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}
In the seismic tomography problem, the subsurface slowness distribution is estimated from the travel-times computed along generally curved rays. For a dense and uniform set of rays, the slowness distribution will be correctly reconstructed. However, for an uneven distribution of rays, the estimated slowness distribution may be influenced by the ray configuration.
{"title":"Variable damping in seismic tomography based on ray coverage","authors":"R. Nowack","doi":"10.1364/srs.1998.stha.2","DOIUrl":"https://doi.org/10.1364/srs.1998.stha.2","url":null,"abstract":"In the seismic tomography problem, the subsurface slowness distribution is estimated from the travel-times computed along generally curved rays. For a dense and uniform set of rays, the slowness distribution will be correctly reconstructed. However, for an uneven distribution of rays, the estimated slowness distribution may be influenced by the ray configuration.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"61 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":"126654366","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}
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}
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}
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}
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}
Periodic gratings have frequently been used for conversion of modes in highly overmoded circular waveguides [1, 2, 3]. These gratings are formed by periodically varying the waveguide radius resulting in a rippled wall structure and are usually analyzed by coupled mode theory. Very high efficiencies have been reported for these gratings but their lengths remain large compared to the waveguide transverse dimension. Various techniques have been implemented to optimize the length of these gratings [3, 4, 5], but the overall conversion length remains limited by the grating period, δ = 2π/|β m – β n |, where β m and β n are the propagation constants for the input and the output modes. The smallest conversion length reported for a TE02 to TE01 mode converter at 60 GHz is equal to one grating period [4]. This converter was designed for a highly overmoded waveguide with a diameter of 2.771 cm using the coupled mode equations. The efficiency reported for this converter is 97.6%.
周期光栅经常用于高过模圆波导中的模式转换[1,2,3]。这些光栅是通过周期性地改变波导半径而形成波纹壁结构，通常用耦合模式理论进行分析。据报道，这些光栅的效率非常高，但与波导横向尺寸相比，它们的长度仍然很大。已经实现了各种技术来优化这些光栅的长度[3,4,5]，但总的转换长度仍然受到光栅周期的限制，δ = 2π/|β m - β n |，其中β m和β n是输入和输出模式的传播常数。据报道，60 GHz的TE02到TE01模式转换器的最小转换长度等于一个光栅周期[4]。利用耦合模式方程，设计了直径为2.771 cm的高过模波导转换器。该转换器的效率为97.6%。
{"title":"Aperiodic Grating for TE02 to TE01 Conversion in a Highly Overmoded Circular Waveguide","authors":"Tanveer ul Haq, K. Webb, N. Gallagher","doi":"10.1364/srs.1995.rtuc2","DOIUrl":"https://doi.org/10.1364/srs.1995.rtuc2","url":null,"abstract":"Periodic gratings have frequently been used for conversion of modes in highly overmoded circular waveguides [1, 2, 3]. These gratings are formed by periodically varying the waveguide radius resulting in a rippled wall structure and are usually analyzed by coupled mode theory. Very high efficiencies have been reported for these gratings but their lengths remain large compared to the waveguide transverse dimension. Various techniques have been implemented to optimize the length of these gratings [3, 4, 5], but the overall conversion length remains limited by the grating period, δ = 2π/|β\u0000 m\u0000 – β\u0000 n\u0000 |, where β\u0000 m\u0000 and β\u0000 n\u0000 are the propagation constants for the input and the output modes. The smallest conversion length reported for a TE02 to TE01 mode converter at 60 GHz is equal to one grating period [4]. This converter was designed for a highly overmoded waveguide with a diameter of 2.771 cm using the coupled mode equations. The efficiency reported for this converter is 97.6%.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"1 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":"129268597","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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