{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T18:57:10Z","timestamp":1776452230868,"version":"3.51.2"},"reference-count":15,"publisher":"Optica Publishing Group","issue":"22","license":[{"start":{"date-parts":[[2020,6,19]],"date-time":"2020-06-19T00:00:00Z","timestamp":1592524800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v1#VOR"},{"start":{"date-parts":[[2020,6,19]],"date-time":"2020-06-19T00:00:00Z","timestamp":1592524800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"funder":[{"name":"Spanish Ministry of Econom\u00eda y\n\t\t\t\t\t\tCompetitividad","award":["FIS2016-77319-C2-1-R"],"award-info":[{"award-number":["FIS2016-77319-C2-1-R"]}]},{"DOI":"10.13039\/501100008530","name":"FEDER","doi-asserted-by":"publisher","award":["Xunta de Galicia\/FEDER ED431E 2018\/08"],"award-info":[{"award-number":["Xunta de Galicia\/FEDER ED431E 2018\/08"]}],"id":[{"id":"10.13039\/501100008530","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Appl. Opt."],"published-print":{"date-parts":[[2020,8,1]]},"abstract":"<jats:p>The concept of curvature sensing is reviewed, and a comprehensive\n\t\t\t\t\tderivation of the curvature polynomials is given, whose inner products\n\t\t\t\t\twith the wavefront curvature data yield the Zernike aberration\n\t\t\t\t\tcoefficients of an aberrated circular wavefront. The data consist of\n\t\t\t\t\tthe Laplacian of the wavefront across its interior and its outward\n\t\t\t\t\tnormal slope at its circular boundary. However, we show that the\n\t\t\t\t\tradial part of the curvature polynomials and their slopes at the\n\t\t\t\t\tboundary of the wavefront have a value of zero, except when the\n\t\t\t\t\tangular frequency of the corresponding Zernike polynomial is equal to\n\t\t\t\t\tits radial degree. As a result, the effect of noise on the\n\t\t\t\t\tcorresponding Zernike coefficients is lower because the noisy data at\n\t\t\t\t\tthe boundary of the wavefront is not used to determine their values.\n\t\t\t\t\tThe use of the curvature polynomials to determine the Zernike\n\t\t\t\t\tcoefficients is demonstrated with simulated noisy curvature data of an\n\t\t\t\t\taberration function consisting of 10 Zernike coefficients, namely\n\t\t\t\t\tdefocus, primary, secondary, and tertiary astigmatism, coma, and\n\t\t\t\t\tspherical aberrations.<\/jats:p>","DOI":"10.1364\/ao.391958","type":"journal-article","created":{"date-parts":[[2020,4,30]],"date-time":"2020-04-30T16:42:09Z","timestamp":1588264929000},"page":"G120","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Zernike coefficients from wavefront curvature data"],"prefix":"10.1364","volume":"59","author":[{"given":"Virendra N.","family":"Mahajan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eva","family":"Acosta","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"285","published-online":{"date-parts":[[2020,6,19]]},"reference":[{"key":"ao-59-22-G120-R1","volume-title":"Optical Imaging and Aberrations, Part\n\t\t\t\t\tII: Wave Diffraction Optics","author":"Mahajan","year":"2011"},{"key":"ao-59-22-G120-R2","volume-title":"Optical Imaging and Aberrations, Part\n\t\t\t\t\tIII: Wavefront Analysis","author":"Mahajan","year":"2013"},{"key":"ao-59-22-G120-R3","doi-asserted-by":"publisher","first-page":"1908","DOI":"10.1364\/JOSAA.34.001908","volume":"34","author":"Mahajan","year":"2017","journal-title":"J.\n\t\t\t\t\tOpt. 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