In fringe projection profilometry (FPP) based on temporal phase unwrapping (TPU), reducing the number of projecting patterns has become one of the most important works in recent years. To remove the 2π ambiguity independently, this paper proposes a TPU method based on unequal phase-shifting code. Wrapped phase is still calculated from N -step conventional phase-shifting patterns with equal phase-shifting amount to guarantee the measuring accuracy. Particularly, a series of different phase-shifting amounts relative to the first phase-shifting pattern are set as codewords, and encoded to different periods to generate one coded pattern. When decoding, Fringe order with a large number can be determined from the conventional and coded wrapped phases. In addition, we develop a self-correction method to eliminate the deviation between the edge of fringe order and the 2π discontinuity. Thus, the proposed method can achieve TPU but need to only project one additional coded pattern (e. g. 3+1), which can significantly benefit dynamic 3D shape reconstruction. The theoretical and experimental analysis verify that the proposed method performs high robustness on the reflectivity of the isolated object while ensuring the measuring speed.

A new 3D measuring method based on computer-generated moiré fringes is proposed. The two AC components of the 0-degree and 90-degree phase-shifted fringe patterns on reference plane are prepared in advance. While the AC component of the single-shot deformed pattern is multiplied by the two prepared AC components, respectively, two computer-generated moiré fringes can be retrieved. The ratio of the two computer-generated moiré fringes is just the tangent of the phase modulated by the object. It is of great potential in real-time or even dynamical 3D measurement due to its single-shot deformed pattern feature, and it avoids the influences of the object’s reflectivity simultaneously. Compared to the Fourier transform profilometry, its error is smaller due to its higher first-order spectrum. Experimental results show the feasibility and validity of the proposed method.

High-speed 3D measurement is receiving increasing attention. However, simultaneously achieving high computational efficiency, algorithmic robustness, and reconstructing ratio is challenging. Therefore, a dynamic phase-differencing profilometry (DPDP) is proposed. By capturing the minimum three phase-shifting sinusoidal deformed patterns and establishing a brand-new model, the phase difference between the object on the reference plane and the reference plane is directly resolved to effectively improve computational efficiency. Although it is wrapped, by using only two auxiliary complementary gratings with a purposely designed lower frequency, a DPDP-based number-theoretical temporal phase unwrapping (NT-TPU) algorithm is also proposed to unwrap the wrapped phase difference rather than the phase itself with high robustness. Furthermore, compared to existing PSP-based NT-TPU, the proposed NT-TPU can normally work under more relaxed restrictions. In order to accomplish a high reconstructing ratio, a pentabasic interleaved projection (PIP) strategy based on time division multiplexing is proposed. It can improve the reconstructing ratio from one reconstruction per every five patterns to an equivalent of one reconstruction per every 1.67 patterns. Experimental results demonstrate that the proposed method achieves high computational efficiency, high algorithmic robustness, and high reconstructing ratio simultaneously and has prospective application in high-speed 3D measurement.

A curtain-type phase unwrapping algorithm is proposed. First, the 2 × 2 closed curve method is used to find out the residual point of the wrapped phase to form the residual template, and the Otsu threshold method is used to binary the modulation of the deformed pattern to form the shadow template. Second, the effective phases of up-down symmetrical points about the starting point are simultaneously unwrapped in turn until all the points in the column are completed. Third, the starting point is taken as the center of left-right symmetry, the effective phases of the nearest symmetric points are simultaneously unwrapped, and the corresponding columns are unwrapped in the same way as above. Fourth, in this way, the effective phases in the corresponding symmetric columns are successively unwrapped in the form of curtain opening until the whole phases are completely unwrapped. In the previous procedure, the shadow template and residual template guide the curtain-type phase unwrapping to avoid error diffusion. Finally, the 8-neighborhood mean algorithm and the cubic b-spline algorithm are employed to unwrap the phase values of residual points and shadow areas, respectively. The proposed method realizes the whole phase unwrapping without phase error diffusion. Experimental results show that the efficiency of the proposed method is 26% higher than that of the diamond algorithm, and its accuracy is significantly improved.

An improved algorithm for phase-to-height mapping in phase-measuring profilometry (PMP) is proposed, in which the phase-to-height mapping relationship is no longer restricted to the condition that the optical axes of the imaging system must be orthogonal to the reference plane in the basic PMP. Only seven coefficients independent of the coordinate system need to be calibrated, and the system calibration can be accomplished using only two different gauge blocks, instead of more than three different standard planes. With the proposed algorithm, both the phase measurement and system calibration can be completed simultaneously, which makes the three-dimensional (3-D) measurement faster and more flexible. Experiments have verified its feasibility and validity.

Patternless binary coding strategies have been a challenge for ultra-fast 3D imaging with structured light. This Letter proposes a big codewords space division multiplexing binary coding method. From the third to the multiple order, a special spatial binary coding instead of the Gray code is created for the first time, to the best of our knowledge, to achieve an ultra-wide unambiguous range with only one auxiliary pattern. Advantageously, a connection domain segmentation technique with anomaly detection is proposed to achieve decoding of the fringe order, which cleverly avoids the misalignment problem. Additionally, a center of gravity method is applied to compensate for the codewords of the residual connected domain. The robustness and effectiveness of the proposed method for complex, isolated, and non-uniform reflectivity objects, as well as the ultra-fast 3D imaging of dynamic measurements, are experimentally verified.