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...
| Main Author: | |
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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 |
| _version_ | 1789406603012734976 |
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| author | Ramos López, Darío |
| author_facet | Ramos López, Darío |
| author_sort | Ramos López, Darío |
| collection | DSpace |
| description | 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 |
| format | info:eu-repo/semantics/article |
| id | oai:repositorio.ual.es:10835-5616 |
| institution | Universidad de Cuenca |
| language | English |
| publishDate | 2018 |
| record_format | dspace |
| spelling | oai:repositorio.ual.es:10835-56162023-04-12T19:38:52Z Optimal sampling patterns for Zernike polynomials Ramos López, Darío 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 2018-02-09T08:44:33Z 2018-02-09T08:44:33Z 2016 info:eu-repo/semantics/article 0096-3003 http://hdl.handle.net/10835/5616 http://dx.doi.org/10.1016/j.amc.2015.11.006 en Attribution-NonCommercial-NoDerivatives 4.0 Internacional http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess |
| spellingShingle | Ramos López, Darío Optimal sampling patterns for Zernike polynomials |
| title | Optimal sampling patterns for Zernike polynomials |
| title_full | Optimal sampling patterns for Zernike polynomials |
| title_fullStr | Optimal sampling patterns for Zernike polynomials |
| title_full_unstemmed | Optimal sampling patterns for Zernike polynomials |
| title_short | Optimal sampling patterns for Zernike polynomials |
| title_sort | optimal sampling patterns for zernike polynomials |
| url | http://hdl.handle.net/10835/5616 http://dx.doi.org/10.1016/j.amc.2015.11.006 |
| work_keys_str_mv | AT ramoslopezdario optimalsamplingpatternsforzernikepolynomials |