Error estimation of phase detection algorithms and comparison of window functions

Abstract

Error estimation method of phase detection in phase shift method is proposed. Phase detection algorithms extract phase of fringes from several interferograms that are acquired during phase shifting. The Fourier domain expression of phase detection algorithms show frequency response for sine and cosine components, and it shows behavior of detected phase in the case if phase shifting error exists. However, these two response functions do not directly show frequency response of phase detection itself. On the contrary, newly proposed frequency response function directly shows frequency response of phase detection. And it clearly shows the behavior of phase detection algorithm when phase tuning error exists. The proposed method is inspired by the Bode plot. It is easy to assume that magnitude plot also can be defined in addition to the phase plot. The magnitude plot can be used for prediction of the sensitivity to the signal and noise. And the phase plot can be used for error estimation of phase detection in the presence of phase tuning error. After some investigations, it was found that there is good agreement between the developed frequency response function and calculated error value. Therefore, it can be used as an error estimation method for phase detection algorithm. A window function modifies specifications of phase detection algorithm. Comparisons of several numbers of window functions on phase detection method were demonstrated using proposed method. Additionally, we discuss window function, which makes phase detection algorithm insensitive to phase detuning.