In the three-dimensional measurement technology of structured light, traditional sinusoidal fringes are lost due to the nonlinear gamma effect of digital micromirror projectors and industrial cameras, which results in phase errors and thus reduces the measurement accuracy and effect. With only two gray values, the binary fringe is not affected by the nonlinear system and can greatly improve the projection speed, and hence, it is widely studied by scholars both at home and abroad. Binary fringe defocused projection technology is widely used in three-dimensional topography measurement. In this technique, the gray sinusoidal fringes of eight bits are discretized and quantized into the binary fringes of one bit, and the sinusoidal fringes are obtained at the imaging end by the micro defocus of the projector. This method can reduce the nonlinear effect of the projector and significantly improve the measurement speed, but it can hardly grasp the defocus degree and will reduce the depth range of measurement. Given the advantages of binary fringes, this paper proposes a measurement method based on binary coded fringes. This method can combine the binary fringes with the phase-shifting technique without defocused projection to improve the measurement accuracy and effect.

This paper proposes a measurement method based on binary coded fringes. The modulation information of the measured object surface is obtained by the projection of multiple binary fringes, and then the sinusoidal fringes are generated by the binary superposition of binary fringes. The projection of binary fringes can avoid the direct projection of sinusoidal fringes and reduce the influence of the nonlinear system. First, the gray value of the traditional sinusoidal fringe that changes sinusoidally in a period is sampled to obtain the discrete decimal gray value of the sinusoidal fringe. The gray value is encoded in binary, and all the code words of the same rank of binary encoding are combined separately to generate binary fringes. Second, the sequential projection is carried out by the digital projector, and the collected fringes are superimposed in binary to generate the sinusoidal fringes modulated by the height information of the object to replace the process of directly projecting the traditional gray sinusoidal fringes. Third, the wrapped phase is obtained by the combination of the proposed method and the four-step phase-shifting technique, and the phase is unwrapped by the complementary Gray-code method to obtain the absolute phase. Through projector and camera calibration, the absolute phase is mapped to three-dimensional point cloud data.

To verify the superiority of the three-dimensional measurement method based on binary coded fringes, this paper uses the binary coded fringe method combined with the four-step phase-shifting technique to measure different objects and carries out a comparison experiment with the traditional four-step phase-shifting method and twelve-step phase-shifting method. In terms of accuracy evaluation, the standard sphere with a diameter of 50.8140 mm is measured, and the local point cloud data is fitted. The average distance between the point cloud data of the proposed method and the fitted standard sphere is 0.0697 mm, while that of the traditional method is 0.1288 mm. Compared with the results of the traditional methods, the accuracy of the proposed method is significantly improved, and the average distance is reduced by 45.88%, as shown in Fig. 5 and Table 2. The measurement of the high-precision plane and the linear fitting of the local data show that the root mean square error (RMSE) of the proposed method is 0.1211 mm, and the sum of the squared error (SSE) is 2.922 mm, as shown in Fig. 7 and Table 3. By the measurement of large-depth objects, the proposed method greatly reduces the periodic errors caused by nonlinear influences compared with the traditional method based on four-step phase-shifting, and the effect is similar to that of the twelve-step phase-shifting method. The local reconstruction results are shown in Fig. 8.

In this paper, a measurement method based on binary coded fringes is proposed. Multiple binary fringes are obtained by binary coding of the gray values within a sinusoidal period, and the modulation information of the measured object is obtained by binary fringe projection, and the collected binary fringes are superimposed in binary. This can replace the direct projection of traditional sinusoidal fringes and fundamentally reduce the measurement error caused by the nonlinear gamma effect. In addition, the proposed method is combined with the four-step phase-shifting method, and the complementary Gray-code method is used to assist in phase unwrapping. The comparison with the traditional four-step phase-shifting method and the twelve-step phase-shifting method demonstrates that the accuracy of the proposed method is significantly higher than that of the traditional four-step phase-shifting method, and on the basis of the principle of four-step phase shifting, the nonlinear effect is reduced. The proposed method not only retains the advantages of the four-step phase shifting but also achieves a similar effect as the twelve-step phase shifting method. Although the proposed method increases the number of projected fringes to a certain extent, it still effectively improves the projection efficiency compared with the projection of gray sinusoidal fringes. However, compared with the traditional method, the proposed method has some shortcomings in the projection. Further research is required to reduce the overall projection number of binary coded fringes. In conclusion, replacing gray sinusoidal fringes with binary coded fringes is a meaningful research idea and can be applied to actual three-dimensional measurement.