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- W2071921337 abstract "The circle polynomials of Zernike play a prominent role in optical analysis. While decompositions of wavefronts into Zernike polynomial series can yield valuable insight, computing with the polynomials themselves is quite inefficient. Here we outline how rational polynomials like those of Zernike, Legendre, Chebyshev and Laguerre can be handled as affine combinations of a Taylor monomial set. We demonstrate how calculations can be performed much more rapidly in the Taylor basis and how to use integer transformations to recover the exact amplitudes in the desired basis. We also explore C++ optimizations for storing the Zernike amplitudes and transforming between Zernike polynomials and Taylor monomials." @default.
- W2071921337 created "2016-06-24" @default.
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- W2071921337 date "2002-09-05" @default.
- W2071921337 modified "2023-09-23" @default.
- W2071921337 title "Efficient computation with special functions like the circle polynomials of Zernike" @default.
- W2071921337 doi "https://doi.org/10.1117/12.481181" @default.
- W2071921337 hasPublicationYear "2002" @default.
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