The digital light processing (DLP) projector has been widely used in fringe projection profilometry (FPP) for three-dimensional (3D) shape measurement. The mostly used bit depth of projected fringe patterns in FPP is 8 bit. It limits the number and switching speed of projected patterns and leads to the limitation of available algorithms for the 3D reconstruction and the redundancy of the camera rate due to the inherent constraints of some DLP projectors. Meanwhile, the binary defocusing projection technique with 1 bit fringe patterns that can obtain a faster refresh rate of patterns is greatly limited in measurement accuracy and the measurement depth range because of the down-sampling of patterns and the defocusing of projectors. In addition to the commonly used 8 bit and 1 bit fringe patterns, there is a lack of research on fringe patterns of 2-7 bit and no selection scheme for the optimal bit depth of projected fringe patterns in different application scenes. To balance the measurement performance in terms of measurement accuracy, speed, and depth range, this study proposes a 3D shape measurement method by projecting arbitrary-bit fringes using DLP projectors and a strategy of determining the optimal bit depth in different application scenes.

The basic idea of the method of projecting arbitrary-bit fringe patterns for 3D shape measurement is to split arbitrary-bit fringe patterns into several 1 bit patterns, load them into the DLP projector in order, and select the corresponding bit depth of fringe patterns for projection. Firstly, the bit depth of the used fringe patterns is determined by the actual measurement system and requirements, and the gray level of a line of the corresponding sinusoidal fringe pattern is calculated. Then, the quantified gray level is converted into a binary number. After that, the same bit binary number is extracted and expanded by row to several 1 bit patterns according to the spatial characteristics of the fringe patterns. Next, these 1 bit patterns are loaded into the DLP projector for projection and shooting, and the suitable 3D reconstruction algorithms in the corresponding systems are used to reconstruct objects' information. As a result, arbitrary-bit fringe patterns can be used in 3D measurement based on FPP. Meanwhile, according to the analytical strategy considering the reconstruction speed or camera shooting speed, the used algorithm, measurement accuracy, and other conditions, the optimal bit depth can be selected.

The results of the measurement for the whiteboard, standard gauges, and complex plaster model demonstrate that the measurement accuracy of the 6 bit fringe projection is close to that of the 8 bit fringe projection (Table 1, Figs. 6 and 7). As the number of allowed projected 6 bit fringe patterns is more than that of 8 bit fringe patterns, 6 bit fringe patterns have the advantages of flexible coding and anti-noise ability in the measurement scene with high noise and can be applied in more 3D measurement scenes (Fig. 8). In addition, they are more resistant to motion-induced errors due to their faster refresh rates in the projector than 8 bit fringe patterns (Figs. 9 and 10). Meanwhile, the measurement depth range of the 6 bit fringe projection method with the focused projector is larger than that of the 1 bit fringe projection method with the defocusing projecting (Fig. 11). Moreover, the 4 bit fringe patterns obtained by the proposed method can be used in 3D measurement based on FPP (Fig. 12), but the measurement performance needs to be improved. Finally, the measurement performance and applicable scenes of fringe projection using different bits are given (Fig. 13), and the corresponding operational parameters of the fringe projection measurement system are summarized to guide the selection of the optimal bit depth of fringe patterns in different application scenes (Fig. 5).

This study proposes a 3D shape measurement method by projecting arbitrary-bit fringes using the DLP projector, which offers diverse options for the bit depth of projection and coding strategies. It demonstrates that 6 bit fringe patterns have the advantages of flexible fringe projection, and they can make full use of the redundancy of the camera rate and expand the range of available algorithms for 3D reconstruction compared with 8 bit fringe patterns. The measurement depth range of the 6 bit fringe projection is larger than that of the 1 bit fringe projection. Considering the characteristics of the DLP projector and the camera, the relationship between the operational parameters of the 3D measurement system based on fringe projection is summarized. On this basis, a method for selecting the bit depth of fringe patterns is proposed, providing a valuable reference for the selection of the optimal bit depth in different measurement systems. The method can make full use of the hardware's performance in the actual applications and enable the flexible usage of different 3D reconstruction algorithms and can be applied to more measurement scenes.