic diagram of the data-collection and processing that constitute the PROCLAIM imaging modality is presented in Fig. 1.
{"title":"Phase Retrieval with an Opacity Constraint in LAser IMaging (PROCLAIM)","authors":"R. Paxman, J. Fienup, M. Reiley, B. Thelen","doi":"10.1364/srs.1998.stuc.3","DOIUrl":"https://doi.org/10.1364/srs.1998.stuc.3","url":null,"abstract":"PROCLAIM is an active-illumination imaging method that utilizes flood illumination of an opaque object with a frequency-tunable laser [1,2,3]. The reflected radiation at a single frequency will create a speckle pattern in the far-field. The intensity of this far-field speckle pattern is directly detected with an array of detectors and without intervening optics. Typically, the illuminating laser will step through several frequencies so that a separate cross-range speckle intensity pattern is collected for each of multiple frequencies. Properly formatted, these data correspond to the modulus squared of the Fourier transform of the object’s 3-D complex reflectivity function [4]. If the object’s Fourier phase can be retrieved, then the Fourier representation of the object will be complete and a 3-D FFT could be used to recover the object’s 3-D complex reflectivity. Thus, phase-retrieval is an integral element of the PROCLAIM imaging modality. A schematic diagram of the data-collection and processing that constitute the PROCLAIM imaging modality is presented in Fig. 1.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"130 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116205723","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We previously developed gradient-search phase-retrieval algorithms and used them to determine the aberrations of the Hubble Space Telescope [1-4]. We were not able to apply these algorithms to all the available data because (i) our algorithms [3-4] required that the images of point objects be of narrow spectral bandwidth, limiting us to using images recorded through narrowband optical filters, and (ii) we required that the measured data in the focal plane be Nyquist sampled for the optical fields, limiting us to the longer wavelengths and the Planetary Camera.
{"title":"Phase Retrieval for Multiple Undersampled Polychromatic Images","authors":"J. Fienup","doi":"10.1364/srs.1998.stuc.5","DOIUrl":"https://doi.org/10.1364/srs.1998.stuc.5","url":null,"abstract":"We previously developed gradient-search phase-retrieval algorithms and used them to determine the aberrations of the Hubble Space Telescope [1-4]. We were not able to apply these algorithms to all the available data because (i) our algorithms [3-4] required that the images of point objects be of narrow spectral bandwidth, limiting us to using images recorded through narrowband optical filters, and (ii) we required that the measured data in the focal plane be Nyquist sampled for the optical fields, limiting us to the longer wavelengths and the Planetary Camera.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130028774","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
E. Hege, M. Cheselka, M. Lloyd-Hart, P. Hinz, W. Hoffmann, J. Christou, S. Jefferies
Iterative physical deconvolution is used for point spread function (psf) calibration of a wide range of astronomical imagery obtained in visible (CCD) through near- and mid-infrared (NICMOS and MIRAC) wavelengths. Psf complications, ranging from those of uncorrected speckle images at large telescopes to those of contemporary high-performance adaptive optics, are accomodated by this algorithm which makes use of a priori physical information about the imaging system. Examples of diffraction-limited and “super-resolved” results are presented for a variety of different astronomical objects.
{"title":"Astronomical Results using Physically-Constrained Iterative Deconvolution","authors":"E. Hege, M. Cheselka, M. Lloyd-Hart, P. Hinz, W. Hoffmann, J. Christou, S. Jefferies","doi":"10.1364/srs.1998.stub.3","DOIUrl":"https://doi.org/10.1364/srs.1998.stub.3","url":null,"abstract":"Iterative physical deconvolution is used for point spread function (psf) calibration of a wide range of astronomical imagery obtained in visible (CCD) through near- and mid-infrared (NICMOS and MIRAC) wavelengths. Psf complications, ranging from those of uncorrected speckle images at large telescopes to those of contemporary high-performance adaptive optics, are accomodated by this algorithm which makes use of a priori physical information about the imaging system. Examples of diffraction-limited and “super-resolved” results are presented for a variety of different astronomical objects.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"1225 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130041878","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Optimization of iterative noise removal and deconvolution establishes the number of iterations needed. One approach to optimization utilizes statistical analysis of numerous trials on noise-added signals. Fixing approximately the signal-to-noise ratio (SNR) for each set of trials makes possible the determination of iteration number and expected error versus SNR as well as the statistical standard deviation of these quantities. The advantage of this approach is that it allows 1) any computer-generated noise type, 2) any criterion for optimization which is calculable, and 3) the use of nonlinear constraints. Analytic approaches to optimization do not in general allow this flexibility. Since nonlinear constraints such as nonnegativity are often the key to superresolution, the ability to perform this type of optimization is quite important. Details concerning the simulations are addressed, including stopping criteria when the rate of change in the optimization measure is very slow. Although minimization of the mean squared error and absolute error have been the main criteria examined thus far in the work because of their current pervasiveness, a number of criteria, especially those related to resolution, may be more appropriate for many data types and goals.
