Absolute phase retrieval based on spatial ternary phase coding with circular fringe projection

Abstract

Fringe projection profilometry (FPP) based on temporal phase unwrapping (TPU) plays a vital role due to its high precision and fast speed in three-dimensional (3D) measurements. However, a fundamental contradiction arises between the necessity for numerous auxiliary patterns and the goal of enhancing measurement efficiency, particularly when ensuring a big codeword space for fringe order. Thus, a spatial ternary phase coding (STPC) method is proposed, which achieves a big codeword space by projecting just one auxiliary coding pattern while ensuring a robust decoding. By equally dividing each fringe period into several segments, ternary coding of fringe order is accomplished using an arccosine operation to code three distinct phase values within each segment. Meanwhile, circular grating is adopted due to its excellent performance in phase sensitivity, which offers a higher measuring accuracy in 3D reconstruction. Accordingly, a robust TPU is achieved by combining the introduced phase unwrapping scheme and the circle center-cosine theorem (CCCT) strategy. Furthermore, high-efficiency measurements are attained through projecting three phase-shifting circular gratings and one STPC grating, rendering it suitable for real-time measurements. Experimental results with various static objects and real-time scene demonstrate the feasibility and validity of the proposed method.