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Modal Reconstruction Methods With Zernike Polynomials
Journal of Refractive Surgery, 2005ABSTRACT 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
2017A 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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Zernike polynomials and aberration balancing
SPIE Proceedings, 2003For small aberrations, the Strehl ratio of an imaging system depends on the aberration variance. If the aberration function is expanded in terms of a complete set of polynomials that are orthogonal over the system aperture, then the variance is given by the sum of the square of the aberration coefficients.
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Three topics in Zernike polynomials
SPIE Proceedings, 2004ABSTRACT Three different topics concerning the Zernike polynomials are investigated. First, the Zernike expansion of a function only of the coordinate x is considered. Second, a set of functions orthogonal for an electromagnetic optical system of high aperture are developed.
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Computation of the circle polynomials of Zernike
SPIE Proceedings, 2003The 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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On the Mathematical Properties of the Zernike Polynomials
Optica Acta: International Journal of Optics, 1976(1976). On the Mathematical Properties of the Zernike Polynomials. Optica Acta: International Journal of Optics: Vol. 23, No. 8, pp. 679-680.
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Mathematics of Zernike polynomials: a review.
Clinical & experimental ophthalmology, 2012Monochromatic aberrations of the eye principally originate from the cornea and the crystalline lens. Aberrometers operate via differing principles but function by either analysing the reflected wavefront from the retina or by analysing an image on the retina.
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