An examination of an iterative method for the solution of the phase problem in optics and electron optics: I. Test calculations

Misell, D L

doi:10.1088/0022-3727/6/18/305

Cited by 119 publications

(53 citation statements)

References 18 publications

(13 reference statements)

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“…Fienup, for example, modified the Gerchberg-Saxton algorithm in order to retrieve the phase from the magnitude of the Fourier transform of an image under the constraint that the desired solution is non-negative [12]. Misell also proposed an iterative procedure similar to the Gerchberg-Saxton algorithm for the case in which the intensity distributions in two slightly defocused planes are known [28]. For each of these iterative procedures, however, it appears that the convergence of the algorithm to the correct solution depends upon the properties of the signal to be recovered as well as on the initial estimate which is used to begin the iteration.…”

Section: 2: the Phase Retrieval Problemmentioning

confidence: 99%

“…For example, in many problems which arise in x-ray crystallography [42], -9-electron microscopy [44], coherence theory [31], and optics [28], only the magnitude of the Fourier transform of an electromagnetic wave may be recorded or is available for measurement. Therefore, the specification of the electromagnetic wave depends upon the retrieval of the Fourier transform phase of the wave from only spectral magnitude information.…”

Section: : Introductionmentioning

confidence: 99%

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Signal reconstruction from phase or magnitude

Hayes

Lim

Oppenheim³

1980

IEEE Trans. Acoust., Speech, Signal Process.

332

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This thesis addresses two issues related to the problem of reconstructing a one-dimensional or a multidimensional sequence from either the phase or the magnitude of its Fourier transform. The first concerns the development of conditions under which a sequence is uniquely defined in terms of only phase or magnitude information. For example, it is shown that a one-dimensional sequence is, in most cases, uniquely specified by the phase of its Fourier transform if the sequence is finite in length. In the case of magnitude, a condition for uniqueness is presented which is a generalization of the minimum and maximum phase constraints and includes them as a special case. For multidimensional sequences, on the other hand, it is shown that a finite support constraint is sufficient, in most cases, for the sequence to be uniquely defined by either the phase or magnitude of its Fourier transform.The second issue which is addressed concerns the development of algorithms for reconstructing a sequence from either the phase or magnitude of its Fourier transform. In particular, several algorithms are presented for reconstructing a sequence from its phase. These algorithms, which include iterative as well as non-iterative approaches, always lead to the correct solution provided the appropriate uniqueness constraints are fulfilled. An iterative procedure is also described for reconstructing a multidimensional sequence from the magnitude of its Fourier transform. However, the convergence of this algorithm to the desired sequence appears to depend upon the availability of an initial estimate which is sufficiently close to the correct solution. Finally, a number of examples are presented which illustrate the use of these algorithms. -2-

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Section: 2: the Phase Retrieval Problemmentioning

confidence: 99%

Section: : Introductionmentioning

confidence: 99%

Signal reconstruction from phase or magnitude

Hayes

Lim

Oppenheim³

1980

IEEE Trans. Acoust., Speech, Signal Process.

332

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show abstract

“…Defocusing of the registered images is one of the popular instruments to get a sufficient phase diversity. [5][6][7][8] In a recent development, a spatial light modulator (SLM) is exploited for defocusing (e.g., see Refs. 9 and 10).…”

Section: Introductionmentioning

confidence: 99%

Sparse superresolution phase retrieval from phase-coded noisy intensity patterns

Katkovnik

Егиазарян

2017

Opt. Eng

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Abstract. We consider a computational superresolution inverse diffraction problem for phase retrieval from phase-coded intensity observations. The optical setup includes a thin lens and a spatial light modulator for phase coding. The designed algorithm is targeted on an optimal solution for Poissonian noisy observations. One of the essential instruments of this design is a complex-domain sparsity applied for complex-valued object (phase and amplitude) to be reconstructed. Simulation experiments demonstrate that good quality imaging can be achieved for high-level of the superresolution with a factor of 32, which means that the pixel of the reconstructed object is 32 times smaller than the sensor's pixel. This superresolution corresponds to the object pixel as small as a quarter of the wavelength.

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“…Misell [9][10][11] has extended the algorithm for any two input and output planes. These approaches are proven to converge to a phase distribution with a minimal mean square error (MSE) 12,13 .…”

Section: Introductionmentioning

confidence: 99%

Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform

Ilovitsh

Zach²,

Zalevsky

2014

JoVE

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We propose a method for increasing the resolution of an object and overcoming the diffraction limit of an optical system installed on top of a moving imaging system, such as an airborne platform or satellite. The resolution improvement is obtained in a two-step process. First, three low resolution differently defocused images are being captured and the optical phase is retrieved using an improved iterative Gerchberg-Saxton based algorithm. The phase retrieval allows to numerically back propagate the field to the aperture plane. Second, the imaging system is shifted and the first step is repeated. The obtained optical fields at the aperture plane are combined and a synthetically increased lens aperture is generated along the direction of movement, yielding higher imaging resolution. The method resembles a well-known approach from the microwave regime called the Synthetic Aperture Radar (SAR) in which the antenna size is synthetically increased along the platform propagation direction. The proposed method is demonstrated through laboratory experiment. Video LinkThe video component of this article can be found at

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An examination of an iterative method for the solution of the phase problem in optics and electron optics: I. Test calculations

Cited by 119 publications

References 18 publications

Signal reconstruction from phase or magnitude

Signal reconstruction from phase or magnitude

Sparse superresolution phase retrieval from phase-coded noisy intensity patterns

Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform

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