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Influence of Lens Systematic Errors on Autocollimator Angle Measurement: Theoretical and Experimental Explanations. [PDF]
Sensors (Basel)Li Y, Zhang S, Chang D, Yu T, Tan J.
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Aberration compensation in Doppler holography of the human eye fundus by subaperture signal correlation. [PDF]
Biomed Opt ExpressBratasz Z +4 more
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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, Andre Fleck
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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, Andre Fleck
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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 ...
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Quaternion Zernike spherical polynomials
Mathematics of Computation, 2014Zernike 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, 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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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-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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Phase wavefront aberration modeling using Zernike and pseudo-Zernike polynomials
Journal of the Optical Society of America A, 2013Orthogonal polynomials can be used for representing complex surfaces on a specific domain. In optics, Zernike polynomials have widespread applications in testing optical instruments, measuring wavefront distributions, and aberration theory. This orthogonal set on the unit circle has an appropriate matching with the shape of optical system components ...
Kambiz, Rahbar +2 more
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