Recently there has been some interest shown in the non-interferometric reconstruction of complex wavefields from intensity measurements [1,2]. At the same time it has been shown that for partially coherent systems this is not, in general, possible because different wavefields can exhibit identical intensity distributions [3]. The more restricted problem of finding the complex wave-field corresponding to the three dimensional intensity in a coherent system may be soluble by iterative phase retrieval techniques, but is not directly soluble. We consider a particular subset of the general problem which is demonstrably soluble by a direct method. The particular subset considered is essentially an optical wavefield propagating in a plane. This reduces the problem from three to two dimensions, resulting in a well-posed inverse problem. Initially we assume the system to be coherent, but we note that there are indications that the partially coherent case is also soluble. The solution presented is not just a theoretical curiosity because systems with the required geometry occur in slab waveguides and slit illumination systems.
{"title":"Direct Method for Phase Retrieval from the Intensity of Cylindrical Wavefronts","authors":"K. Larkin, C. Sheppard","doi":"10.1364/JOSAA.16.001838","DOIUrl":"https://doi.org/10.1364/JOSAA.16.001838","url":null,"abstract":"Recently there has been some interest shown in the non-interferometric reconstruction of complex wavefields from intensity measurements [1,2]. At the same time it has been shown that for partially coherent systems this is not, in general, possible because different wavefields can exhibit identical intensity distributions [3]. The more restricted problem of finding the complex wave-field corresponding to the three dimensional intensity in a coherent system may be soluble by iterative phase retrieval techniques, but is not directly soluble. We consider a particular subset of the general problem which is demonstrably soluble by a direct method. The particular subset considered is essentially an optical wavefield propagating in a plane. This reduces the problem from three to two dimensions, resulting in a well-posed inverse problem. Initially we assume the system to be coherent, but we note that there are indications that the partially coherent case is also soluble. The solution presented is not just a theoretical curiosity because systems with the required geometry occur in slab waveguides and slit illumination systems.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128183112","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}
Phase retrieval problem is the recovering of the lost phase information of an optical field. Usually the directly measurable quantity in an optical system is the intensity of the image or diffractive pattern. Consequently, substantial information available encoded in the phase is lost. In order to reconstruct the image, one needs both the amplitude and phase information. Therefore, it is important to reconstruct the image from the intensity measurements only.1 Various algorithms for the phase retrieval have already been proposed, including the iterative algorithms,2-5 the direct methods,6,7 and so on.8-10
{"title":"Phase retrieval in the Fresnel transform system : A recursive algorithm","authors":"W. Cong, N. Chen, B. Gu","doi":"10.1364/JOSAA.16.001827","DOIUrl":"https://doi.org/10.1364/JOSAA.16.001827","url":null,"abstract":"Phase retrieval problem is the recovering of the lost phase information of an optical field. Usually the directly measurable quantity in an optical system is the intensity of the image or diffractive pattern. Consequently, substantial information available encoded in the phase is lost. In order to reconstruct the image, one needs both the amplitude and phase information. Therefore, it is important to reconstruct the image from the intensity measurements only.1 Various algorithms for the phase retrieval have already been proposed, including the iterative algorithms,2-5 the direct methods,6,7 and so on.8-10","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121983808","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}
Proteins are remarkable molecular machines that are essential for life. They can do many things ranging from the precise control of blood clotting to synthesizing complex organic compounds. Pictures of protein molecules are in high demand in biotechnology because they are important for applications such as drug discovery and for engineering enzymes for commercial use.
{"title":"Protein Crystallography: From X-ray diffraction spots to a three-dimensional image","authors":"T. Terwilliger, J. Berendzen","doi":"10.1364/srs.1998.swa.1","DOIUrl":"https://doi.org/10.1364/srs.1998.swa.1","url":null,"abstract":"Proteins are remarkable molecular machines that are essential for life. They can do many things ranging from the precise control of blood clotting to synthesizing complex organic compounds. Pictures of protein molecules are in high demand in biotechnology because they are important for applications such as drug discovery and for engineering enzymes for commercial use.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129549322","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}
It is well known that atmospheric turbulence limits the resolution available to ground based astronomical observations to 0.5-1.0 arcseconds in the infrared. The advent of speckle interferometry in the 1970’s [1] has allowed the recovery of diffraction limited Fourier modulus information of astronomical objects of interest to be attempted routinely. A number of methods have since been proposed to obtain diffraction limited Fourier phase information, and thus image recovery. In the visible, where D/r o is large, it is now generally accepted that phase recovery from the average image bispectrum (or equivalently the triple correlation) appears to be the most successful [2] [3] [4].
