The binary defocusing fringe projection profilometry (FPP) technique has demonstrated various advantages for high-speed and high-accuracy three-dimensional (3D) surface measurement. However, higher fringe frequency does not necessarily give better measurements in binary defocusing FPP. To improve the 3D geometry measurement accuracy, this paper proposes an optimal frequency selection approach by analyzing the phase error distribution under different defocusing degrees. The phase error is analyzed theoretically based on the multi-frequency temporal phase unwrapping process, and the associated relationship with fringe frequency, system defocusing degree, noise, and other influencing factors is established. Meanwhile, optimal fringe frequency in a specific system is selected by the theoretical model combined with the validation of simulation experiments. Finally, the measurement accuracy could be effectively enhanced by the generated binary fringe patterns of optimal frequency. Both simulations and experiments verify the effectiveness and robustness of the proposed method.

The binary encoding method has been widely used for three-dimensional (3D) shape measurement due to the high-speed projection characteristics of its digital mirror device (DMD)-based projector. However, traditional binary encoding methods require a larger defocus to achieve a good sinusoidality, leading to a reduction in the measurement depth of field and signal-to-noise ratio (SNR) of captured images, which can adversely affect the accuracy of phase extraction, particularly high-frequency fringes for 3D reconstruction. This paper proposes a spatial-temporal binary encoding method based on dynamic threshold optimization for 3D shape measurement. The proposed method decomposes an 8-bit sinusoidal fringe pattern into multiple(K) binary patterns, which can be outlined into two steps: determining the dynamic threshold and then performing temporal-spatial error diffusion encoding. By using an integral imaging strategy, approximate sinusoidal patterns can be obtained under nearly focused projection, which can then be subjected to absolute phase unwrapping and 3D reconstruction. The experiments show that compared to the three comparative algorithms under the same experimental conditions, this proposed method improves the reconstruction error of measuring a plane and an object by at least 13.66% and 12.57% when K=2. The dynamic experimental result on the palm confirms that the proposed method can reliably reconstruct the 3D shape of the moving object.