Multi-aperture telescopes at the quantum limit of superresolution imaging : Detecting subRayleigh object near a star

Abstract

Angular resolution is a critical aspect of astronomical observation, as it determines the minimum resolvable angle between two objects. This is governed by the Rayleigh criterion, which states that the minimum resolvable angle is proportional to the wavelength ($\lambda$) over the diameter ($D$) of the aperture of a monolithic telescope. While larger aperture telescopes have advantages such as smaller angular resolution and higher sensitivity to dim and small exoplanets, they also have disadvantages such as higher launch cost, design intricacies, and high mission cost. Using multi-aperture telescopes can be a cost-effective alternative as they work on the principles of baseline interferometry, making the minimum resolvable angle proportional to $\lambda /B$, where $B$ is the baseline. In this work, we compare the performance of a single monolithic telescope to a multi-aperture alternative with the same effective glass area in the context of hypothesis testing between two scenarios - $H_1$ (a star) and $H_2$ (a star with an exoplanet). We formulate the theory based on likelihood ratio tests and find that the multi-aperture telescope performs better than the monolithic telescope when direct detection is used on the focal plane. While this is expected, the performance can be further improved by using quantum-inspired detecting strategies. We utilize Quantum Binary Spatial Mode Demultiplexing (BSPADE) to process the point spread function (PSF) of the telescopes and find better performance compared to the respective direct detection measurement. Therefore, our efforts can be viewed as one of the initial steps toward employing quantum-inspired detection techniques in sparse aperture configurations for high-contrast imaging applications. In conclusion, our work shows that multi-aperture telescopes are an effective alternative to monolithic telescopes for object discrimination and potentially for super-resolution imaging and their performance can be further improved by using quantum-inspired detection strategies. With their cost-effectiveness (see Appendix C) and potential for high performance, multi-aperture telescopes can significantly advance our ability to observe and study exoplanets and other celestial objects. Future research can explore ways to optimize the performance of multi-aperture telescopes and further improve their capabilities for astronomical observation, potentially facilitating the detection and imaging of Earth-like exoplanets.