Multi-Objective System Design of an Active Imaging Mode for a Sparse Aperture Telescope

Imaging of small and distant targets under conditions where limited photons passively reach the target can be extremely challenging due to resolution and signal-to-noise ratio constraints. Conventional small aperture telescopes have an inability to spatially resolve these types of targets according to the Rayleigh criterion. Large aperture telescopes, on the other hand, can resolve such targets but are prohibitively expensive to produce. An alternative solution known as optical interferometry can potentially allow for high resolution imaging without the extreme cost of large aperture systems via its use of a sparse aperture array. A sparse aperture imaging array enhances resolution while minimizing the total light collection area by combining the light collection capabilities of distributed small apertures. While the sparse aperture array can potentially solve the resolution problem, it does not solve the problem of limited photons being reflected by the target. In this study, we therefore perform an initial exploration on the feasibility of combining a sparse aperture array with active imaging techniques to achieve imaging of targets with small angular extents under photon-starved conditions. A Multi-Objective Optimization (MOO) framework is developed where the sparsity of the sub-apertures, the wavelength of the actively propagated pulse, and the energy of the actively propagated pulse are optimized under the consideration of target signal-to-noise, beam combining difficulty, and imaging resolution constraints. We discuss the implications of this initial design on factors such the Point Spread Function (PSF) angular extent, target contrast, and expected photons returned to the telescope aperture after round-trip beam propagation.