Dispersed fringe cophasing method based on principal component analysis

With the success of the Webb telescope, dispersed fringe sensing (DFS), with the significant merit of a large capture range, is proving to be a promising cophasing approach for a large-aperture segmented telescope. In this Letter, a novel, to the best of our knowledge, piston error extraction method based on principal component analysis (PCA) technology is proposed. In this method, all the one-dimension intensity distributions along the dispersion axis for different interference positions are regarded as a set of random phase-shifted interference signals. PCA technology is utilized to obtain its corresponding continuous principal phase and the piston error could be directly estimated proportionally from the slope of the phase-wavenumber line. This method avoids nonlinear operations, similar to Shi's traditional framework; no active move is needed for fine cophasing, and the method is also free of characteristic constant calibration in sidelobe peak displacement- and slope-based methods. Preliminary simulations of the method's coarse-then-fine cophasing ability with high accuracy are presented here to show its potential.