Results 11 to 20 of about 2,467 (209)
Optimal sampling patterns for Zernike polynomials [PDF]
Applied Mathematics and Computation, 2016 A pattern of interpolation nodes on the disk is studied, for which the interpolation problem is theoretically unisolvent, and which renders a minimal numerical condition for the collocation matrix when the standard basis of Zernike polynomials is used.
Darío Ramos-López +3 more
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Recursive computation of generalised Zernike polynomials
Journal of Computational and Applied Mathematics, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Iván Area +2 more
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An FPGA Architecture for Extracting Real-Time Zernike Coefficients from Measured Phase Gradients [PDF]
Measurement Science Review, 2015 Zernike modes are commonly used in adaptive optics systems to represent optical wavefronts. However, real-time calculation of Zernike modes is time consuming due to two factors: the large factorial components in the radial polynomials used to define them
Moser Steven +2 more
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Zernike expansion of derivatives and Laplacians of the Zernike circle polynomials [PDF]
Journal of the Optical Society of America A, 2014 The partial derivatives and Laplacians of the Zernike circle polynomials occur in various places in the literature on computational optics. In a number of cases, the expansion of these derivatives and Laplacians in the circle polynomials are required. For the first-order partial derivatives, analytic results are scattered in the literature, starting as
Janssen, A.J.E.M., Janssen, AJEM Guido
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Generalized Zernike or disc polynomials
Journal of Computational and Applied Mathematics, 2005 The paper is devoted to the study of the generalized Zernike or disc polynomials, which are orthogonal 2D polynomials on the unit disc and can be expressed by Jacobi polynomials of transformed arguments. Two differential equations, a first-order and a second-order one with a certain degree of freedom, and the operators of lowering and raising of the ...
Wünsche, Alfred
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Stable Evaluation of 3D Zernike Moments for Surface Meshes
Algorithms, 2022 The 3D Zernike polynomials form an orthonormal basis of the unit ball. The associated 3D Zernike moments have been successfully applied for 3D shape recognition; they are popular in structural biology for comparing protein structures and properties. Many
Jérôme Houdayer, Patrice Koehl
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Accuracy and reliability of orthogonal polynomials in representing corneal topography
Medicine in Novel Technology and Devices, 2022 Fitting of corneal topography data to analytical surfaces has been necessary in many clinical and experimental applications, yet absolute superiority of fitting methods was still unclear, and their overfitting risks were not well studied.
Junjie Wang +9 more
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Zernike polynomials and their applications
Journal of Optics, 2022 Abstract The Zernike polynomials are a complete set of continuous functions orthogonal over a unit circle. Since first developed by Zernike in 1934, they have been in widespread use in many fields ranging from optics, vision sciences, to image processing.
Kuo Niu, Chao Tian
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Simultaneous quantification of longitudinal and transverse ocular chromatic aberrations with Hartmann–Shack wavefront sensor [PDF]
Journal of Innovative Optical Health Sciences, 2018 A simple method to objectively and simultaneously measure eye’s longitudinal and transverse chromatic aberrations was proposed. A dual-wavelength wavefront measurement system using two Hartmann–Shack wavefront sensors was developed. The wavefronts of the
Yangchun Deng +3 more
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Reconstruction of wavefront distorted by atmospheric turbulence using a Shack-Hartman sensor [PDF]
Компьютерная оптика, 2019 The reconstruction of a wave front containing random phase distortions of the light field is considered. The reconstruction is performed by a Hartmann method based on the approximation of the wave function by Zernike polynomials using estimates of local ...
Vitaly Lavrinov, Lidiya Lavrinova
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