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Codewords are important in encoded absolute phase retrieval techniques such as two-frequency, gray-code, and phase-coding. Each sinusoidal fringe is marked by a unique codeword so that an absolute fringe order can be determined by decoding the codeword. However, due to the limited number of unique codewords, sinusoidal fringe patterns do not contain high-frequency fringes without the use of additional patterns. A multi-subzone coding and decoding algorithm is thus proposed to overcome this limitation. Three multi-subzone coding methods based on two-frequency, gray-code, and phase-coding techniques are presented. The coding creates multiple subzones of unique codewords and the decoding enables it to use non-unique codewords to identify absolute fringe order. Specifically, the range of fringe order is estimated by the use of a wrapped phase map and the absolute fringe order is identified by a codeword. Experimental studies demonstrate the advantages of the proposed algorithm over existing coding methods. The proposed algorithm is suitable to measure objects with large step-height surface discontinuities.

Absolute phase retrieval is essential for height measurement in digital fringe projection. However, projections of additional structured patterns that are normally required for phase unwrapping increase the measurement complexity. In this paper, we propose two reference-plane-based pixel-by-pixel absolute phase retrieval techniques with as few projections as possible, suitable for different object depth ranges. The wrapped phase on the object is absolutely unwrapped by referring just to the absolute phase map on the reference plane. Single-frequency absolute phase retrieval with one-reference-plane-based calibration is first proposed for objects within a height limit that equals a calibrated system constant. To extend the measurement depth range, dual-frequency absolute phase retrieval with two parallel reference planes is further proposed. The additional low frequency is used to choose the unwrapping reference from the two reference plane phases for unwrapping the high-frequency phase. Moreover, the proposed techniques are capable of high-frequency absolute phase unwrapping for objects with step-height surface discontinuities. Experiments have been conducted to demonstrate the efficiency of the proposed two techniques.

Digital fringe projection is one of the most widely adopted optical non-contact methods used for high-precision depth measurement in industry. Nevertheless, new approaches with less measurement complexity and higher accuracy are still emerging in the research field. In this paper, we first analyze the efficiency of the reference-plane-based dual-frequency (RDF) pixel-by-pixel absolute phase retrieval method. The RDF method is able to provide a high-precision phase measurement, but the constraint of measurement depth range limits its application. We therefore propose an enhanced reference-plane-based dual-frequency (ERDF) pixel-by-pixel absolute phase retrieval method. The proposed ERDF method overcomes the constraint of measurement depth range and preserves the merits of the RDF method. In the ERDF method, the lower-frequency phase map is completely unwrapped with reference-plane-based single-frequency method, and the higher-frequency phase map is completely unwrapped using the lower-frequency unwrapped phase. The ERDF method is suitable for measuring objects with step-height surface discontinuities. Experiments have been conducted to demonstrate the advantages of the proposed ERDF method as compared to the RDF method.