Accommodation of speckle in object-based phasing.

This work addresses the physical basis of the measurement process for object-based phasing of an array of telescopes. In this regard an enhanced least-squares estimator that is capable of differentiating among three families of array aberrations in an object-based phasing system is developed. In a system of this nature the system to be phased illuminates the object of interest and the return radiation is detected. Telescope aberrations, atmospheric aberrations, and speckle-induced aberrations are all reported by the estimator to facilitate correction of telescope and atmospheric aberrations. This is accomplished by proper handling of the unobservable modes and recognizing that the five global aberrations-telescope array piston, atmospheric array piston and tilt, and speckle array piston and tilt-cannot be measured accurately so they need to be projected out of the estimated piston commands. Except for these relatively benign array aberrations, the disturbances for all three families of array aberrations are estimated exactly. An interesting feature of the speckle array aberrations is that a synthetic aperture is developed that is almost twice as large as the array of telescopes under consideration.