Phase retrieval is concerned with recovery of an image from measurements of the amplitude of its Fourier transform [1]. It is of considerable practical importance in areas such as microscopy, ultrasonic imaging, astronomy, and crystallography. There are a number of applications, such as in x-ray crystallography, electron microscopy, ultrasonic imaging, and geophysical imaging, where the image to be reconstructed is three-dimensional. Uniqueness properties of phase problems in higher dimensions are examined, and implications in a number of applications of x-ray crystallography are described.
{"title":"Properties and Implications of Phase Problems for Multidimensional Images","authors":"R. Millane","doi":"10.1364/srs.1995.rwd4","DOIUrl":"https://doi.org/10.1364/srs.1995.rwd4","url":null,"abstract":"Phase retrieval is concerned with recovery of an image from measurements of the amplitude of its Fourier transform [1]. It is of considerable practical importance in areas such as microscopy, ultrasonic imaging, astronomy, and crystallography. There are a number of applications, such as in x-ray crystallography, electron microscopy, ultrasonic imaging, and geophysical imaging, where the image to be reconstructed is three-dimensional. Uniqueness properties of phase problems in higher dimensions are examined, and implications in a number of applications of x-ray crystallography are described.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"28 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":"122040082","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 will pursue the rather appealing analogy1-4 between the behavior of electromagnetic waves in artificial, 3-dimensionally periodic, dielectric structures, and the rather more familiar behavior of electron waves in natural crystals.
{"title":"Design of Photonic Bandgap Structures","authors":"E. Yablonovich","doi":"10.1364/srs.1998.swb.2","DOIUrl":"https://doi.org/10.1364/srs.1998.swb.2","url":null,"abstract":"We will pursue the rather appealing analogy1-4 between the behavior of electromagnetic waves in artificial, 3-dimensionally periodic, dielectric structures, and the rather more familiar behavior of electron waves in natural crystals.","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":"123823494","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}
Markov random fields (MRFs) [1, 2, 3, 4] provide attractive statistical models for multidimensional signals. However, unfortunately, optimal Bayesian estimators tend to require large amounts of computation. We present an approximation to a particular Bayesian estimator which requires much reduced computation and an example illustrating low-light unknown-blur imaging. See [7] for an alternative approximation based on approximating the MRF lattice by a system of trees and for an alternative cost function.
{"title":"Markov random fields as a priori information for image restoration","authors":"Chi-hsin Wu, P. Doerschuk","doi":"10.1364/srs.1995.rwc2","DOIUrl":"https://doi.org/10.1364/srs.1995.rwc2","url":null,"abstract":"Markov random fields (MRFs) [1, 2, 3, 4] provide attractive statistical models for multidimensional signals. However, unfortunately, optimal Bayesian estimators tend to require large amounts of computation. We present an approximation to a particular Bayesian estimator which requires much reduced computation and an example illustrating low-light unknown-blur imaging. See [7] for an alternative approximation based on approximating the MRF lattice by a system of trees and for an alternative cost function.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"40 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":"114736742","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}
The interferometric measurements are among the most popular methods of non- contact, non-intrusive surface and volume characterization. Figure 1 shows an interferogram [1 of 3 minimally in the phase shifting interferometry1,2 (PSI)], that has several features that are considered challenging in the phase reconstruction: it has many fringes, some closed and some open; it high intensity gradients with a non-uniform contrast; and it is defined within a circular boundary on a rectangular array. We report a novel method for the phase determination, applicable to the majority of the existing phase reconstruction techniques.
{"title":"Phase retrieval from modulated intensity patterns","authors":"G. Páez, M. Strojnik","doi":"10.1364/srs.1998.stud.3","DOIUrl":"https://doi.org/10.1364/srs.1998.stud.3","url":null,"abstract":"The interferometric measurements are among the most popular methods of non- contact, non-intrusive surface and volume characterization. Figure 1 shows an interferogram [1 of 3 minimally in the phase shifting interferometry1,2 (PSI)], that has several features that are considered challenging in the phase reconstruction: it has many fringes, some closed and some open; it high intensity gradients with a non-uniform contrast; and it is defined within a circular boundary on a rectangular array. We report a novel method for the phase determination, applicable to the majority of the existing phase reconstruction techniques.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"6 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":"126239911","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}
Star light, scattered from even most smoothly polished optical surfaces, prevents detection of a faint planet light because of the enormous brightness ratio between them. Figure 1 shows two point sources: a dark (Earth-like) planet rotates slowly around a bright star. At the time of observation the planet is assumed to be on x-axis. The wavefronts originating from the star and the planet, respectively, are incident on the aperture at a distant observation plane as plane waves with the propagation vector parallel to the optical axis and tilted with the direction cosine vector (1, 0, n).
