Imaging faint sources with the extended solar gravitational lens

TL;DR

This paper analyzes how the Sun's extended gravitational field, especially its quadrupole moment, affects high-resolution imaging of faint distant sources like exoplanets using the solar gravitational lens, developing models to understand and mitigate these effects.

Contribution

It introduces a new diffraction integral and semi-analytical models to evaluate the impact of solar oblateness on the imaging capabilities of the SGL, enhancing understanding of its practical use.

Findings

Solar quadrupole moment significantly perturbs the projected image.

Most photons from extended sources still fall within the monopole image area.

Despite perturbations, the SGL can still achieve high-resolution imaging of exoplanets.

Abstract

We consider resolved imaging of faint sources with the solar gravitational lens (SGL) while treating the Sun as an extended gravitating body. We use our new diffraction integral that describes how a spherical electromagnetic wave is modified by the static gravitational field of an extended body, represented by series of multipole moments characterizing its interior mass distribution. Dominated by the solar quadrupole moment, these deviations from spherical symmetry significantly perturb the image that is projected by the Sun into its focal region, especially at solar equatorial latitudes. To study the optical properties of the quadrupole SGL, we develop an approximate solution for the point spread function of such an extended lens. We also derive semi-analytical expressions to estimate signal levels from extended targets. With these tools, we study the impact of solar oblateness on imaging with the SGL. Given the small value of the solar quadrupole moment, the majority of the signal photons arriving from an extended target still appear within the image area projected by the monopole lens. However, these photons are scrambled, thus reducing the achievable signal-to-noise ratio during image recovery process (i.e., deconvolution). We also evaluate the spectral sensitivity for high-resolution remote sensing of exoplanets with the extended SGL. We assess the impact on image quality and demonstrate that despite the adverse effects of the quadrupole moment, the SGL remains uniquely capable of delivering high-resolution imaging and spectroscopy of faint, small and distant targets, notably terrestrial exoplanets within ~30--100 parsec from us.