Sparse-array phasing algorithm based on recursive estimation of fringe contrast

This paper describes a novel real-time algorithm for optically phasing sub-apertures of a sparse-array telescope system based on recursive estimation of the sub-aperture placement that maximizes a fringe-contrast metric. The sub-apertures are phased in pairs using broad spectral band flood-illumination of the sparse-array, while blocking reflections from all but two sub-apertures. The resulting Young's geometry at the pupil produces an interference pattern that is characterized to determine spatial-frequency filters that are utilized to generate a contrast metric from the fringe patterns. This contrast metric is shown to generate a near-Gaussian variation as a function of optical path-length difference (OPD), with the maximum contrast occurring at zero OPD. The functional relationship between fringe contrast and subaperture position based on a common-path, laser-based relative-piston measurement system is developed into an estimator for maximization of fringe contrast (and therefore phasing of sub-apertures). The recursive algorithm produces real-time estimates of the zero OPD value of the relative position that improves as additional data is acquired.