Zernike aberrations when pupil varies: Selection rules, missing modes and graphical method to identify modes
Aberrations of the eye and other image-forming systems are often analyzed by expanding the wavefront aberration function for a given pupil in Zernike polynomials. In previous articles explicit analytical formulae to transform Zernike coefficients of up to seventh order corresponding to wavefront abe...
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2009
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14644258_v11_n8_p_Comastri http://hdl.handle.net/20.500.12110/paper_14644258_v11_n8_p_Comastri |
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paper:paper_14644258_v11_n8_p_Comastri2023-06-08T16:16:44Z Zernike aberrations when pupil varies: Selection rules, missing modes and graphical method to identify modes Ocular aberrations Pupil size and centring Zernike coefficients Analytical formulas Coefficient values Displacement direction Graphical methods Image-forming systems Ocular aberrations Pupil size and centring Selection Rules Transformation matrices Wavefront aberrations Zernike aberrations Zernike coefficient Zernike coefficients Zernike polynomials Graphic methods Three term control systems Wavefronts Aberrations Aberrations of the eye and other image-forming systems are often analyzed by expanding the wavefront aberration function for a given pupil in Zernike polynomials. In previous articles explicit analytical formulae to transform Zernike coefficients of up to seventh order corresponding to wavefront aberrations for an original pupil into those related to a contracted transversally displaced new pupil are obtained. In the present paper, selection rules for the direct and inverse coefficients' transformation are given and missing modes associated with certain displacement directions are analyzed. Taking these rules into account, a graphical method to qualitatively identify which are the elements of the transformation matrix and their characteristic dependence on pupil parameters is presented. This method is applied to fictitious systems having only one non-zero original coefficient and, for completeness, the new coefficient values are also analytically evaluated. © 2009 IOP Publishing Ltd. 2009 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14644258_v11_n8_p_Comastri http://hdl.handle.net/20.500.12110/paper_14644258_v11_n8_p_Comastri |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Ocular aberrations Pupil size and centring Zernike coefficients Analytical formulas Coefficient values Displacement direction Graphical methods Image-forming systems Ocular aberrations Pupil size and centring Selection Rules Transformation matrices Wavefront aberrations Zernike aberrations Zernike coefficient Zernike coefficients Zernike polynomials Graphic methods Three term control systems Wavefronts Aberrations |
| spellingShingle |
Ocular aberrations Pupil size and centring Zernike coefficients Analytical formulas Coefficient values Displacement direction Graphical methods Image-forming systems Ocular aberrations Pupil size and centring Selection Rules Transformation matrices Wavefront aberrations Zernike aberrations Zernike coefficient Zernike coefficients Zernike polynomials Graphic methods Three term control systems Wavefronts Aberrations Zernike aberrations when pupil varies: Selection rules, missing modes and graphical method to identify modes |
| topic_facet |
Ocular aberrations Pupil size and centring Zernike coefficients Analytical formulas Coefficient values Displacement direction Graphical methods Image-forming systems Ocular aberrations Pupil size and centring Selection Rules Transformation matrices Wavefront aberrations Zernike aberrations Zernike coefficient Zernike coefficients Zernike polynomials Graphic methods Three term control systems Wavefronts Aberrations |
| description |
Aberrations of the eye and other image-forming systems are often analyzed by expanding the wavefront aberration function for a given pupil in Zernike polynomials. In previous articles explicit analytical formulae to transform Zernike coefficients of up to seventh order corresponding to wavefront aberrations for an original pupil into those related to a contracted transversally displaced new pupil are obtained. In the present paper, selection rules for the direct and inverse coefficients' transformation are given and missing modes associated with certain displacement directions are analyzed. Taking these rules into account, a graphical method to qualitatively identify which are the elements of the transformation matrix and their characteristic dependence on pupil parameters is presented. This method is applied to fictitious systems having only one non-zero original coefficient and, for completeness, the new coefficient values are also analytically evaluated. © 2009 IOP Publishing Ltd. |
| title |
Zernike aberrations when pupil varies: Selection rules, missing modes and graphical method to identify modes |
| title_short |
Zernike aberrations when pupil varies: Selection rules, missing modes and graphical method to identify modes |
| title_full |
Zernike aberrations when pupil varies: Selection rules, missing modes and graphical method to identify modes |
| title_fullStr |
Zernike aberrations when pupil varies: Selection rules, missing modes and graphical method to identify modes |
| title_full_unstemmed |
Zernike aberrations when pupil varies: Selection rules, missing modes and graphical method to identify modes |
| title_sort |
zernike aberrations when pupil varies: selection rules, missing modes and graphical method to identify modes |
| publishDate |
2009 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14644258_v11_n8_p_Comastri http://hdl.handle.net/20.500.12110/paper_14644258_v11_n8_p_Comastri |
| _version_ |
1768544054438526976 |