The transfer function of an optical system in the presence of off-axis aberrations is evaluated via Gauss quadrature. The transfer function in the presence of third-order coma is studied and the phase of the transfer function is shown to be a smooth function. The variance of the wavefront is obtained for all third- and fifth-order aberrations and its use is illustrated for an actual system along with the transfer function.
RICHARD BARAKAT and AGNES HOUSTON, "Transfer Function of an Optical System in the Presence of Off-Axis Aberrations," J. Opt. Soc. Am. 55, 1142-1148 (1965)