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

SILVIA A COMASTRI; KARINA BASTIDA; ARTURO BIANCHETTI; LILIANA I PEREZ; GERVASIO D PEREZ; GABRIEL MARTIN

JOURNAL OF OPTICS. A, PURE AND APPLIED OPTICS (PRINT)

IOP Publishing

Año: 2009 vol. 11 p. 1 - 10

1464-4258

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.