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Astrophysical lensing has typically been studied in two regimes: diffractiveoptics and refractive optics. Diffractive optics is characterized by aperturbative expansion of the Kirchhoff-Fresnel diffraction integral, whilerefractive optics is characterized by the stationary phase approximation.Previously, it has been assumed that the Fresnel scale, $R_F$ , is the relevantphysical scale that separates these two regimes. With the recent introductionof Picard-Lefschetz theory to the field of lensing, it has become possible togeneralize the refractive description of discrete images to all waveparameters, and, in particular, exactly evaluate the diffraction integral atall frequencies. In this work, we assess the regimes of validity of refractiveand diffractive approximations for a simple one-dimensional lens model throughcomparison with this exact evaluation. We find that, contrary to previousassumptions, the true separation scale between these regimes is given by $R_F /\sqrt{\kappa}$, where $\kappa$ is the convergence of the lens. Thus, when thelens is strong, refractive optics can hold for arbitrarily small scales. Wealso argue that intensity variations in diffractive optics are genericallysmall, which has implications for the study of strong diffractive scintillation(DISS).

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