Objective In fringe projection profilometry (FPP), the speed of fringe projection and image acquisition is a critical parameter determining the efficiency of three-dimensional measurement. Therefore, the rapid acquisition of fringe images has become an important research focus. Conventional methods based on DLP typically require a projector to occupy 255 pulse cycles for projection and rely on temporal integration imaging with a camera to obtain a single 8-bit sinusoidal fringe image. For phase-shifting (PS) algorithms that require at least three fringe images, this process is considerably time-consuming and fails to fully utilize the maximum refresh rate of the projector, making it difficult to meet the demands of dynamic 3D measurement. Moreover, the nonlinear responses of the projector and camera in traditional method introduce significant measurement errors, thereby reducing the overall measurement accuracy. To address these issues, this paper proposes a sinusoidal fringe image acquisition method based on line-shifted binary focusing projection.

Methods The core of this paper is to propose a binary focused projection method based on line-shifted encoding to achieve efficient acquisition of sinusoidal fringe images. First, a line-shifted encoding strategy adapted to binary focused projection is proposed to realize the refined design of even-numbered binary encoded patterns. Within any period of the binary pattern, only one column is encoded as a normalized grayscale value of 1, and all other columns are assigned a value of 0. As the number of projection steps increases, different vertical patterns are projected one by one, and the encoded column set to a grayscale value of 1 switches column by column along the horizontal direction until it covers all horizontal columns in the projector's imaging plane. Second, a targeted sinusoidal fringe synthesis model is constructed to complete the accurate conversion of binary patterns into standard sinusoidal fringe images. This model is based on the principle of weighted grayscale superposition, assigns corresponding weights according to the contribution of each binary image in fringe synthesis, and synthesizes m binary encoded patterns into n standard sinusoidal fringe images with arbitrary steps through grayscale superposition operations. On this basis, a phase-shift algorithm is used to accurately extract phase information, and complementary gray codes are combined to assist in phase unwrapping, achieving high-precision and high-speed three-dimensional measurement.

Results and Discussions To systematically verify the performance of the proposed method, three groups of controlled experiments are designed and conducted in this paper, with detailed experimental contents and results as follows: i) Performance verification experiment; it shows that as the coding period increases, the measurement accuracy gradually improves and tends to be stable when the period is 16 pixels. ii) Static comparison experiment; it shows that the measurement accuracy of the proposed method is significantly better than that of the binary defocus method, and slightly better than that of the traditional sinusoidal fringe projection method and the bitwise projection method. iii) Dynamic comparison experiment; it shows that the proposed method is suitable for dynamic measurement scenarios. Compared with the binary defocus method, although the proposed method needs to project more patterns, the measurement accuracy is significantly improved. Compared with the bitwise projection method, the proposed method can still achieve further improvement in accuracy under the condition that the number of fringe patterns is reduced by 63.64%. Compared with the traditional sinusoidal fringe projection method, although the number of required patterns is increased, since the digital projector can project binary patterns at a rate of thousands of frames per second, which is much higher than the hundred-frame level speed of projecting 8-bit sinusoidal fringes, the overall projection efficiency of the system is still effectively improved while ensuring the reconstruction accuracy.

Conclusions In conclusion, this paper proposes a method for acquiring sinusoidal images based on line-shifted binary focused projection. This method performs focused projection on the encoded binary patterns and combines the constructed sinusoidal image synthesis model to synthesize multiple binary images into high-quality sinusoidal fringe images, thereby achieving the rapid acquisition of sinusoidal images. Verified by comprehensive comparative experiments under both static and dynamic scenarios, the proposed method can fully exploit the limit of the projector’s refresh rate and meet the application requirements of dynamic three-dimensional (3D) measurement. It not only significantly improves the 3D measurement speed, but also effectively suppresses the nonlinear errors of the measurement system, thereby further optimizing the measurement accuracy.