In a previously proposed method for wavefront detection and correction, a deformable mirror is ideally constructed with segmentations using the polar coordinate system. The method is based on the detection and removal of binary aberration modes, in the form of modified Walsh functions, with the help of a single-mode optical fiber. This paper extends the technique to adaptive optics systems that employ the more common type of deformable mirrors: the Cartesian-style deformable mirrors. A study indicates that the deviation from the orthogonality between the fiber propagation mode and the aberration modes is negligible for practical purposes. An iterative algorithm is proposed for wavefront correction by means of successive suppression of the binary aberration modes in the wavefronts. A numerical model is constructed and employed to carry out a large number of trials. The results demonstrate that the system can remove aberrations from the wavefronts in few cycles of the routine and settle the deformable mirror in configurations that are theoretically optimal.
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