Abstract: The basic principles of phase-shifting interferometry （PSI） and generalized phase-shifting interferometry （ GPSI ） are explained within the framework of fundamental optics , the former needs special equal phase shift, while the latter can use arbitrary unknown phase shift. Some algorithms for the blind extraction of unknown phase shifts and then for wave-front reconstruction in GPSI are introduced. These discussion may provide a useful connection between basic and modern optics.

Key words: phase- shifting interferometry, generalized phase- shifting interferometry, digital holography, wave-front reconstruction, blind extraction of unknown phase shift