A Zernike expansion over a circle is given for an arbitrary function of a single linear spatial coordinate. The example of a half-plane mask (Hilbert filter) is considered. The expansion can also be applied to cylindrical aberrations over a circular pupil. A product of two such series can thus be used to expand an arbitrary separable function of two Cartesian coordinates.
© 2004 Optical Society of America
Original Manuscript: October 4, 2003
Revised Manuscript: April 22, 2004
Published: July 10, 2004
Colin J. R. Sheppard, Sam Campbell, and Michael D. Hirschhorn, "Zernike expansion of separable functions of Cartesian coordinates," Appl. Opt. 43, 3963-3966 (2004)