Fabry-Perot (FP) etalons are used as filters and sensors in a range of optical systems. The reflected and transmitted fields associated with an FP etalon have traditionally been predicted by the Airy function, which assumes a plane wave illumination. FP etalons are, however, often illuminated by non-collimated beams, rendering the Airy function invalid. To address this limitation, we describe the angular Airy function which calculates the reflected and transmitted fields for arbitrary illumination beams, using angular spectrum decomposition. Combined with realistic models of the experimental illumination beams and detection optics, we show that the angular Airy function can accurately predict experimental wavelength resolved intensity measurements. Based on the angular Airy function, we show that the fundamental operating principle of an FP etalon is as an angular-spectral filter. Based on this interpretation we explain the asymmetry, broadening and visibility reduction seen on wavelength resolved intensity measurements from high Q-factor FP etalons illuminated with focused Gaussian beams.