A Fourier Optics Method for Calculating Stellar Occultation Light Curves by Objects With Thin Atmospheres

Abstract

A stellar occultation occurs when a solar system object passes in front of a distant star. The light curves resulting from stellar occultations can reveal many aspects of the obscuring object. For airless bodies, the diffraction light curve specifies the object's size, distance and, if several chords are observed, shape. Occultation light curves are especially sensitive to the presence of atmospheres; the refraction light curve is a function of the atmosphere's density, pressure, and temperature profiles. The goal of this paper is to develop a practical algorithm to model the simultaneous effects of diffraction and refraction for objects in which both phenomena are observable. The algorithm we present is flexible: it can be used to calculate light curves by objects with arbitrary shapes and arbitrary atmospheres (including the presence of opacity sources such as hazes), provided that the atmosphere can be represented by a thin screen with a phase delay and an opacity defined at each location in the screen. Because the algorithm is limited at present to thin atmospheres (in which rays from a star are bent but undergo virtually no translation as they pass through an atmosphere), the gas giants, Earth, Mars, and Venus are not treated. Examples of stellar occultations are presented for round or irregularly shaped objects having thin atmospheres of various column densities.

Global climate model occultation lightcurves tested by August 2018 ground-based stellar occultation

“…Model OPIF and lightcurves are generated with GCM (Bertrand et al, 2020) and Fourier optics method (Young, 2012). The results are compared with observed lightcurves in the 15-AUG-2018…”

Uniform asymptotics of paraxial boundary diffraction waves

“…One of the motivations of the present work has to do with the possibility of grasping the basic features of the wavefields scattered from "large" tridimensional objects in terms of paraxial diffraction from equivalent planar apertures, a topic that continues to receive attention, even in recent times [40], also in light of its intriguing astronomical applications [41]. In particular, we believe that the approach outlined here could be helpful in the study of diffraction effects observed during celestial occultation experiments [42][43][44][45][46].…”

Phase retrieval applied to stellar occultation for asteroid silhouette characterization

“…Results such as those in [4,5] give a length estimate of an occluding object in the Kuiper belt but provide no information about the shape of the object, because they neglect some of the details of the diffraction effects. Most efforts in this field have been formulated to give a nominal radius of the occluding object, such as the discussions in [6]. The discussions in [7] expand the circular problem to include ellipses.…”

“…Propagating the field from the point source to the object plane and then to the observation plane using the Huygens-Fresnel principle applied to shadows gives the Fresnel diffraction equation [6,[8][9][10][11]]…”

“…(3) contains the exponential term expiπzθ • θ∕λ, which introduces a periodic phase shift into the field. The equation thus cannot be discretized and turned into a discrete Fourier transform, as is done in the traditional phase retrieval problem, unless the discretization yields elements much smaller than the wavelength of these frequencies [6]. Since often times z∕λ ≫ 10 10 , such a resolution would be prohibitive computationally when considering an object plane large enough to encompass an astronomical object.…”