The Absolute Phase Retrieval Based on the Rotation of Phase-Shifting Sequence

Abstract

The absolute phase retrieval has been the focus of developments in three-dimensional (3D) shape measurement. The traditional absolute phase retrievals based on phase-shifting algorithm mainly utilize extra patterns to generate fringe order map, which decreases the measuring speed and income more phase shift error. In this paper, the cue of fringe order is directly embedded into phase-shifting patterns to minimize the number of projecting patterns. Fringe order is encoded by rotating the sequence of phase shift amounts, causing the 2&#x03C0; discontinuity to be extended into &#x00B1;2&#x03C0;/<i>N</i>, &#x00B1;4&#x03C0;/<i>N</i>,..., &#x00B1;2(<i>N</i>-1)&#x03C0;/<i>N</i>, &#x00B1;2&#x03C0;. Due to the coding periodicity, the regional wrapped phase without 2&#x03C0; ambiguity can be extracted from different wrapped phase maps. When decoding, the coding phase jump points can be located and identified from one or multiple wrapped phase maps, and then used to determine fringe order by the bidirectional data processing. Experimental results have proved that the proposed method without extra coding patterns not only provides high robustness to shadow and considerable accuracy closed to that of traditional phase-coded method, but also inherits the performance to measure the complex and colorful object using traditional sinusoidal phase-shifting patterns.