Accuracy of Zernike polynomials in characterizing optical aberrations and the corneal surface of the eye
Autor(a) principal: | |
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Data de Publicação: | 2005 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNIFESP |
Texto Completo: | http://repositorio.unifesp.br/handle/11600/28319 http://dx.doi.org/10.1167/iovs.04-1222 |
Resumo: | PURPOSE. Zernike polynomials have been successfully used for approximately 70 years in many different fields of optics. Nevertheless, there are some recent discussions regarding the precision and accuracy of these polynomials when applied to surfaces such as the human cornea. the main objective of this work was to investigate the absolute accuracy of Zernike polynomials of different orders when fitting several types of theoretical corneal and wave-front surface data.METHODS. A set of synthetic surfaces resembling several common corneal anomalies was sampled by using cylindrical coordinates to simulate the height output files of commercial video-keratography systems. the same surfaces were used to compute the optical path difference (wave-front [WF] error), by using a simple ray-tracing procedure. Corneal surface and WF error was fit by using a least-squares algorithm and Zernike polynomials of different orders, varying from 1 to 36 OSA-VSIA convention terms.RESULTS. the root mean square error (RMSE) ranged - from the most symmetric corneal surface (spherical shape) through the most complex shape (after radial keratotomy [RK]) for both the optical path difference and the surface elevation for 1 through 36 Zernike terms - from 421.4 to 0.8 mu m and 421.4 to 8.2 mu m, respectively. the mean RMSE for the maximum Zernike terms for both surfaces was 4.5 mu m.CONCLUSIONS. These results suggest that, for surfaces such as that present after RK, in keratoconus, or after keratoplasty, even more than 36 terms may be necessary to obtain minimum accuracy requirements. the author suggests that the number of Zernike polynomials should not be a global fixed conventional or generally accepted value but rather a number based on specific surface properties and desired accuracy. |
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Carvalho, Luis Alberto [UNIFESP]Universidade de São Paulo (USP)Universidade Federal de São Paulo (UNIFESP)2016-01-24T12:37:53Z2016-01-24T12:37:53Z2005-06-01Investigative Ophthalmology & Visual Science. Rockville: Assoc Research Vision Ophthalmology Inc, v. 46, n. 6, p. 1915-1926, 2005.0146-0404http://repositorio.unifesp.br/handle/11600/28319http://dx.doi.org/10.1167/iovs.04-122210.1167/iovs.04-1222WOS:000229504600007PURPOSE. Zernike polynomials have been successfully used for approximately 70 years in many different fields of optics. Nevertheless, there are some recent discussions regarding the precision and accuracy of these polynomials when applied to surfaces such as the human cornea. the main objective of this work was to investigate the absolute accuracy of Zernike polynomials of different orders when fitting several types of theoretical corneal and wave-front surface data.METHODS. A set of synthetic surfaces resembling several common corneal anomalies was sampled by using cylindrical coordinates to simulate the height output files of commercial video-keratography systems. the same surfaces were used to compute the optical path difference (wave-front [WF] error), by using a simple ray-tracing procedure. Corneal surface and WF error was fit by using a least-squares algorithm and Zernike polynomials of different orders, varying from 1 to 36 OSA-VSIA convention terms.RESULTS. the root mean square error (RMSE) ranged - from the most symmetric corneal surface (spherical shape) through the most complex shape (after radial keratotomy [RK]) for both the optical path difference and the surface elevation for 1 through 36 Zernike terms - from 421.4 to 0.8 mu m and 421.4 to 8.2 mu m, respectively. the mean RMSE for the maximum Zernike terms for both surfaces was 4.5 mu m.CONCLUSIONS. These results suggest that, for surfaces such as that present after RK, in keratoconus, or after keratoplasty, even more than 36 terms may be necessary to obtain minimum accuracy requirements. the author suggests that the number of Zernike polynomials should not be a global fixed conventional or generally accepted value but rather a number based on specific surface properties and desired accuracy.Univ São Paulo, IFSC, Grp Opt, São Paulo, BrazilUniversidade Federal de São Paulo, Escola Paulista Med, Dept Oftalmol, São Paulo, BrazilUniversidade Federal de São Paulo, Escola Paulista Med, Dept Oftalmol, São Paulo, BrazilWeb of Science1915-1926engAssoc Research Vision Ophthalmology IncInvestigative Ophthalmology & Visual ScienceAccuracy of Zernike polynomials in characterizing optical aberrations and the corneal surface of the eyeinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UNIFESPinstname:Universidade Federal de São Paulo (UNIFESP)instacron:UNIFESP11600/283192022-07-08 10:45:12.088metadata only accessoai:repositorio.unifesp.br:11600/28319Repositório InstitucionalPUBhttp://www.repositorio.unifesp.br/oai/requestopendoar:34652022-07-08T13:45:12Repositório Institucional da UNIFESP - Universidade Federal de São Paulo (UNIFESP)false |
