“…The correction of the piston error can usually be divided into two types: intensity techniques, in which measurements are made directly from intensity distributions or streaks, such as modified Shack-Hartmann sensing [8,9], dispersed fringes sensors [10], pyramidal sensors [11], and interferometry with masks and diffracting components [12,13]; and modulation transfer function (MTF) techniques, which can extract the peak around the MTF from piston errors, such as chromatic phase diversity (PD) [14,15], inter-segment piston sensors [16], and calibration-retrieve sensing [17,18]. When these methods are used for piston correction, complex optics need to be introduced into the optical path.…”