{"title":"Comparison of shift-and-add & bispectrum image reconstruction methods for astronomy in the near-infrared","authors":"V. Klückers, N. Wooder, J. Dainty, A. Longmore","doi":"10.1364/JOSAA.13.001577","DOIUrl":"https://doi.org/10.1364/JOSAA.13.001577","url":null,"abstract":"It is well known that atmospheric turbulence limits the resolution available to ground based astronomical observations to 0.5-1.0 arcseconds in the infrared. The advent of speckle interferometry in the 1970’s [1] has allowed the recovery of diffraction limited Fourier modulus information of astronomical objects of interest to be attempted routinely. A number of methods have since been proposed to obtain diffraction limited Fourier phase information, and thus image recovery. In the visible, where D/r\u0000 o\u0000 is large, it is now generally accepted that phase recovery from the average image bispectrum (or equivalently the triple correlation) appears to be the most successful [2] [3] [4].","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126584063","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}
Frequency-Resolved Optical Gating (FROG) is a method for measuring the time-dependent intensity and phase of an ultrashort laser pulse. In FROG a nonlinear autocorrelation signal is frequency-resolved by a spectrometer to produce a "FROG trace", which is a type of spectrogram of the pulse [1]. The FROG trace, a two-dimensional image (intensity vs. frequency and delay) is then input into a phase-retrieval-based iterative algorithm [2], that determines the intensity and phase of the laser pulse. Although the FROG algorithm performs well, it requires a minute or more to converge for complex pulse shapes. It is therefore desirable in many situations to have a direct (i.e., non-iterative) computational method capable of quickly inverting the highly non-linear and complex function that relates the ultrashort pulse intensity and phase to its experimental FROG trace. In this work, we show that computational neural networks can directly obtain the intensity and phase of a pulse from its FROG trace in less than one second, independent of the pulse shape. Our demonstration using a serial personal computer is a proof of this principle, utilizing a set of pulses defined by only five parameters. Because neural networks now take advantage of very simple, fast, and powerful parallel-processing hardware, however, future waveform recovery, even in the general case of arbitrary pulses, could be nearly instantaneous.
{"title":"Direct Ultrashort-Pulse Retrieval Using Frequency-Resolved Optical Gating and a Computational Neural Network","authors":"C. Ladera, K. Delong, R. Trebino, D. Fittinghoff","doi":"10.1364/srs.1995.rtud2","DOIUrl":"https://doi.org/10.1364/srs.1995.rtud2","url":null,"abstract":"Frequency-Resolved Optical Gating (FROG) is a method for measuring the time-dependent intensity and phase of an ultrashort laser pulse. In FROG a nonlinear autocorrelation signal is frequency-resolved by a spectrometer to produce a \"FROG trace\", which is a type of spectrogram of the pulse [1]. The FROG trace, a two-dimensional image (intensity vs. frequency and delay) is then input into a phase-retrieval-based iterative algorithm [2], that determines the intensity and phase of the laser pulse. Although the FROG algorithm performs well, it requires a minute or more to converge for complex pulse shapes. It is therefore desirable in many situations to have a direct (i.e., non-iterative) computational method capable of quickly inverting the highly non-linear and complex function that relates the ultrashort pulse intensity and phase to its experimental FROG trace. In this work, we show that computational neural networks can directly obtain the intensity and phase of a pulse from its FROG trace in less than one second, independent of the pulse shape. Our demonstration using a serial personal computer is a proof of this principle, utilizing a set of pulses defined by only five parameters. Because neural networks now take advantage of very simple, fast, and powerful parallel-processing hardware, however, future waveform recovery, even in the general case of arbitrary pulses, could be nearly instantaneous.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1995-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115710110","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 recovery of an optical field with respect to position when only the intensity can be measured is an important problem in image science. In this case a priori information in the form of constraints can be applied and advantage can be taken of the inherently two-dimensional nature of the problem in order to reconstruct the full complex field from the available information. A similar recovery problem also arises with temporally varying data. One such case is the measurement of the complete time-dependent intensity and phase of an ultrashort laser pulse. This problem is particularly difficult for two reasons. First, it is inherently one-dimensional, so phase-retrieval methods, so successful for the spatial problem, do not directly apply. Second, such pulses are shorter than all possible measuring devices, so even the intensity cannot be measured. Traditionally, optical scientists working with ultrashort laser pulses have had only partial diagnostics, typically the intensity autocorrelation and the spectral intensity of the pulse. These diagnostics are not enough to completely characterize the laser pulse.
