Fourier phasing is the problem of retrieving Fourier phase information from Fourier intensity data. The error-reduction (ER) algorithm consists of two projections on the subspaces generated by the Fourier magnitude co...
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Fourier phasing is the problem of retrieving Fourier phase information from Fourier intensity data. The error-reduction (ER) algorithm consists of two projections on the subspaces generated by the Fourier magnitude constraint and the object-domain constraint. The random phase illumination (RPI) and the real-valued constraint on the object significantly reduce the complexity of the intersection of the two subspaces. In this paper, we study how to approximate the projection of the starting point onto the subspace generated by the Fourier magnitude constraint by its projection on the tangent plane and estimate the approximation error by orthogonal decompositions. Moreover, we prove that the local geometric convergence rate of the ER algorithm is less than one almost surely and can be characterized as the cosine of the angle between the two projection spaces. A theoretical estimate of the convergence rate is derived and validated by some numerical experiments.
Rendering circles on digital platforms is essential in computer graphics. The widely adopted midpoint circle algorithm is a premier tool for this task. This article dives deep into the foundational aspects of this alg...
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Rendering circles on digital platforms is essential in computer graphics. The widely adopted midpoint circle algorithm is a premier tool for this task. This article dives deep into the foundational aspects of this algorithm, highlighting its prowess in enabling accurate and effortless circle depiction on digital displays. It further contrasts its merits with alternative circle drawing techniques. Importantly, our research presents a refined technique aimed at minimizing inaccuracies inherent in the standard cartesian-based Midpoint Circle Drawing algorithm (MPCDA). By incorporating an error-reduction strategy, we ensure greater accuracy in depicting circles. Comparative tests on diverse circle sizes and placements confirmed the efficacy of our enhanced method. When set against results from the traditional MPCDA, our approach showcases significant improvements.
Using a Digital Micromirror Device (DMD), the 3D-reconstruction of programmable rough particles (centrosymmetric or non-centrosymmetric) are done from a set of 120 interferometric images. This can be done using the er...
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Using a Digital Micromirror Device (DMD), the 3D-reconstruction of programmable rough particles (centrosymmetric or non-centrosymmetric) are done from a set of 120 interferometric images. This can be done using the error-reduction (ER) algorithm for the 2D shape reconstructions and the filtered back-projection for the 3D tomographic reconstruction. (C) 2022 Elsevier Ltd. All rights reserved.
Multiple image encryption (MIE) was proposed to increase the efficiency of encrypting images by processing several images simultaneously. Because of the advantage of optical technology in processing two-dimensional im...
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Multiple image encryption (MIE) was proposed to increase the efficiency of encrypting images by processing several images simultaneously. Because of the advantage of optical technology in processing two-dimensional images at high throughput, MIE has been significantly improved by use of methods originating from optics. Phase retrieval was the process of algorithmically finding solutions to the phase loss problem due to light detectors only capturing the intensity. It was to retrieve phase information for the determination of a structure from diffraction data. error-reduction algorithm is a typical phase retrieval method. Here, we employ it to illustrate that methods in phase retrieval are able to encrypt multiple images and compress them into encrypted data simultaneously. Moreover, the decryption is also designed to handle multiple images at the same time. The whole process including both the encryption and decryption is proposed to improve MIE with respect to the compression and efficiency. The feasibility and encryption of the MIE scheme is demonstrated with encryption experiments under Gaussian white noise and unauthorized access. (C) The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication.
A Lohmann-type computer-generated hologram (CGH) is fabricated using an electron-beam lithographic system. A high-resolution groove width of 0.2 mu m is attained in relief gratings by changing the e-beam exposures. A ...
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A Lohmann-type computer-generated hologram (CGH) is fabricated using an electron-beam lithographic system. A high-resolution groove width of 0.2 mu m is attained in relief gratings by changing the e-beam exposures. A diffraction efficiency close to similar to 30.4% is obtained by using resist-on-silicon recording materials and cell-structural apertures in a CGH. The reconstructed images exhibit fewer phase noises owing to the incorporation of a non-overflow cell structure into a CGH. The CGH is designed for reconstruction-noise reduction by using an iterative error-reduction algorithm. The designed CGH exhibits fewer reconstruction noises such that the performance function in the convergence is smaller by a factor of 1/3 than that in the first iteration. Experiments demonstrating the performance of CGHs obtained by electron-beam lithography are presented. (C) 2012 The Japan Society of Applied Physics
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