Phase retrieval from experimental far-field intensity data

Perez-Ilzarbe, M.J.; Nieto‐Vesperinas, M.; Navarro, Rafael

doi:10.1364/josaa.7.000434

Cited by 11 publications

(2 citation statements)

References 25 publications

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“…The PR system is the wave-front detector of focal plane waves. A laser spotlight on the object plane is a target designated from the focal plane image acquisition, using the acquired image, the defocus of the corresponding image, and the known pupil size and shape to reverse solve the aberration of the optical system [ 23 , 24 ]. The structure of the PR system is shown in Figure 1 .…”

Section: The Principle Of Prmentioning

confidence: 99%

Research on Optical Metrology for Complex Optical Surfaces with Focal Plane Wavefront Sensing

Ma,

Wang,

Wang

et al. 2023

Micromachines

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Complex optical elements have the advantages of improving image quality and optical performance and expanding the field of view. Therefore, it is widely used in X-ray scientific devices, adaptive optical elements, high-energy laser systems, and other fields and is a hot research direction in precision optics. Especially for precision machining, there is a greater need for high-precision testing technology. However, how to measure complex surfaces efficiently and accurately is still an important research topic in optical metrology technology. In order to verify the ability of optical metrology for complex optical surfaces with wavefront sensing based on image information of the focal plane, some experiment platforms in different types of optical surfaces were set up. In order to validate the feasibility and validity of wavefront-sensing technology based on image information of focal planes, a large number of repetitive experiments were carried out. The measurement results with wavefront sensing based on image information of the focal plane were compared with the measurement results with the ZYGO interferometer. The experimental results demonstrate that good agreement is obtained among the error distribution, PV value, and RMS value of the ZYGO interferometer, which shows the feasibility and validity of wavefront sensing based on image information of focal plane technology in optical metrology for the complex optical surface.

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Section: The Principle Of Prmentioning

confidence: 99%

Research on Optical Metrology for Complex Optical Surfaces with Focal Plane Wavefront Sensing

Ma,

Wang,

Wang

et al. 2023

Micromachines

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“…¸ = z − ε for a binary medium (ε is the porosity). To the two expressions for R Z (h) (Eqs 2 and 5), note that an additional constraint of nonnegativity is always imposed on at the fourth step of the iterative Fourier transform algorithm to form g k+1 (Sault, 1984;Pérez-Ilzarbe et al, 1990;Schultz & Snyder, 1992). In this work, this constraint of non-negativity was not enforced.…”

Section: (5)mentioning

confidence: 99%

Practical modelling of porous media from second‐order statistics: the phase‐retrieval problem and the interpretation of the covariance

Anguy

Trong

Ehrlich

2005

Journal of Microscopy

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Key words. Covariance, image modelling, models of random porous microstructures, phase retrieval problem. SummaryIn many disciplines, binary numerical porous media are commonly generated as realizations of a random process characterized by a limited set of morphological measurements, e.g. the conditioning and truncated Gaussian random field (GRF) model or the Monte Carlo simulated annealing (SA) reconstruction. Whether the output microstructures of a model are quantitative or qualitative depends largely on the information carried by the constraints that are implemented. We focus on the standard two-point correlation function, also referred to as the covariance. The isotropic situation has been previously extensively studied. Here, we concentrate on a vector distancedependent covariance. Relying on practical solutions to the phase-retrieval problem (retrieving an object from its Fourier modulus) encountered in general imaging, we show empirically that a finite binary two-or three-dimensional actual sample can be recovered systematically to within a pixel from its correlation integral (the volume average covariance to within a scale factor). In random modelling, this characteristic, describing uniquely a single sample of finite size, must be simplified, i.e. reduced to its statistical content, prior to be fitted in a random model (GRF, SA) as the characteristic of a series of realizations of a porous medium. We consider a common simplification, i.e. truncation, in which that part of the covariance relating to the small-scale features of the observed sample is preserved only. This arbitrary simplification is empirically supported by numerous published numerical experiments showing that the small-scale content of a volume-averaged covariance can be fairly well reproduced in realizations of various random models: its statistical nature is thus illustrated with the GRF model. The unique solution to the phase-retrieval problem confers an important sense to this numerical agreement: the correlation integral being the most complete descriptor, the actual sample and the model outputs are considered as true analogues over scales smaller or equal to the cutoff length attached to the truncation. Thus, awareness of the phase-retrieval problem supports on an empirical basis the generation of synthetic binary objects from a direct measurement on an available sample. IntroductionIn many disciplines including biology, medicine, petroleum engineering and water exploration, it may be of the greatest interest to generate numerical media from morphological information measured on a finite support [a two-dimensional (2D) digitized thin section or a 3D image obtained by X-ray microtomography] of size smaller than the whole system of interest. The conditioning and truncated Gaussian random field (GRF) model is an example of a widely used technique for producing synthetic media from a minimal set of morphological descriptors: the standard one-point and two-point correlation functions. The one-point correlation function is the classical s...

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1994

Principles of Electron Optics

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Phase retrieval from experimental far-field intensity data

Cited by 11 publications

References 25 publications

Research on Optical Metrology for Complex Optical Surfaces with Focal Plane Wavefront Sensing

Research on Optical Metrology for Complex Optical Surfaces with Focal Plane Wavefront Sensing

Practical modelling of porous media from second‐order statistics: the phase‐retrieval problem and the interpretation of the covariance

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