Results 131 to 140 of about 1,511 (175)

Zernike polynomials and atmospheric turbulence*

Journal of the Optical Society of America, 1976
This 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
exaly   +2 more sources

Quaternion Zernike spherical polynomials

Mathematics of Computation, 2014
Zernike spherical polynomials (ZSP) form a complete and orthonormal system on the unit sphere and they are most conveniently expressed in terms of a spherical coordinate system. Like the classical Zernike polynomials defined on the unit disk as product of radial polynomials (expressed in terms of classical Jacobi polynomials) by a pair of trigonometric
Morais, J., Cação, I.
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Orthogonality of Zernike polynomials

SPIE Proceedings, 2002
Zernike 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, Gregory J. Michels, Keith B. Doyle   +2 more
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Zernike annular polynomials and atmospheric turbulence

Journal of the Optical Society of America A, 2007
Imaging 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, 2010
We 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, 1980
Work 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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A new method for comparing Zernike circular polynomials with Zernike annular polynomials in annular pupils

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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Modal Reconstruction Methods With Zernike Polynomials

Journal of Refractive Surgery, 2005
ABSTRACT PURPOSE: To compare the advantages and disadvantages of different techniques for fitting Zernike polynomials to surfaces. METHODS: Two different methods, Orthogonal Projection and Gram-Schmidt orthogonalization, are compared in terms of speed and performance at fitting a complex object.
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Zernike Polynomials and Wavefronts

2017
A wavefront from a source at infinity arrives as a plane wave having no structure related to the nature of the source. However, as the wavefront is reflected from or passes through an optical system, it can become aberrated; i.e., the plane wave changes from being flat to taking on structure.
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Computation of the circle polynomials of Zernike

SPIE Proceedings, 2003
The circle polynomials of Zernike are a vital tool in the analysis of optical systems. Decomposition of wavefronts into Zernike polynomials can be insightful. Computation in the Zernike basis, however, is quite cumbersome and inefficient. This paper will address how rational polynomials such as Zernike, Laguerre, Legendre and Chebyshev can be ...
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