Digital four-step phase-shifting technique from a single fringe pattern using Riesz transform

A digital four-step phase-shifting method for obtaining the optical phase distribution from a single fringe pattern is proposed in this Letter. By computing the first-, second-, and third-order Riesz transform components for a given fringe pattern, three π/2 phase-shifted fringe patterns are generated from the obtained Riesz components and, finally, the wrapped phase map is extracted. The validity of the proposed method is demonstrated on both the simulated and experimentally obtained fringe patterns. The performance of the proposed method is evaluated by using the image quality index and edge preservation index. Further, the performance of the proposed method is tested on speckled correlation fringes obtained from digital speckle pattern interferometry, and the resulting phase from the proposed method is compared with the phase obtained from three experimentally recorded phase-shifted fringe patterns. The obtained results reveal that the proposed method provides a simple and robust solution for optical phase extraction from a single fringe pattern with good accuracy and, therefore, make it suitable for real-time measurement applications.