Zernike expansion of separable functions of cartesian coordinates.
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.
Sheppard
Colin J R
CJ
Division of Bioengineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117576, Singapore. colin@nus.edu.sg
Campbell
Sam
S
Hirschhorn
Michael D
MD