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
Colin J. R. Sheppard, Sam Campbell, and Michael D. Hirschhorn, "Zernike Expansion of Separable Functions of Cartesian Coordinates," Appl. Opt. 43, 3963-3966 (2004)