Image recovery with the solar gravitational lens

TL;DR

This paper demonstrates that the solar gravitational lens can be used for high-resolution imaging of exoplanets by applying deconvolution techniques to overcome blurring, with manageable noise penalties and optimized data collection strategies.

Contribution

It introduces a computer code for simulating image formation with the SGL and analyzes deconvolution methods, noise effects, and data strategies for practical exoplanet imaging.

Findings

Deconvolution can reconstruct original images from blurred SGL data.

Noise penalty in image recovery can be reduced with larger sampling spacing and filtering.

Feasible strategies for detailed exoplanet imaging within realistic mission durations.

Abstract

We report on the initial results obtained with an image convolution/deconvolution computer code that we developed and used to study the image formation capabilities of the solar gravitational lens (SGL). Although the SGL of a spherical Sun creates a greatly blurred image, knowledge of the SGL's point-spread function (PSF) makes it possible to reconstruct the original image and remove the blur by way of deconvolution. We discuss the deconvolution process, which can be implemented either with direct matrix inversion or with the Fourier quotient method. We observe that the process introduces a ``penalty'' in the form of a reduction in the signal-to-noise ratio (SNR) of a recovered image, compared to the SNR at which the blurred image data is collected. We estimate the magnitude of this penalty using an analytical approach and confirm the results with a series of numerical simulations. We find that the penalty is substantially reduced when the spacing between image samples is large compared to the telescope aperture. The penalty can be further reduced with suitable noise filtering, which can yield ${\cal O}(10)$ or better improvement for low-quality imaging data. Our results confirm that it is possible to use the SGL for imaging purposes. We offer insights on the data collection and image processing strategies that could yield a detailed image of an exoplanet within image data collection times that are consistent with the duration of a realistic space mission.