Dispersed fringe cophasing method based on principal component analysis

Abstract

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.