{"title":"Optimizing Iterative Noise Removal and Deconvolution by Simulation","authors":"J. Leclere, A. M. Amini, G. Ioup, J. Ioup","doi":"10.1364/srs.1995.rtue4","DOIUrl":"https://doi.org/10.1364/srs.1995.rtue4","url":null,"abstract":"Optimization of iterative noise removal and deconvolution establishes the number of iterations needed. One approach to optimization utilizes statistical analysis of numerous trials on noise-added signals. Fixing approximately the signal-to-noise ratio (SNR) for each set of trials makes possible the determination of iteration number and expected error versus SNR as well as the statistical standard deviation of these quantities. The advantage of this approach is that it allows 1) any computer-generated noise type, 2) any criterion for optimization which is calculable, and 3) the use of nonlinear constraints. Analytic approaches to optimization do not in general allow this flexibility. Since nonlinear constraints such as nonnegativity are often the key to superresolution, the ability to perform this type of optimization is quite important. Details concerning the simulations are addressed, including stopping criteria when the rate of change in the optimization measure is very slow. Although minimization of the mean squared error and absolute error have been the main criteria examined thus far in the work because of their current pervasiveness, a number of criteria, especially those related to resolution, may be more appropriate for many data types and goals.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117326469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we are concerned with characterizing the internal structure of 2D strongly scattering objects, using a single illumination direction or view and constant wavenumber k0 = 2π / λ0. The object is illuminated with the plane wave eik0r^ i ⋅r and simulated scattered far-fields are calculated on a circular aperture in the plane of the object's cross section. A differential cepstral filter is applied to a single-view backpropagated image which relates to the product of the scattering potential and the total field. This nonlinear filter avoids the phase wrapping problems associated with homomorphic filtering, and is used to isolate the scattering potential from single-view backpropagated images.
{"title":"Nonlinear Filtering Applied to Single-view Backpropagated Images of Strongly Scattering Objects","authors":"J. B. Morris, M. Fiddy","doi":"10.1364/srs.1995.rtua3","DOIUrl":"https://doi.org/10.1364/srs.1995.rtua3","url":null,"abstract":"In this paper, we are concerned with characterizing the internal structure of 2D strongly scattering objects, using a single illumination direction or view and constant wavenumber k0 = 2π / λ0. The object is illuminated with the plane wave \u0000eik0r^\u0000 i\u0000 ⋅r and simulated scattered far-fields are calculated on a circular aperture in the plane of the object's cross section. A differential cepstral filter is applied to a single-view backpropagated image which relates to the product of the scattering potential and the total field. This nonlinear filter avoids the phase wrapping problems associated with homomorphic filtering, and is used to isolate the scattering potential from single-view backpropagated images.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121456521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Physically constrained iterative deconvolution attempts to realize the solution of an ill-posed problem, the iterative estimation of both the object function and the corresponding set of image point- spread-functions given a set of noisy realizations of images obtained with less than perfect optical imaging systems. Conjugate gradient-driven iterative estimation is used with physical constraints to guide the result to a physically consistent solution. The Art of using physically constrained iterative deconvolution in astronomical imaging, with and without adaptive optics, is discussed.
