Generalized Zernike or disc polynomials
نویسندگان
چکیده
منابع مشابه
Strehl ratio and amplitude-weighted generalized orthonormal Zernike-based polynomials.
The concept of orthonormal polynomials is revisited by developing a Zernike-based orthonormal set for a non-circular pupil that is transmitting an aberrated, non-uniform field. We refer to this pupil as a general pupil. The process is achieved by using the matrix form of the Gram-Schmidt procedure on Zernike circle polynomials and is interpreted as a process of balancing each Zernike circle pol...
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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. Alternative representations are presented.
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Abstract. Over the past few years considerable attention has been given to the role played by the Zernike polynomials (ZPs) in many di↵erent fields of geometrical optics, optical engineering, and astronomy. The ZPs and their applications to corneal surface modeling played a key role in this development. These polynomials are a complete set of orthogonal functions over the unit circle and are co...
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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. It is shown that these nodes have an excellent performance also from several alternative points of view, providing a numerically stable surface ...
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To identify the content of motion sequences such as gestures and video sequences, we propose a compact representation of flow fields using a basis of complex Zernike polynomials. Moments derived from projection of these polynomials have been used in recognition. Previously, local descriptions learned from examples, or specified a priori, have been used to identify local flow events. Affine expa...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2005
ISSN: 0377-0427
DOI: 10.1016/j.cam.2004.04.004