There are two primary three-dimensional (3D) measurement error sources of structural light based on the phase shift method: phase shift error and nonlinear error. With the development of a digital projector, the computer can produce standard sinusoidal stripes to eliminate the phase shift error. However, the nonlinear error of the projector and camera will cause the stripe to lose particular sinusoidal properties, affecting the measurement accuracy and effect. To reduce the nonlinear error of the system, global scholars have put forward various solutions, among which the binary stripe method is the most widely studied. The binary stripe is not affected by nonlinearity because it has only two gray values. The projection speed can be significantly improved by a digital projector projecting 1-bit binary stripes. In the study of many binary stripes, the binary coded stripe method uses multiple binary stripes to generate a sinusoidal stripe, which avoids defocusing projection, effectively reduces the nonlinear effect of the system, and improves measurement accuracy and projection efficiency. Based on the binary coded stripe method, this paper proposes a method of reusing weighted binary coded stripes, which significantly reduces the number of binary stripes weighted with a sinusoidal stripe and further improves the projection efficiency.

This paper proposes a method of reusing weighted binary coded stripes. The binary coded stripe method samples the gray value of sinusoidal stripes uniformly to obtain the discrete decimal gray values of a sinusoidal stripe. The gray values are then processed by binary coding, and all of the code words with the same level of binary code words are combined to generate binary stripes. After sequential projection by a digital projector, the collected stripe images are weighted in binary to generate a sinusoidal stripe modulated by object depth information. In the implementation process of binary coded stripes, a certain number of repeated binary stripes will appear under a specific gray-value sampling number. After comparison, 12 gray values are uniformly sampled within a sinusoidal period, and the binary coding generates binary stripes. After unique processing, the same binary stripes only need to be projected once, and repeated weighting is performed in the calculation process. As a result, only four binary stripes are required to generate a sinusoidal stripe. Finally, the method is combined with the three-step phase shift technique. The complementary gray code method is also used to carry out the phase unwrapping, which can realize an efficient 3D measurement with 20 binary stripes in the state of constant focus.

This paper uses the proposed method, three-step phase shift method, and the four-step phase shift method to measure different objects and carry out comparison experiments of different gray values, and the comparison experiment with the traditional methods aims to verify the superiority of the method of reusing weighted binary coded stripes. In the first experiment, through the measurement of a standard sphere, the average distance difference between local point cloud data obtained by different gray values and fitted standard sphere is small. The average distance obtained by the three-step phase shift optimization method is 0.0153 mm, and that by the four-step phase shift optimization method is 0.0107 mm (Fig. 6 and Table 3). As shown in Fig. 7, the actual item is measured, and the reconstructed results are comparable, which verifies that the proposed method of reusing weighted binary coded stripes can still maintain high accuracy and measurement impact after reducing the number of projections. In the comparison experiment with the traditional methods, sinusoidal fitting is carried out on the sinusoidal stripe obtained by the traditional methods and the proposed method. The root-mean-square error (RMSE) of the sinusoidal fitting is 3.6082 and 3.3125, and the sum of squared errors (SSE) is 3529.3 and 3028.4 (Fig. 8 and Table 4). Linear fitting is performed on the measurement results of the high-precision plane. The RMSE is 0.0415 and 0.0388 mm, respectively, and the SSE is 0.4804 and 0.4493 mm (Fig. 9 and Table 5). As demonstrated in Fig. 10 and Table 6, after measuring the standard sphere, the average distance between the local point cloud and the fitted standard sphere is reduced by 72.3% when compared with that by the traditional three-step phase shift method. For the measurement of the plaster head, whose surface depth varies greatly, the traditional three-step and four-step phase shift methods have strip-like systematic errors due to the nonlinear effects of the system. However, the surface reconstruction effect of the proposed method is better (Fig. 11).

This paper proposes a method of reusing weighted binary coded stripes. A better sampling scheme is designed by further studying the principle of the binary coded stripe method. After the unique processing of binary coding and binary stripes, the method of reusing weighted binary coded stripes generates sinusoidal stripes to reduce the actual projection number of binary stripes. In order to generate a sinusoidal stripe, eight weighted binary stripes are reduced to four binary stripes. As a result, only 20 binary stripes are required to complete the 3D measurement by the three-step phase shift method and the complementary gray code phase unwrapping method. The results of comparison experiments show that the proposed method will not reduce the measurement accuracy and effect while significantly reducing the projection number by the binary coded stripe method. Compared with the traditional phase shift method, the proposed method can significantly reduce the nonlinear effect of the system and further improve the projection rate of the DLP projector. In conclusion, the proposed method effectively reduces the projection number required by the binary coded stripe method and provides technical support for high-speed 3D measurement based on phase shift stripe analysis.