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Pre-shifted phase coding approach for absolute phase retrieval

The phase coding approach has been extensively applied to three-dimensional (3-D) shape measurement, in which the fringe order determined by the phase coding patterns is utilized to unfold the wrapped phase calculated by the phase-shifted patterns. However, due to inevitable random noises and projector/camera defocus, the fringe order can not be accurately aligned with the wrapped phase, thereby introducing the abnormal jump phase errors. To this end, this paper presents a simple and practical approach with no accuracy loss and no extra patterns to remove the abnormal jump phase errors. Firstly, the designed phase coding patterns are pre-shifted by half fringe period relative to the phase-shifted sinusoidal patterns for ensuring that the decoding order changes and the 2π phase jumps of the wrapped phase are staggered. Then, by analyzing the intensity variations of the phase-shifted sinusoidal patterns, a virtual binary code is generated, which is essentially shifted by a quarter of the fringe period relative to the phase-shifted sinusoidal patterns. Subsequently, the decoding order is divided into three subregions by referring to the distribution of the virtual binary code and the wrapped phase. After completing the segmentation, a regional correction operation (RCO) is implemented. For each subregion, the decoding order remains unchanged or is adjusted to get the correct fringe order. As a result, the interval of the wrapped phase can be accurately identified at the pixel level for phase unwrapping successfully. Benefitting from the simple pre-shifted strategy used for the phase coding patterns and the virtual binary code extracted by the phase-shifted patterns, the proposed approach can completely avoid the abnormal jump phase errors without projecting additional patterns. Moreover, compared with the conventional median filtering approach, the proposed approach has the capability to preserve sharp edges, and thus it is noninvasive. The measurement results demonstrate the reliability and accuracy of the proposed approach in measuring different objects containing intricate surface profiles.