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.
© 2008 Optical Society of America
Original Manuscript: March 3, 2008
Revised Manuscript: October 17, 2008
Manuscript Accepted: October 17, 2008
Published: December 24, 2008
Richard J. Eastwood, Anne Marie Johnson, and Alan H. Greenaway, "Calculation and correction of piston phase aberration in synthesis imaging," J. Opt. Soc. Am. A 26, 195-205 (2009)