A scanning micro phase measuring profilometry based on optical flow pixel matching

In recent years, fringe projection profilometry has emerged as a powerful tool for measuring and inspecting the three-dimensional (3D) morphology of objects. Among them, phase measurement profilometry (PMP) has garnered significant attention due to its high precision. Traditionally, at least three deformed fringe images are required for phase retrieval. To achieve higher precision, even more deformed fringe images are typically needed. In industrial applications, such as inspections on production lines where new samples continuously flow in and out, or to measure large samples with a set of small fields of views for high precision. This necessitates a motion scheme to complete the inspection process. Therefore, it will be promising to integrate the phase-shifting process of PMP with lateral motion. This type of lateral scanning process has been validated in white light interferometry and structured illumination microscopy. This paper proposes a scanning microscopic PMP that combines phase shifting with object translation, reducing measurement complexity and enhancing measurement efficiency. In this design, the measuring unit is fixed and the measuring object is moved along the translation stage. The camera is synchronized with the translation stage and the switching of the white light and structured light illuminations. Then sequential images will be captured with one deformed image and one white light image continuously. The phase drilling process consists of two main steps. The first step is pixel matching, which is used to align the images captured at different positions. The white light images are used to find the amount of pixel shift by optical flow methods, which can reach a sub-pixel level precision via linear interpolation. Then the pixel matching of the fringe images will be fulfilled while we assume the translation is consistent. The second step is to decipher the phase with these matched fringe images. Here, an arbitrary N-step phase-shifting technique is adopted instead of the classical N-step phase-shifting approach. Moreover, a telecentric optical path system is employed to ensure consistency between the actual object movement and pixel shift. The initial phase shift is determined by the offset pixels and the initially estimated fringe period, which is optimized through a probability density function. The experiments in this paper compare static and dynamic results, with the static position fixed as the starting point for dynamic measurements to ensure consistent comparison. The results demonstrate the feasibility of the proposed method, achieving measurement accuracy comparable to traditional PMP systems, with a maximum measurement accuracy of 0.008 mm in planar validation experiments.