Phase Unwrapping Method Based on Vibrational Phase Shifting for 3-D Measurement

The temporal phase unwrapping (TPU) method is widely utilized for its high performances. However, the existing TPU methods require projecting fringe patterns other than phase shifting patterns to assist in determining phase orders, which significantly affects the measurement efficiency and speed. To address this issue, we propose a phase unwrapping method based on vibrational phase shifting (VPS) for 3-D measurement. The method improves the conventional phase shifting fringes by changing the light intensity of different fringes, thereby embedding period information within the phase shifting fringes. The period information is utilized to help determine phase orders, thereby avoiding projecting additional patterns during the phase unwrapping process. The method first utilizes the sinusoidal patterns for phase calculation and then employs two specific sinusoidal patterns with a sum phase shifting amount of $2\pi $ to obtain periodically distributed phase orders. Through the period information embedded in the phase shifting fringes, the periodically distributed phase orders are converted into continuous ones, thereby completing phase unwrapping and achieving measurement of the object. Measurements on a sphere and a sculpture were conducted to verify the feasibility of the proposed method. Experimental results demonstrate that the method enables the measurement of objects without projecting additional fringe patterns, offering faster measurement speed and higher measurement efficiency compared to other TPU methods.