Three-dimensional (3D) reconstruction is an essential task in structured light field (SLF) related techniques and applications. This paper presents a new method to reconstruct a 3D object point by using many auxiliary points adjacent to it. The relationship between two points in a SLF system is derived. Different from conventional “direct” methods that reconstruct 3D coordinates of the object point by using phase, slope, disparity etc., the proposed method is an “indirect” method as the 3D coordinates of auxiliary points are not needed. Based on the auxiliary point theory, the wrapped phase obtained by 4-step phase-shifting method is sufficient for 3D reconstruction, without the need for phase unwrapping. To the best of our knowledge, this is the first strategy that combines the intrinsic characteristics of structured light and light field for phase-unwrapping-free 3D reconstruction. This paper also analyzes the constraints between system architecture parameters and phase rectification, phase to depth ratio, and presents a relatively simple criterion to guide the system design. Experimental results show that, with an appropriate system architecture, the proposed method can realize accurate, unambiguous, and reliable 3D reconstruction without phase unwrapping.

Calibration is essential for the three-dimensional light field endoscope, and the two-step calibration method based on line features was proposed by us to accomplish it before. In the second step of the two-step calibration method, the relationship between the projections of virtual feature points on the microlens image and the central sub-aperture image was used to calibrate the parameters about the microlens array, but we find that the feasibility of the calibration method has a depth constraint on the border of the checkerboard. In this paper, we deduce and demonstrate this constraint, and an optimization algorithm is designed to improve the accuracy of the second step calibration due to the inaccurate black-and-white boundary detection. Experimental results show that our method is effective and accurate for the calibration of the three-dimensional light field endoscope.