Imaging extended sources with the solar gravitational lens

TL;DR

This paper analyzes how the solar gravitational lens can be used to image extended sources by modeling electromagnetic wave propagation and diffraction effects in the Sun's gravitational field, providing insights for future imaging applications.

Contribution

It develops a vector diffraction theory for the SGL considering extended sources and finite distances, advancing understanding of the lens's optical properties and imaging potential.

Findings

Derived the EM field distribution in all four regions behind the Sun.

Presented the power density profile for imaging with the SGL.

Analyzed the impact of extended sources on the SGL's imaging capabilities.

Abstract

We investigate the optical properties of the solar gravitational lens (SGL) with respect to an extended source located at a large but finite distance from the Sun. The static, spherically symmetric gravitational field of the Sun is modeled within the first post-Newtonian approximation of the general theory of relativity. We consider the propagation of monochromatic electromagnetic (EM) waves near the Sun. We develop, based on a Mie theory, a vector theory of diffraction that accounts for the refractive properties of the solar gravitational field. The finite distance to a point source can be accounted for using a rotation of the coordinate system to align its polar axis with the axis directed from the point source to the center of the Sun, which we call the optical axis. We determine the EM field and study the key optical properties of the SGL in all four regions formed behind the Sun by an EM wave diffracted by the solar gravity field: the shadow, geometric optics, and weak and strong interference regions. Extended sources can then be represented as collections of point sources. We present the power density of the signal received by a telescope in the image plane. Our discussion concludes with considering the implications for imaging with the SGL.