Zernike modes when pupil is contracted, decentred and rotated: analytical and graphical methods- Modos Zernike al contraer, descentrar y rotar la pupila: métodos analítico y gráfico

SILVIA. A. COMASTRI; LILIANA PEREZ; GABRIEL MARTIN; ARTURO BIANCHETTI; GERVASIO D. PÉREZ

OPTICA PURA Y APLICADA

Sociedad Española de Óptica

Año: 2009 vol. 42 p. 163 - 176

0030-3917

Zernike polynomials are often used to expand the wavefront aberration of manufactured opticalsystems and of the eye. In previous articles we present an analytical method to find explicitexpressions for the elements of a matrix which transforms Zernike coefficients of up to 7th ordercomputed for a circular pupil into those corresponding to another contracted and decentred pupiland we develop a graphical method to identify new coefficients in terms of original ones or viceversa for any order of the expansion. In the present paper we synthesize fundamental concepts ofboth methods and, taking into account the rotation matrix, we generalize them to transformcoefficients when pupil is contracted, decentred and rotated. We illustrate how to employ ourmethods showing two applications in which we find the new coefficients and we obtain thecorresponding spot diagrams at the image plane.