Regimes in astrophysical lensing: refractive optics, diffractive optics, and the Fresnel scale

Astrophysical lensing has typically been studied in two regimes: diffractive optics and refractive optics. Previously, it has been assumed that the Fresnel scale, R-F, is the relevant physical scale that separates these two regimes. With the recent introduction of Picard-Lefschetz theory to the field of lensing, it has become possible to generalize the refractive description of discrete images to all wave parameters, and, in particular, exactly evaluate the diffraction integral at all frequencies. In this work, we assess the regimes of validity of refractive and diffractive approximations for a simple one-dimensional lens model through comparison with this exact evaluation. We find that, contrary to previous assumptions, the true separation scale between these regimes is given by R-F/root kappa, where kappa is the convergence of the lens. Thus, when the lens is strong, refractive optics can hold for arbitrarily small scales. We also argue that intensity variations in diffractive optics are generically small, which has implications for the study of strong diffractive interstellar scintillation.