Fast phase retrieval with four-quadrant analysis in phase-shifting interferometry with blind phase shifts

- Reason of the sign uncertainty of phase shift is analyzed.
- Change of the interference wave vector with the phase shift quadrant is discussed.
- The inner product feature of difference between two interferograms is described.
- A method for extracting the phase shift within the range of [0,2π] is proposed.
- Results of two kinds of fringes are given to verify the above method.

Phase-shifting interferometry (PSI) is one of the most effective techniques in optical measurement, in which phase retrieval with high efficiency is an important procedure. In this paper, a simple non-iterative method is proposed to extract the generalized phase shift with the four-quadrant analysis in three-frame PSI. In this method, the possible value of the phase shift is firstly worked out with the inner product algorithm, and then a criterion is put forward to accurately determine its principal value within the range [0,2π], based on the change relationship of the interference wave vector in four quadrants. Thus, this method provides a possible method to solve the uncertainty of phase shift existing in some common algorithms. Subsequently, the phase can be retrieved easily without any other measurements. Both simulation and experimental results have fully proved the feasibility and high accuracy of the method. Moreover, it works well on open- and closed-fringed patterns.