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

Abstract

Astrophysical lensing has typically been studied in two regimes: diffractive optics and refractive optics. Diffractive optics is characterized by a perturbative expansion of the Kirchhoff-Fresnel diffraction integral, while refractive optics is characterized by the stationary phase approximation. 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 / √ 𝜅, where 𝜅 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 scintillation (DISS).

Existence of Real Time Quantum Path Integrals

“…It is defined as a configuration of the dynamical system for which one or more real, classical trajectories coincide [58]. (It is worth noting here the close correspondence between real time quantum physics and lensing in wave optics [42,46]). A small perturbation of the system either makes one or more classical solutions ''disappear" (or, more accurately, move into the space of complex classical trajectories) or split up into multiple real classical trajectories.…”

“…Whether this insight is ultimately useful for understanding the origin and meaning of ''resurgence" remains to be seen. More recently, similar Picard-Lefschetz methods have also led to improved methods for the numerical evaluation of real time path integral both in quantum physics [see for example35 -41] and in radio astronomy [42][43][44][45][46].…”

Existence of real time quantum path integrals

“…It is defined as a configuration of the dynamical system for which one or more real, classical trajectories coincide [48]. (It is worth noting here the close correspondence between real time quantum physics and lensing in wave optics [40,49]). A small perturbation of the system either makes one or more classical solutions "disappear" (or, more accurately, move into the space of complex classical trajectories) or split up into multiple real classical trajectories.…”