Results 161 to 170 of about 2,467 (209)
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Journal of Modern Optics, 2011
In this paper we review a special set of orthonormal functions, namely Zernike polynomials which are widely used in representing the aberrations of optical systems. We give the recurrence relations, relationship to other special functions, as well as scaling and other properties of these important polynomials.
Vasudevan Lakshminarayanan +1 more
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In this paper we review a special set of orthonormal functions, namely Zernike polynomials which are widely used in representing the aberrations of optical systems. We give the recurrence relations, relationship to other special functions, as well as scaling and other properties of these important polynomials.
Vasudevan Lakshminarayanan +1 more
exaly +3 more sources
Vector polynomials orthogonal to the gradient of Zernike polynomials
Optics Letters, 1982A set of vector polynomials is constructed, and it is shown that they are orthonormal to the gradient of the Zernike polynomials. Such a set can be used to obtain directly the Zernike decomposition of the wave front from the measurements involving the gradient of the wave front.
Athanasios Gavrielides
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Zernike Polynomials and Optical Aberrations
Applied Optics, 1995The use of Zernike polynomials to calculate the standard deviation of a primary aberration across a circular, annular, or a Gaussian pupil is described. The standard deviation of secondary aberrations is also discussed briefly.
Virendra N Mahajan
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Wave-front interpretation with Zernike polynomials
Applied Optics, 1980Several low-order Zernike modes are photographed for visualization. These polynomials are extended to include both circular and annular pupils through a Gram-Schmidt orthogonalization procedure. Contrary to the traditional understanding, the classical least-squares method of determining the Zernike coefficients from a sampled wave front with ...
J Y, Wang, D E, Silva
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Zernike polynomials and atmospheric turbulence*
Journal of the Optical Society of America, 1976This paper discusses some general properties of Zernike polynomials, such as their Fourier transforms, integral representations, and derivatives. A Zernike representation of the Kolmogoroff spectrum of turbulence is given that provides a complete analytical description of the number of independent corrections required in a wave-front compensation ...
Robert J Noll
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Orthogonality of Zernike polynomials
SPIE Proceedings, 2002Zernike polynomials are an orthogonal set over a unit circle and are often used to represent surface distortions from FEA analyses. There are several reasons why these coefficients may lose their orthogonality in an FEA analysis. The effects, their importance, and techniques for identifying and improving orthogonality are discussed.
Victor L. Genberg +2 more
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Zernike annular polynomials and atmospheric turbulence
Journal of the Optical Society of America A, 2007Imaging through atmospheric turbulence by systems with annular pupils is discussed using the Zernike annular polynomials. Fourier transforms of these polynomials are derived analytically to facilitate the calculation of variance and covariance of the aberration coefficients.
Guang-Ming, Dai, Virendra N, Mahajan
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Zernike Polynomials and Beyond
Latin America Optics and Photonics Conference, 2010We discuss why we use Zernike circle polynomials in optics, when to use them, and what to use in their place when not to use them.
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Zernike-Tatian polynomials for interferogram reduction
Applied Optics, 1980Work on orthogonal polynomials by Tatian has been incorporated into a computer program for interferogram analysis. For obscured-aperture optical systems, the data reduction is far more accurate than with programs based only on Zernike polynomials. Results are shown for spherical aberration, coma, and astigmatism.
W H, Swantner, W H, Lowrey
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2010 International Conference on Computer, Mechatronics, Control and Electronic Engineering, 2010
To compare the difference between Zernike annular polynomial and Zernike circular polynomial, an approximate mathematic relationship between Zernike annular polynomial coefficients and SEIDEL coefficients is proposed. A new method is applied in comparing experiment.
null Shao Jing, null Ma Dongmei
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To compare the difference between Zernike annular polynomial and Zernike circular polynomial, an approximate mathematic relationship between Zernike annular polynomial coefficients and SEIDEL coefficients is proposed. A new method is applied in comparing experiment.
null Shao Jing, null Ma Dongmei
openaire +1 more source