3-D Shape Measurement Method Based on Phase Shifting Fringe Multiplexing

The temporal phase unwrapping (TPU) method is widely utilized for its high measurement accuracy and robustness. Existing TPU methods require additional fringe patterns to determine phase orders, converting wrapped phase values into continuous ones. This process significantly impacts measurement speed. To address this issue, we propose a 3-D shape measurement method based on phase-shifting fringe multiplexing. This method employs phase-shifting fringe patterns to assist in phase unwrapping, eliminating the need for additional fringe patterns. The method first calculates the wrapped phase using all phase-shifting fringe patterns. Then, it applies a binary operation involving two fringe patterns with a sum phase shifting amount of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2\pi $ </tex-math></inline-formula> to obtain periodically distributed phase orders. A phase order self-increasing algorithm is used to convert periodical phase orders into continuous ones, uniquely marking the phase periods. Surface contour information is then obtained through stereo-matching operations. The feasibility of the proposed method was verified through measurements on the POM sphere, a cross pyramid, and the Medici sculpture. Experimental results show that the proposed method offers faster measurement speeds while maintaining accuracy compared to previous methods. Additionally, it enables 3-D shape measurements using traditional stereo vision systems without changing the hardware system.