Objective  With the rapid development of modern information technology, optical three-dimensional (3D) profiling measurement technology has gradually matured. Among numerous optical 3D profiling measurement technologies, due to its non-contact and high-accuracy measurement, digital fringe projection（DFP） technology is increasingly applied in the fields such as biomedical monitoring, virtual reality, and computer vision, and has broad prospects for development due to its non-contact and high measurement accuracy. However, this technology still faces some technical challenges: 1) Due to the limited depth of field of the system equipment (such as cameras and projectors), only the 3D shape of objects within a limited depth of field can be reconstructed; 2) Nonlinearity problems caused by the γ-effect of commercial projectors may affect measurement accuracy. To overcome these problems, this paper proposes a method to extend the measurement depth range, which can achieve high-accuracy measurement of multiple objects at different depths or objects with a large depth range.

  Methods  The paper proposes a novel method for measuring the 3D shape of objects with a large depth range. Firstly, defocus technique is used to measure the dithering pattern in a simulated sinusoidal mode, avoiding the influence of projector non-linear errors on 3D measurement of fringe projection and increasing the measurement speed. Then, by analyzing the relationship between the degree of defocusing of the fringe and the depth (Fig.1-2), this paper analyses the relationship between fringe defocus and depth and finds that the defocus degree of fringes at different frequencies is inconsistent with the depth variation nodes. Based on this, a multi-frequency phase selection method is proposed in this paper. The optimal frequency mode determination algorithm (Fig.4) is used to select the bayer dithering algorithm and the floyd-steinberg dithering algorithm to generate dithering patterns. After comparing the phase error distribution of the fringe images within the range of 12-60 pixel in period at 25 defocus levels, the defocusing selection range of the corresponding fringe frequency is screened to determine the optimal selection of fringe frequency at different defocusing degrees. Then, in order to obtain a binary pattern with the highest quality sinusoidal structure, 8 different scanning orders are used based on the selection results of the optimal frequency mode which is to select the optimal dithering mode for the current frequency (Tab.1). Finally, the method uses the selected dithering fringe pattern within the optimal frequency range to obtain the 3D shape of the object. The proposed method can extend the measurement range of object depth by selecting multi-frequency dithering fringe and determining the optimal frequency at different defocus degrees.

  Results and Discussions   This paper presents qualitative and quantitative comparison experiments between the standard sinusoidal fringe and the proposed method. In the qualitative experiment, both methods are used to reconstruct the 3D shape of an object with a depth of 22.5 cm (Fig. 9). The measurement results of the proposed method are better than those of the standard sinusoidal fringe method with complete shape, clear details and without ripple phenomenon. Moreover, in the quantitative experiment, the maximum absolute error of the proposed method is 0.033 mm (Tab.2), which is comparable to the measurement accuracy of traditional DFP technology. Therefore, the proposed method not only ensures measurement accuracy but also extends the measurement depth range, and effectively solves the problem of measuring the 3D shape of objects with a large depth in the DPF field.

  Conclusions  This paper proposes a MFPS method based on dithering algorithms to solve the limited measurement depth range and nonlinearity problem of the existing DFP technology. By using defocusing dithering techniques, the impact of projector nonlinearity error is overcome. Moreover, the MFPS method is used to generate dithering fringe patterns for measurement, which extends the measurement depth range. Experimental results demonstrate that the proposed method effectively extends the measurement depth range and achieve 3D shape measurements of objects in a large depth range.