{"title":"Psf calibration in astronomical imaging - physical constraints for a noisy problem","authors":"E. Hege","doi":"10.1364/srs.1998.stua.1","DOIUrl":"https://doi.org/10.1364/srs.1998.stua.1","url":null,"abstract":"Physically constrained iterative deconvolution attempts to realize the solution of an ill-posed problem, the iterative estimation of both the object function and the corresponding set of image point- spread-functions given a set of noisy realizations of images obtained with less than perfect optical imaging systems. Conjugate gradient-driven iterative estimation is used with physical constraints to guide the result to a physically consistent solution. The Art of using physically constrained iterative deconvolution in astronomical imaging, with and without adaptive optics, is discussed.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124584505","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
There has been considerable interest over the years in the so-called Fourier phase retrieval problem. Applications abound and it still remains a difficult problem. Based on the analytic properties of bandlimited functions, it is well known that the 1D phase retrieval problem generally has no unique solution. The lack of uniqueness arises from the existence of complex zeros located off the real axis, i.e. in the complex plane. These analytic properties also suggest that in 2D or higher dimensional problems there is a unique solution1. The question is how to find this “unique” solution, especially when only noisy sampled power spectral data are available. Indeed, the meaning of uniqueness needs to be redefined under these circumstances.
{"title":"New findings on the Zeros of Fourier Integrals","authors":"A. J. Noushin, M. Fiddy","doi":"10.1364/srs.1998.stud.2","DOIUrl":"https://doi.org/10.1364/srs.1998.stud.2","url":null,"abstract":"There has been considerable interest over the years in the so-called Fourier phase retrieval problem. Applications abound and it still remains a difficult problem. Based on the analytic properties of bandlimited functions, it is well known that the 1D phase retrieval problem generally has no unique solution. The lack of uniqueness arises from the existence of complex zeros located off the real axis, i.e. in the complex plane. These analytic properties also suggest that in 2D or higher dimensional problems there is a unique solution1. The question is how to find this “unique” solution, especially when only noisy sampled power spectral data are available. Indeed, the meaning of uniqueness needs to be redefined under these circumstances.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124309883","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper is an overview of mathematical techniques for finding images whose transforms satisfy equality and/or inequality constraints. Applications include microlithography, diffractive optics, and holography.
本文概述了寻找变换满足等式和/或不等式约束的图像的数学技术。应用包括微光刻、衍射光学和全息摄影。
{"title":"Techniques for Signal Synthesis in Microlithography and Diffractive Optics","authors":"B. Saleh","doi":"10.1364/srs.1998.swb.1","DOIUrl":"https://doi.org/10.1364/srs.1998.swb.1","url":null,"abstract":"This paper is an overview of mathematical techniques for finding images whose transforms satisfy equality and/or inequality constraints. Applications include microlithography, diffractive optics, and holography.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"179 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121267521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Blind deconvolution is an important problem that arises in many fields of research. It is of particular relevance to imaging through turbulence where the point spread function can only be modelled statistically, and direct measurement may be difficult. We describe this problem by a noisy convolution, where f(x, y) represents the true image, h(x, y) the instantaneous atmospheric blurring, g(x, y) the noise free data and n(x, y) is the noise present on the detected image. We use to denote an estimate of these quantities and our objective is to recover both f(x, y) and h(x, y) from the observed data d(x, y).
{"title":"Regularized blind deconvolution","authors":"R. Lane, R. A. Johnston, R. Irwan, T. J. Connolly","doi":"10.1364/srs.1998.stua.2","DOIUrl":"https://doi.org/10.1364/srs.1998.stua.2","url":null,"abstract":"Blind deconvolution is an important problem that arises in many fields of research. It is of particular relevance to imaging through turbulence where the point spread function can only be modelled statistically, and direct measurement may be difficult. We describe this problem by a noisy convolution, where f(x, y) represents the true image, h(x, y) the instantaneous atmospheric blurring, g(x, y) the noise free data and n(x, y) is the noise present on the detected image. We use to denote an estimate of these quantities and our objective is to recover both f(x, y) and h(x, y) from the observed data d(x, y).","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116731569","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider Inverse Scattering Problem (ISP) for the Diffusion Equation (1) The ISP consists in determination of either of coefficients D(x) or a(x) given function u(x,t)|∂-Ω = φ(x,t), where ∂ Ω is a boundary of a bounded domain Ω ⊂ ℝn.
{"title":"Two Numerical Methods of Image Reconstruction in Diffusion Tomography","authors":"S. Gutman, M. Klibanov, Hua Song","doi":"10.1364/srs.1995.rtua2","DOIUrl":"https://doi.org/10.1364/srs.1995.rtua2","url":null,"abstract":"We consider Inverse Scattering Problem (ISP) for the Diffusion Equation (1) The ISP consists in determination of either of coefficients D(x) or a(x) given function u(x,t)|∂-Ω = φ(x,t), where ∂ Ω is a boundary of a bounded domain Ω ⊂ ℝn.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116806271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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