Algorithm to Improve Reconstruction Exoplanet Images from Gravity Lensing

Going beyond physical limitations of telescopes, Stanford University astrophysicists have been working on a new conceptual imaging technique that would be 1,000 times more precise than the strongest imaging technology currently in use. By taking advantage of gravity’s warping effect on space-time, called lensing, scientists could potentially manipulate this phenomenon to create imaging far more advanced than any present today.

Researchers describe a way to manipulate solar gravitational lensing to view planets outside our solar system. By positioning a telescope, the sun, and exoplanet in a line with the sun in the middle, scientists could use the gravitational field of the sun to magnify light from the exoplanet as it passes by. As opposed to a magnifying glass which has a curved surface that bends light, a gravitational lens has a curved space-time that enables imaging far away objects.

Slava Turyshev of California Institute of Technology’s Jet Propulsion Laboratory described a technique where a space-based telescope could use rockets to scan around the rays of light from a planet to reconstruct a clear picture, but the technique would require a lot of fuel and time.

Building on Turyshev’s work, Alexander Madurowicz, a PhD student at KIPAC, invented a new method that can reconstruct a planet’s surface from a single image taken looking directly at the sun. By capturing the ring of light around the sun formed by the exoplanet, the algorithm Madurowicz designed can undistort the light from the ring by reversing the bending from the gravitational lens, which turns the ring back into a round planet.

In order to capture an exoplanet image through the solar gravitational lens, a telescope would have to be placed at least 14 times farther away from the sun than Pluto, past the edge of our solar system, and further than humans have ever sent a spacecraft. This is about 4 light days away instead of four light years or one hundred light years.

The Astrophysical Journal – Integral Field Spectroscopy with the Solar Gravitational Lens

The prospect of combining integral field spectroscopy with the solar gravitational lens (SGL) to spectrally and spatially resolve the surfaces and atmospheres of extrasolar planets is investigated. The properties of hyperbolic orbits visiting the focal region of the SGL are calculated analytically, demonstrating trade-offs between departure velocity and time of arrival, as well as gravity assist maneuvers and heliocentric angular velocity. Numerical integration of the solar barycentric motion demonstrates that navigational acceleration is needed to obtain and maintain alignment. Obtaining target ephemerides of sufficient precision is an open problem. The optical properties of an oblate gravitational lens are reviewed, including calculations of the magnification and the point-spread function that forms inside a telescope. Image formation for extended, incoherent sources is discussed when the projected image is smaller than, approximately equal to, and larger than the critical caustic. Sources of contamination that limit observational signal-to-noise ratio (S/N) are considered in detail, including the Sun, the solar corona, the host star, and potential background objects. A noise mitigation strategy of spectrally and spatially separating the light using integral field spectroscopy is emphasized. A pseudo-inverse-based image reconstruction scheme demonstrates that direct reconstruction of an Earth-like source from single measurements of the Einstein ring is possible when the critical caustic and observed S/N are sufficiently large. In this arrangement, a mission would not require multiple telescopes or navigational symmetry breaking, enabling continuous monitoring of the atmospheric composition and dynamics on other planets.

Background stars or other astronomical objects could be reimaged into the Einstein ring, and the probability of observing a background star depends on the target’s galactic coordinates, with the direction of the galactic center being least optimal. A complete strategy to characterize, model, and mitigate all sources of noise has yet to be demonstrated. A pure coronagraphic approach would be limited to a narrow bandpass, and a major advantage of the SGL over direct imaging is the enormous quantity of available photons for high-dispersion spectroscopy. A starshade could be an achromatic solution to obtain high contrast across a wide bandpass. The strategy of spectrally and spatially resolving the light in the vicinity of the Einstein ring potentially has the capability to disentangle all sources of noise, but our results are not conclusive. A complete instrument model is outside the scope of this work. As the desire for knowledge locked behind immense observational barriers increases, further understanding of instrumentation from a universal perspective will be necessary to overcome human limitations in the construction of physical and optical instruments.