Common form of the complex wave error caused by arbitrary phase shift errors in generalized phase-shifting interferometry and its digital correction

Our analysis reveals that the complex wave error caused by arbitrary phase-shift errors in generalized phase-shifting interferometry (PSI) with arbitrary frames and arbitrary phase shift design takes the common form: a linear combination of the correct complex wave and its conjugation. Consequently, the simple method of digital wave correction we proposed recently for standard PSI is extended to the generalized PSI of any algorithms. Computer simulations show that this method can depress both the amplitude error and the phase error simultaneously and significantly by 2-3 orders of magnitude for arbitrary irregular phase shift errors as large as up to 20% without the need of calibration or the knowledge of the actual phase shifts.