On the effect of narrow-band filters on the diffraction limited resolution of astronomical telescopes

Sometimes Fabry-Perot and other narrow band filters are used for astronomical imaging in the so-called telecentric mode. In it the pupil is collimated through the filter, resulting in different incidence angles on the filter for rays coming from different parts of the objective. This results in variations of the central transmission wavelength, which broaden the effective filter bandpath. In addition each wavelength within this filter bandpath sees a different illumination of the pupil when viewed from behind the filter. This causes the diffraction limited point-spread-function to vary with wavelength. With the advent of diffraction limited imaging using adaptive optics, this can cause complications. In this note I examine the magnitude of this effect.