Phase measurement deflectometry based on composite circular fringes

The traditional phase shift measurement technique necessitates two orthogonally oriented fringe patterns to complete the phase measurement, which is time-consuming, and the phase modulation of the traditional fringe image exhibits only a gradient change in a single direction of the horizontal-vertical fringes, or a smooth gradient change in the tangential direction of the circular fringes. To enhance the measurement speed and improve the adaptability to large curvature measured specular surfaces, this paper proposes a phase measurement deflectometry (PMD) technique based on composite circular fringes. The composite circular fringes demonstrate a steeper slope in the phase change, enabling the acquisition of finer surface features under identical measurement conditions, effectively improving the detection sensitivity to small shape changes and enhancing the ability to discern fine details. To reduce the number of fringe projection images, a phase extraction algorithm based on the maximum contrast factor is proposed. The composite circular fringe technique halves the number of required projected fringe images, and only four fringe images are necessary to obtain the phase information of the object. The experimental results demonstrate that the root-mean-square error (RMSE) is 6.79 times higher and the peak-to-valley (PV) value is 8.93 times higher than that of the traditional fringe method in the horizontal-vertical directions. Compared with the traditional fringe method in the radial-tangential directions, the RMSE is improved by 26.04% and the PV value is improved by 28.28%. © 2025 Optica Publishing Group (formerly OSA). All rights reserved.