{"title":"Phase retrieval and time-frequency methods in the measurement of ultrasnort laser pulses","authors":"K. Delong, D. Fittinghoff, C. Ladera, R. Trebino","doi":"10.1364/srs.1995.rtuc1","DOIUrl":"https://doi.org/10.1364/srs.1995.rtuc1","url":null,"abstract":"The recovery of an optical field with respect to position when only the intensity can be measured is an important problem in image science. In this case a priori information in the form of constraints can be applied and advantage can be taken of the inherently two-dimensional nature of the problem in order to reconstruct the full complex field from the available information. A similar recovery problem also arises with temporally varying data. One such case is the measurement of the complete time-dependent intensity and phase of an ultrashort laser pulse. This problem is particularly difficult for two reasons. First, it is inherently one-dimensional, so phase-retrieval methods, so successful for the spatial problem, do not directly apply. Second, such pulses are shorter than all possible measuring devices, so even the intensity cannot be measured. Traditionally, optical scientists working with ultrashort laser pulses have had only partial diagnostics, typically the intensity autocorrelation and the spectral intensity of the pulse. These diagnostics are not enough to completely characterize the laser pulse.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1995-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114927224","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 recovered object in sheared beam imaging is an accumulated average of instantaneous "speckled" image frames. Atmospheric perturbations cause a random tilt in the phase of the return speckle pattern. This tilt induces a random translation in each reconstructed image. This random misregistration of individual frames with respect to each other degrades image quality by blurring the average resultant image.
{"title":"Comparative Analysis of Image Registration Techniques in Sheared Beam Imaging","authors":"David F. Olson, B. Landesman, R. Pierson","doi":"10.1364/srs.1995.rtue5","DOIUrl":"https://doi.org/10.1364/srs.1995.rtue5","url":null,"abstract":"The recovered object in sheared beam imaging is an accumulated average of instantaneous \"speckled\" image frames. Atmospheric perturbations cause a random tilt in the phase of the return speckle pattern. This tilt induces a random translation in each reconstructed image. This random misregistration of individual frames with respect to each other degrades image quality by blurring the average resultant image.","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":"123138206","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}
N. Cohen, Á. D. De Pierro, Clarice Favaretto Salvador
This work is concerned with the Phase Retrieval (PR) problem [3]. In its general formulation, the PR problem consists of retrieving the Fourier phase for a signal f whose Fourier transform F is known only in magnitude. In the applications, some additional information on f is available, e.g. the magnitude |f|. We shall be interested in the 2-D case where the additional information is the nonnegativity of f and the autocorrelation support. Iterative algorithms are commonly used to solve this problem [4]. Whereas these algorithms are the most successful in the applications, they do not enjoy ensured convergence, and often do not converge to a solution. Quite often they wind up either oscillating between two non-solutions, or converging very slowly towards a non- solution. In [2] a geometric characterization of the solution set is presented as well as experimental results suggesting an automatic way to avoid stagnation in the context of the retrieval algorithms mentioned above. For concreteness, let us consider the Error Reduction (ER) method. We observe that oscillations for the ER always occur between one fixed toroid [2] and the nonnegative orthant. The point x′ of stagnation on the toroid is external to the (convex) orthant. It is reasonable, as a means to avoid stagnation, to move from x′ to the point x” on the toroid which is “antipodal” to x′, thereby (roughly speaking) overrelaxing the operation of (convex) projection onto the orthant. More precisely, let c be the center of the toroid in question. It has been observed before [2] that c is in the positive orthant. We set x” = 2c − x′. We then use x” as an initial value for the ER algorithm. To summarize, we propose the following method : suppose that the algorithm stagnated in an image g k , that has a projection g k ′ onto the toroids set; then we get a new initial estimate for the algorithm by setting g o =−g k ′+2c with c representing the center of the toroid. This new starting point automatically satisfies the Fourier magnitude constraints, but not necessarily the positivity constraint, unless it happens to be a solution. In principle, the new initial point may lead to a renewed stagnation. However, in practice the phase retrieval improves considerably from one stagnation to another, leading to a good approximate solution. We have performed numerous experiments, using the ER algorithm with this stagnation breaker, and in all the cases it was not necessary to repeat the stagnation breaker more than twice per example. One advantage of the suggested method is that it is automatic, i.e. there is no need to identify on-line the stagnation type. A typical experiment using our new method is shown below. Two overrelaxations were necessary in this case, in order to obtain an acceptable approximation to the solution. The starting image that begins the process was taken random. Figure 1 is the image to be retrieved, Figure 2, the result after 100 iterations of ER.
