Zernike aberrations when pupil varies: Selection rules, missing modes and graphical method to identify modes

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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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Autores principales: Comastri, S.A., Bastida, K., Bianchetti, A., Perez, L.I., Pérez, G.D., Martin, G.
Formato: JOUR
Materias:
Ocular aberrations
Pupil size and centring
Zernike coefficients
Analytical formulas
Coefficient values
Displacement direction
Graphical methods
Image-forming systems
Selection Rules
Transformation matrices
Wavefront aberrations
Zernike aberrations
Zernike coefficient
Zernike polynomials
Graphic methods
Three term control systems
Wavefronts
Aberrations
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_14644258_v11_n8_p_Comastri
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_14644258_v11_n8_p_Comastri2023-10-03T16:17:09Z Zernike aberrations when pupil varies: Selection rules, missing modes and graphical method to identify modes Comastri, S.A. Bastida, K. Bianchetti, A. Perez, L.I. Pérez, G.D. Martin, G. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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
Comastri, S.A.
Bastida, K.
Bianchetti, A.
Perez, L.I.
Pérez, G.D.
Martin, G.
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.
format JOUR
author Comastri, S.A.
Bastida, K.
Bianchetti, A.
Perez, L.I.
Pérez, G.D.
Martin, G.
author_facet Comastri, S.A.
Bastida, K.
Bianchetti, A.
Perez, L.I.
Pérez, G.D.
Martin, G.
author_sort Comastri, S.A.
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
url http://hdl.handle.net/20.500.12110/paper_14644258_v11_n8_p_Comastri
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