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. PÉREZ; 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 thewavefront aberration function for a given pupil in Zernike polynomials. In previous articlesexplicit analytical formulae to transform Zernike coefficients of up to seventh ordercorresponding to wavefront aberrations for an original pupil into those related to a contractedtransversally displaced new pupil are obtained. In the present paper, selection rules for thedirect and inverse coefficients’ transformation are given and missing modes associated withcertain displacement directions are analyzed. Taking these rules into account, a graphicalmethod to qualitatively identify which are the elements of the transformation matrix and theircharacteristic dependence on pupil parameters is presented. This method is applied to fictitioussystems having only one non-zero original coefficient and, for completeness, the newcoefficient values are also analytically evaluated.