Optimal sampling patterns for Zernike polynomials
A pattern of interpolation nodes on the disk is studied, for which the inter- polation 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 excel...
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| Format: | info:eu-repo/semantics/article |
| Language: | English |
| Published: |
2018
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| Online Access: | http://hdl.handle.net/10835/5616 http://dx.doi.org/10.1016/j.amc.2015.11.006 |
| Summary: | A pattern of interpolation nodes on the disk is studied, for which the inter-
polation 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 numer-
ically stable surface reconstruction, starting from both the elevation and the
slope data. Sampling at these nodes allows for a more precise recovery of the
coefficients in the Zernike expansion of a wavefront or of an optical surface.
Keywords:
Interpolation
Numerical condition
Zernike polynomials
Lebesgue constants |
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