这项工作涉及相位检索(PR)问题[3]。在它的一般公式中，PR问题包括对一个信号f的傅里叶变换f求出傅里叶相位，而这个信号的傅里叶变换f只知道其幅度。在应用中，关于f的一些附加信息是可用的，例如f的幅度。我们将对二维情况感兴趣，其中附加信息是f的非负性和自相关支持。通常采用迭代算法来解决这一问题[4]。虽然这些算法在应用中是最成功的，但它们不能保证收敛，而且通常不能收敛到一个解决方案。它们经常在两个非解之间振荡，或者非常缓慢地向一个非解收敛。在[2]中提出了解集的几何表征以及实验结果，提出了在上述检索算法的背景下避免停滞的自动方法。具体来说，让我们考虑误差减少(ER)方法。我们观察到ER的振荡总是发生在一个固定环面[2]和非负正交面之间。环面上的停滞点x '在(凸)正交线的外部。作为避免停滞的一种手段，从x '移动到与x '“对映”的环面上的点x '是合理的，因此(粗略地说)过度放松(凸)投影到正交面的操作。更准确地说，设c为所讨论的环面中心。之前[2]已经观察到c在正正交上。设x ' = 2c - x '。然后我们使用x '作为ER算法的初始值。综上所述，我们提出以下方法:假设算法停滞在一个图像g k上，该图像在环面集合上有一个投影g k ';然后设go = - g k′+2c, c代表环面中心，得到了新的算法初始估计。这个新的起点自动满足傅里叶幅度约束，但不一定满足正性约束，除非它恰好是一个解。原则上，新的起点可能导致新的停滞。然而，在实践中，相位恢复从一个停滞到另一个停滞有很大的改善，导致一个很好的近似解。我们已经进行了许多实验，使用ER算法和这个停滞断路器，在所有情况下，每个示例都不需要重复两次以上的停滞断路器。所建议的方法的一个优点是它是自动的，即不需要在线识别停滞类型。使用我们的新方法的典型实验如下所示。在这种情况下，为了获得可接受的近似解，需要两次过松弛。开始该过程的起始映像是随机选取的。图1为待检索的图像，图2为ER迭代100次后的结果。
{"title":"Algorithms for the Phase Retrieval Problem: an automatic Way to Overcome Stagnation","authors":"N. Cohen, Á. D. De Pierro, Clarice Favaretto Salvador","doi":"10.1364/srs.1998.stuc.4","DOIUrl":"https://doi.org/10.1364/srs.1998.stuc.4","url":null,"abstract":"This work is concerned with the Phase Retrieval (PR) problem [3]. In its general formulation, the PR problem consists of retrieving the Fourier phase for a signal f whose Fourier transform F is known only in magnitude. In the applications, some additional information on f is available, e.g. the magnitude |f|. We shall be interested in the 2-D case where the additional information is the nonnegativity of f and the autocorrelation support. Iterative algorithms are commonly used to solve this problem [4]. Whereas these algorithms are the most successful in the applications, they do not enjoy ensured convergence, and often do not converge to a solution. Quite often they wind up either oscillating between two non-solutions, or converging very slowly towards a non- solution. In [2] a geometric characterization of the solution set is presented as well as experimental results suggesting an automatic way to avoid stagnation in the context of the retrieval algorithms mentioned above. For concreteness, let us consider the Error Reduction (ER) method. We observe that oscillations for the ER always occur between one fixed toroid [2] and the nonnegative orthant. The point x′ of stagnation on the toroid is external to the (convex) orthant. It is reasonable, as a means to avoid stagnation, to move from x′ to the point x” on the toroid which is “antipodal” to x′, thereby (roughly speaking) overrelaxing the operation of (convex) projection onto the orthant. More precisely, let c be the center of the toroid in question. It has been observed before [2] that c is in the positive orthant. We set x” = 2c − x′. We then use x” as an initial value for the ER algorithm. To summarize, we propose the following method : suppose that the algorithm stagnated in an image g\u0000 k\u0000 , that has a projection \u0000g\u0000 k\u0000 ′ onto the toroids set; then we get a new initial estimate for the algorithm by setting \u0000g\u0000 o\u0000 =−g\u0000 k\u0000 ′+2c with c representing the center of the toroid. This new starting point automatically satisfies the Fourier magnitude constraints, but not necessarily the positivity constraint, unless it happens to be a solution. In principle, the new initial point may lead to a renewed stagnation. However, in practice the phase retrieval improves considerably from one stagnation to another, leading to a good approximate solution. We have performed numerous experiments, using the ER algorithm with this stagnation breaker, and in all the cases it was not necessary to repeat the stagnation breaker more than twice per example. One advantage of the suggested method is that it is automatic, i.e. there is no