{"title":"Star-Light Suppression with a rotating Rotational-Shearing Interferometer for Extra-Solar Planet Detection","authors":"M. Scholl","doi":"10.1364/srs.1995.rtue2","DOIUrl":"https://doi.org/10.1364/srs.1995.rtue2","url":null,"abstract":"Star light, scattered from even most smoothly polished optical surfaces, prevents detection of a faint planet light because of the enormous brightness ratio between them. Figure 1 shows two point sources: a dark (Earth-like) planet rotates slowly around a bright star. At the time of observation the planet is assumed to be on x-axis. The wavefronts originating from the star and the planet, respectively, are incident on the aperture at a distant observation plane as plane waves with the propagation vector parallel to the optical axis and tilted with the direction cosine vector (1, 0, n).","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":"132012674","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}
The Air Force Electro Optics Division is pursuing advanced laser target identification technologies under its Enhanced Recognition and Sensing Ladar (ERASER) program. Long range, eyesafe target identification is of central importance in many regional operations. Building on advancements in laser sources, detectors1 and signal processing, direct detection ladar can provide ID well beyond the range of conventional imaging sensors. High temporal resolution laser radar can produce range resolved (ID) scattering profiles, which are unique to each aircraft relatively independent of target range2,3. This allows a variety of ID techniques to be applied at ranges well beyond the resolution limits of comparably sized imaging apertures. The ID profiles can be applied to automatic target recognition systems for classification and identification. However, in-class variation as well as large numbers of unclassified targets may limit these techniques. In this paper, we investigate the use of tomographic reconstruction to enhance long range identification. The reconstruction is based on compilations of ID signatures obtained at various angles due to relative target sensor motion. We describe the ladar system used to measure the ID returns of an F-4 aircraft. Based on the measured capabilities of the ERASER ladar, we use the IRMA computer model to generate sets of data consistent with the measured ladar data. Finally, we utilize the filtered back-projection method to investigate the reconstruction model data for both the ideal and limited-data cases.
{"title":"High temporal resolution laser radar tomography for long range target identification","authors":"M. Dierking, F. Heitkamp, L. Barnes","doi":"10.1364/srs.1998.sthc.2","DOIUrl":"https://doi.org/10.1364/srs.1998.sthc.2","url":null,"abstract":"The Air Force Electro Optics Division is pursuing advanced laser target identification technologies under its Enhanced Recognition and Sensing Ladar (ERASER) program. Long range, eyesafe target identification is of central importance in many regional operations. Building on advancements in laser sources, detectors1 and signal processing, direct detection ladar can provide ID well beyond the range of conventional imaging sensors. High temporal resolution laser radar can produce range resolved (ID) scattering profiles, which are unique to each aircraft relatively independent of target range2,3. This allows a variety of ID techniques to be applied at ranges well beyond the resolution limits of comparably sized imaging apertures. The ID profiles can be applied to automatic target recognition systems for classification and identification. However, in-class variation as well as large numbers of unclassified targets may limit these techniques. In this paper, we investigate the use of tomographic reconstruction to enhance long range identification. The reconstruction is based on compilations of ID signatures obtained at various angles due to relative target sensor motion. We describe the ladar system used to measure the ID returns of an F-4 aircraft. Based on the measured capabilities of the ERASER ladar, we use the IRMA computer model to generate sets of data consistent with the measured ladar data. Finally, we utilize the filtered back-projection method to investigate the reconstruction model data for both the ideal and limited-data cases.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"59 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":"132868624","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}
Because ultrashort laser pulses (as short as 10-14 seconds) are the shortest technological events ever created, their measurement remained a frustrating endeavor for many years. In order to measure an event in time, one generally requires a shorter event—which did not exist.
{"title":"Signal Recovery in the Measurement of Ultrashort Laser Pulses—Recent Progress","authors":"R. Trebino, M. Krumbügel","doi":"10.1364/srs.1998.sthd.3","DOIUrl":"https://doi.org/10.1364/srs.1998.sthd.3","url":null,"abstract":"Because ultrashort laser pulses (as short as 10-14 seconds) are the shortest technological events ever created, their measurement remained a frustrating endeavor for many years. In order to measure an event in time, one generally requires a shorter event—which did not exist.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"24 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":"127871147","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}
The so-called “small spherical viruses” are viruses with a shell of protein (the so-called “capsid”) surrounding an inner core of nucleic acid. The capsid is “crystalline” in the sense that it is constructed from many repetitions of the same polypeptides and the entire capsid is invariant under the rotational symmetries of the icosahedron. The icosahedron, as shown in Figure 1, is constructed from 20 equilateral triangles and has 60 rotational symmetries: a 5-fold axis where 5 triangles meet, a 3-fold axis through the center of each triangle, and a 2-fold axis at the midpoint of each edge between two triangles. For the viruses discussed in this paper, the outer radius of the capsid is about 140Å.
