Relating wavefront error, apodization, and the optical transfer function: on-axis case

The incoherent optical transfer function (OTF) describes contrast degradation and phase shifts of sinusoidal objects of all spatial frequencies and orientations. The OTF is calculated as either an autocorrelation of the pupil function or the Fourier transform of the point spread function. Even with fast algorithms, these calculations can be slow for a densely sampled pupil. Here, a linear expansion of the OTF is developed in which the expansion coefficients are related to the wavefront error and apodization coefficients. The advantage of such a representation is that the OTF can be quickly generated from parameters of the optical system.