dc.title.en.fl_str_mv |
Accuracy of Zernike polynomials in characterizing optical aberrations and the corneal surface of the eye |
title |
Accuracy of Zernike polynomials in characterizing optical aberrations and the corneal surface of the eye |
spellingShingle |
Accuracy of Zernike polynomials in characterizing optical aberrations and the corneal surface of the eye Carvalho, Luis Alberto [UNIFESP] |
title_short |
Accuracy of Zernike polynomials in characterizing optical aberrations and the corneal surface of the eye |
title_full |
Accuracy of Zernike polynomials in characterizing optical aberrations and the corneal surface of the eye |
title_fullStr |
Accuracy of Zernike polynomials in characterizing optical aberrations and the corneal surface of the eye |
title_full_unstemmed |
Accuracy of Zernike polynomials in characterizing optical aberrations and the corneal surface of the eye |
title_sort |
Accuracy of Zernike polynomials in characterizing optical aberrations and the corneal surface of the eye |
author |
Carvalho, Luis Alberto [UNIFESP] |
author_facet |
Carvalho, Luis Alberto [UNIFESP] |
author_role |
author |
dc.contributor.institution.none.fl_str_mv |
Universidade de São Paulo (USP) Universidade Federal de São Paulo (UNIFESP) |
dc.contributor.author.fl_str_mv |
Carvalho, Luis Alberto [UNIFESP] |
description |
PURPOSE. Zernike polynomials have been successfully used for approximately 70 years in many different fields of optics. Nevertheless, there are some recent discussions regarding the precision and accuracy of these polynomials when applied to surfaces such as the human cornea. the main objective of this work was to investigate the absolute accuracy of Zernike polynomials of different orders when fitting several types of theoretical corneal and wave-front surface data.METHODS. A set of synthetic surfaces resembling several common corneal anomalies was sampled by using cylindrical coordinates to simulate the height output files of commercial video-keratography systems. the same surfaces were used to compute the optical path difference (wave-front [WF] error), by using a simple ray-tracing procedure. Corneal surface and WF error was fit by using a least-squares algorithm and Zernike polynomials of different orders, varying from 1 to 36 OSA-VSIA convention terms.RESULTS. the root mean square error (RMSE) ranged - from the most symmetric corneal surface (spherical shape) through the most complex shape (after radial keratotomy [RK]) for both the optical path difference and the surface elevation for 1 through 36 Zernike terms - from 421.4 to 0.8 mu m and 421.4 to 8.2 mu m, respectively. the mean RMSE for the maximum Zernike terms for both surfaces was 4.5 mu m.CONCLUSIONS. These results suggest that, for surfaces such as that present after RK, in keratoconus, or after keratoplasty, even more than 36 terms may be necessary to obtain minimum accuracy requirements. the author suggests that the number of Zernike polynomials should not be a global fixed conventional or generally accepted value but rather a number based on specific surface properties and desired accuracy. |
publishDate |
2005 |
dc.date.issued.fl_str_mv |
2005-06-01 |
dc.date.accessioned.fl_str_mv |
2016-01-24T12:37:53Z |
dc.date.available.fl_str_mv |
2016-01-24T12:37:53Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
Investigative Ophthalmology & Visual Science. Rockville: Assoc Research Vision Ophthalmology Inc, v. 46, n. 6, p. 1915-1926, 2005. |
dc.identifier.uri.fl_str_mv |
http://repositorio.unifesp.br/handle/11600/28319 http://dx.doi.org/10.1167/iovs.04-1222 |
dc.identifier.issn.none.fl_str_mv |
0146-0404 |
dc.identifier.doi.none.fl_str_mv |
10.1167/iovs.04-1222 |
dc.identifier.wos.none.fl_str_mv |
WOS:000229504600007 |
identifier_str_mv |
Investigative Ophthalmology & Visual Science. Rockville: Assoc Research Vision Ophthalmology Inc, v. 46, n. 6, p. 1915-1926, 2005. 0146-0404 10.1167/iovs.04-1222 WOS:000229504600007 |
url |
http://repositorio.unifesp.br/handle/11600/28319 http://dx.doi.org/10.1167/iovs.04-1222 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.ispartof.none.fl_str_mv |
Investigative Ophthalmology & Visual Science |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
1915-1926 |
dc.publisher.none.fl_str_mv |
Assoc Research Vision Ophthalmology Inc |
publisher.none.fl_str_mv |
Assoc Research Vision Ophthalmology Inc |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UNIFESP instname:Universidade Federal de São Paulo (UNIFESP) instacron:UNIFESP |
instname_str |
Universidade Federal de São Paulo (UNIFESP) |
instacron_str |
UNIFESP |
institution |
UNIFESP |
reponame_str |
Repositório Institucional da UNIFESP |
collection |
Repositório Institucional da UNIFESP |
repository.name.fl_str_mv |
Repositório Institucional da UNIFESP - Universidade Federal de São Paulo (UNIFESP) |
repository.mail.fl_str_mv |
|
_version_ |
1802764151394664448 |