Relating wavefront error, apodization, and the optical transfer function: General case

In a previous paper, a technique was developed for decomposing the incoherent optical transfer function (OTF) into a linear combination of basis functions [J. Opt. Soc. Am. A 31, 2476 (2014)]. The expansion coefficients for the OTF are directly related to wavefront error coefficients and apodization factors. This earlier work assumed rotational symmetry, so that only the on-axis wavefront error components, defocus and various orders of spherical aberration, and rotationally symmetric apodization were handled. In this paper, the technique is generalized to handle arbitrary wavefront errors and apodization. Analytic expressions for the basis functions as well as an example expansion are provided.