need to identify on-line the stagnation type. A typical experiment using our new method is shown below. Two overrelaxations were necessary in this case, in order to obtain an acceptable approximation to the solution. The starting image that begins the process was taken random. Figure 1 is the image to be retrieved, Figure 2, the result after 100 iterations of ER.","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":"125193746","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 structure completion problem in x-ray fiber diffraction analysis, a crystallographic method for studying polymer structures, involves reconstructing an incomplete image from a known part and experimental data in the form of the squared amplitudes of the Fourier coefficients. Formulating this as a Bayesian estimation problem allows explicit expressions for MMSE and MAP estimates to be obtained. Calculations using simulated fiber diffraction data show that the MMSE estimate out- performs current methods that correspond to certain MAP estimates.
{"title":"Bayesian Image Reconstruction in X-ray Fiber Diffraction","authors":"S. Baskaran, R. Millane","doi":"10.1364/srs.1998.swa.3","DOIUrl":"https://doi.org/10.1364/srs.1998.swa.3","url":null,"abstract":"The structure completion problem in x-ray fiber diffraction analysis, a crystallographic method for studying polymer structures, involves reconstructing an incomplete image from a known part and experimental data in the form of the squared amplitudes of the Fourier coefficients. Formulating this as a Bayesian estimation problem allows explicit expressions for MMSE and MAP estimates to be obtained. Calculations using simulated fiber diffraction data show that the MMSE estimate out- performs current methods that correspond to certain MAP estimates.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"7 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":"123421556","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}
Phase diversity techniques use the information in the 3-D volume near the focal plane to measure the optical wavefront errors present in an imaging system. Usually, the "focal volume" is sampled by recording an image at the best focus and an additional image taken slightly out of focus. Since phase diversity techniques do not require a point source, they are well suited for making wavefront measurements from extended objects. Once the wavefront errors are determined, the OTF associated with the optical aberrations can be deconvolved from both the focused and the defocused images to make a more accurate estimation of the object.
{"title":"Image reconstruction and isoplanatic patch measurements with phase diversity in day and night-time astronomy","authors":"D. S. Acton, D. Soltau","doi":"10.1364/srs.1995.rwb4","DOIUrl":"https://doi.org/10.1364/srs.1995.rwb4","url":null,"abstract":"Phase diversity techniques use the information in the 3-D volume near the focal plane to measure the optical wavefront errors present in an imaging system. Usually, the \"focal volume\" is sampled by recording an image at the best focus and an additional image taken slightly out of focus. Since phase diversity techniques do not require a point source, they are well suited for making wavefront measurements from extended objects. Once the wavefront errors are determined, the OTF associated with the optical aberrations can be deconvolved from both the focused and the defocused images to make a more accurate estimation of the object.","PeriodicalId":184407,"journal":{"name":"Signal Recovery and Synthesis","volume":"4 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":"122599917","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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