A novel algorithm based on sub-fringe integration method for direct two-dimensional unwrapping phase reconstruction from the intensity of one-shot two-beam interference fringes

Abstract

Phase reconstruction is extremely important in optical interferometry, where the quantitative and qualitative information is encoded in the form of two-dimensional interference interferograms. Most often, a majority of phase calculation methods return results of the wrapped phase limited in the range (? ?, ?) due to the fundamental properties of the mathematical arctangent function. It would be helpful if we could avoid the unwrapping phase step and calculate the phase directly. In this paper, we present an algorithm of phase reconstruction based on the sub-fringe integration method to avoid the ambiguities due to the properties of the arctangent function. The theoretical considerations of the proposed algorithm were presented. Also, the main steps required to implement the algorithm, in addition to providing the flowchart outlined for those steps, were presented. The algorithm is suitable to analyze the two-beam interference fringe. The proposed algorithm adds a power element to the sub-fringe method, which does not need the unwrapping process. Besides, it needs neither hardware to introduce phase shift, nor more than one interferogram. Both simulation and experimental results demonstrate the usefulness of the proposed algorithm to extract the phase from the two-beam interference interferogram, even if the fringe shifts are variable along the fiber and with the irregularity of the fiber radius across the interferogram. Appropriate and adequate interferograms were presented to clarify the basic idea of the article.