RESUMEN
We extend the redundant spacings calibration method for finding piston coefficients affecting the elements of a dilute aperture array so that tilt phase coefficients can also be calculated and corrected without the need for assumptions about the object. The tilt coefficient retrieval method is successfully demonstrated in simulation, and the specifics of correction by image sharpness are discussed, showing that in dilute aperture systems this method does not necessarily produce a unique image.
RESUMEN
The principle of redundant spacings calibration has previously been described for the purpose of calibrating piston phase aberration affecting elements of a dilute aperture array using a system of linear equations in terms of the aperture phases as well as object phase information. Here we develop matrices for the correction of piston phase aberration by use of image sharpness and also by phase retrieval. These are both presented in wavefront sensor formulation in order to draw analogy between the approaches. We then discuss solution ambiguity affecting both methods and describe array design criteria to prevent such ambiguity. The problem of increased image aliasing under image sharpness correction is also highlighted.