{"title":"Symmetry as a priori information: low-resolution reconstruction of viral structure from solution x-ray scattering data","authors":"Yibin Zheng, P. Doerschuk, John E. Johnson","doi":"10.1364/srs.1995.rtub2","DOIUrl":"https://doi.org/10.1364/srs.1995.rtub2","url":null,"abstract":"The so-called “small spherical viruses” are viruses with a shell of protein (the so-called “capsid”) surrounding an inner core of nucleic acid. The capsid is “crystalline” in the sense that it is constructed from many repetitions of the same polypeptides and the entire capsid is invariant under the rotational symmetries of the icosahedron. The icosahedron, as shown in Figure 1, is constructed from 20 equilateral triangles and has 60 rotational symmetries: a 5-fold axis where 5 triangles meet, a 3-fold axis through the center of each triangle, and a 2-fold axis at the midpoint of each edge between two triangles. For the viruses discussed in this paper, the outer radius of the capsid is about 140Å.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"31 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":"114813001","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}
Microwave imaging and inverse scattering, although closely related disciplines, have nonethe-less evolved separately over the last few years because of the differences in their respective applications. While both seek to characterize a scattering object (the “target”) from measurements of its scattered field, the methodology used historically to achieve this end differs. Although there is no formal delineation between the two, microwave imaging techniques typically construct a spatial distribution of a field or source-like quantity, such as current, reflectivity, or scattering centers, which is linearly related to the scattered field, but which is often nonliteral and difficult to interpret. Inverse scattering methods, on the other hand, generate reconstructions of the target’s intrinsic characteristics, namely shape and materials properties, which are nonlinearly related to the measured data, and hence require significant computational resources for their implementation. For these reasons, inverse scattering is considered more rigorous and quantitative, while imaging is generally applicable to a wider class of targets, particularly those which are electrically large and complex.
{"title":"A Comparison of Microwave Inverse Scattering and Imaging Techniques","authors":"I. Lahaie","doi":"10.1364/srs.1998.sthc.1","DOIUrl":"https://doi.org/10.1364/srs.1998.sthc.1","url":null,"abstract":"Microwave imaging and inverse scattering, although closely related disciplines, have nonethe-less evolved separately over the last few years because of the differences in their respective applications. While both seek to characterize a scattering object (the “target”) from measurements of its scattered field, the methodology used historically to achieve this end differs. Although there is no formal delineation between the two, microwave imaging techniques typically construct a spatial distribution of a field or source-like quantity, such as current, reflectivity, or scattering centers, which is linearly related to the scattered field, but which is often nonliteral and difficult to interpret. Inverse scattering methods, on the other hand, generate reconstructions of the target’s intrinsic characteristics, namely shape and materials properties, which are nonlinearly related to the measured data, and hence require significant computational resources for their implementation. For these reasons, inverse scattering is considered more rigorous and quantitative, while imaging is generally applicable to a wider class of targets, particularly those which are electrically large and complex.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"47 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":"124670578","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}
Signal recovery problems are generally posed in the form of rigid constraints (constraint sets), flexible constraints (optimization functional) or a combination thereof. Minimum cross-entropy methods1,2 belong to this third category due to an implicit rigid non-negativity constraint. An elegant approach to solving problems of the first category for convex constraint sets is the Projection Onto Convex Sets (POCS)3 technique. POCS has been limited primarily to least-squares projections, although other distance measures have been proposed.4 In this paper, minimum cross-entropy methods are interpreted as parallel cross-entropic POCS algorithms. This interpretation provides a theoretical basis for including rigid constraints in iterative super-resolution algorithms.
{"title":"A Projection-Onto-Convex-Sets Interpretation of Cross-Entropy Based Image Super-Resolution Algorithms","authors":"M. Nadar, P. J. Sementilli, B. Hunt","doi":"10.1364/srs.1995.rwc3","DOIUrl":"https://doi.org/10.1364/srs.1995.rwc3","url":null,"abstract":"Signal recovery problems are generally posed in the form of rigid constraints (constraint sets), flexible constraints (optimization functional) or a combination thereof. Minimum cross-entropy methods1,2 belong to this third category due to an implicit rigid non-negativity constraint. An elegant approach to solving problems of the first category for convex constraint sets is the Projection Onto Convex Sets (POCS)3 technique. POCS has been limited primarily to least-squares projections, although other distance measures have been proposed.4 In this paper, minimum cross-entropy methods are interpreted as parallel cross-entropic POCS algorithms. This interpretation provides a theoretical basis for including rigid constraints in iterative super-resolution algorithms.","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":"123107839","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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