Phase closure and object reconstruction algorithm for Fourier Telescopy applied to fast-moving targets

Fourier Telescopy (FT) is an active imaging method which interferes spatially diverse, frequency-encoded laser beams on a distant target, and records a time history of the reflected intensity measured by a single photodetector on a large receiver. FT has been studied extensively for imaging Geostationary objects, using high-energy pulsed lasers to project triplets of laser beams, by gradually stepping over time through the multitude of u,v-plane baselines required for accurate object reconstruction. Phase closure among the received triplets plays a key role in canceling out random atmospheric phase errors between laser beams. A new method has been devised to apply FT to rapidly moving targets, such as LEO space objects. In order to implement the thousands of baselines in a short engagement time, approximately 20 continuous-wave laser beams are simultaneously broadcast, and the baseline configurations are rapidly changed through a dynamic optical element. In order to eliminate unknown atmospheric errors, a new type of global phase closure has been developed, which allows image reconstruction from the time history of measured total reflected intensity, originating from the complex 20-beam interference patterns. In this paper, we summarize the new FT LEO method, and give a detailed derivation of the phase closure and image reconstruction algorithms that will lead to ultra-high resolution images of fast-moving space objects.