Orthonormal vector general polynomials derived from the Cartesian gradient of the orthonormal Zernike-based polynomials
نویسندگان
چکیده
منابع مشابه
Orthonormal vector polynomials in a unit circle, Part I: Basis set derived from gradients of Zernike polynomials.
Zernike polynomials provide a well known, orthogonal set of scalar functions over a circular domain, and are commonly used to represent wavefront phase or surface irregularity. A related set of orthogonal functions is given here which represent vector quantities, such as mapping distortion or wavefront gradient. These functions are generated from gradients of Zernike polynomials, made orthonorm...
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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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Many discrete transforms, such as the discrete cosine transform (DCT), are derived from sets of orthonormal polynomials. These sets of polynomials all possess recursion relationships, derived from a classic identity. In this paper, this recursion is used to derive generalized systolic arrays for the forward and inverse transform operations.
متن کاملOrthonormal vector polynomials in a unit circle, Part II : Completing the basis set.
Zernike polynomials provide a well known, orthogonal set of scalar functions over a circular domain, and are commonly used to represent wavefront phase or surface irregularity. A related set of orthogonal functions is given here which represent vector quantities, such as mapping distortion or wavefront gradient. Previously, we have developed a basis of functions generated from gradients of Zern...
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ژورنال
عنوان ژورنال: Journal of the Optical Society of America A
سال: 2018
ISSN: 1084-7529,1520-8532
DOI: 10.1364/josaa.35.000840