Image formation process with the solar gravitational lens

Abstract

We study image formation with the solar gravitational lens (SGL). We consider a point source that is positioned at a large but finite distance from the Sun. We assume that an optical telescope is positioned in the image plane, in the focal region of the SGL. We model the telescope as a convex lens and evaluate the intensity distribution produced by the electromagnetic field that forms the image in the focal plane of the convex lens. We first investigate the case when the telescope is located on the optical axis of the SGL or in its immediate vicinity. This is the region of strong interference where the SGL forms an image of a distant source, which is our primary interest. We derive analytic expressions that describe the progression of the image from an Einstein ring corresponding to an on-axis telescope position, to the case of two bright spots when the telescope is positioned some distance away from the optical axis. At greater distances from the optical axis, in the region of weak interference and that of geometric optics, we recover expressions that are familiar from models of gravitational microlensing, but developed here using a wave-optical treatment. We discuss applications of the results for imaging and spectroscopy of exoplanets with the SGL.

Evolving Morphology of Resolved Stellar Einstein Rings

“…In Turyshev & Toth (2019, 2020a, 2020b, 2020c, 2021a, 2021b, 2021c, 2021d, while dealing with the solar gravitational lens, we developed a comprehensive wave-optical formalism to describe gravitational lensing by a realistic extended mass distribution, characterized by an infinite series of mass multipole moments. This approach allows us to explore the theory beyond microlensing (Liebes 1964;Paczyński 1986;Schneider et al 1992), by providing a wave-optical treatment of the gravitational lensing phenomena by any extended compact lens.…”

“…Depending on the separation from the primary optical axis, ρ 0 , there are two lensing regions formed by a lens, including the strong and weak interference regions; for comparison purposes, we also consider the geometric optics region characterized by gravitational bending of light, and the free-space region where no lensing is present (see Figure 4). Based on our prior work (Turyshev & Toth 2017, 2020a, 2020c, for a point source, we characterize these regions as follows:…”

“…A solution for the EM field for the weak interference region consists of a combination of the gravitymodified incident wave and also the scattered wave that results from the diffraction of the incident wave on the solar gravity field (Turyshev & Toth 2017). Following the approach presented in Turyshev & Toth (2019, 2020a, 2020c, we use the method of stationary phase to develop solutions for Maxwell's equations in the weak field approximation to describe the incident and scattered EM fields and derive the expression to determine the intensity distribution for the signals received in these two regions.…”

“…It is here, in the strong interference region, that light from a compact source forms the image of an Einstein ring (Turyshev & Toth 2017). Here, we present a brief summary of our recently developed wave-theoretical description (see, e.g., Turyshev & Toth 2020a, 2020b, 2020c of the formation of Einstein rings.…”

“…In recent years, we developed a comprehensive wavetheoretical treatment of gravitational lensing by a compact extended lens (Turyshev & Toth 2017, 2020b, 2020c, 2021a, 2021b, 2021c, 2021d in the weak field limit of the theory of gravitation. We can model and simulate highresolution lensed images of the Einstein crosses, rings, arcs and more (Turyshev & Toth 2020a, 2021c, 2022a.…”