  If the optical system of a telescope is perturbed from rotational symmetry,
the Zernike wavefront aberration coefficients describing that system can be
expressed as a function of position in the focal plane using spin-weighted
Zernike polynomials. Methodologies are presented to derive these polynomials to
arbitrary order. This methodology is applied to aberration patterns produced by
a misaligned Ritchey Chretian telescope and to distortion patterns at the focal
plane of the DESI optical corrector, where it is shown to provide a more
efficient description of distortion than conventional expansions.
