3-D shape measurement of rail achieved by a novel phase measurement profilometry based on virtual reference fringe generated by image interpolation

The 3-D measurement of rail shape is important for the safety of railway transportation. Phase Measurement Profilometry (PMP) is chosen to measure rail shape in this paper for its advantages of non-contact, high accuracy and fast speed. In traditional Phase Measurement Profilometry (T-PMP), the setting of the reference plane plate plays an important role, and it is a critical step to capture the reference fringe pattern projected onto the reference plane plate. However, it is sometimes difficult to choose or place the physical reference plane plate in practical applications with complex environments, such as in rail shape measurement. In this paper, a novel PMP based on virtual reference fringe (VRF-PMP) is proposed to deal with the problem. The virtual reference fringe is obtained through extending a partial undeformed fringe pattern intercepted from the whole fringe pattern using image interpolation methods, including Nearest Interpolation, Bilinear Interpolation, Bicubic Interpolation and a proposed One-dimensional New Edge-directed Interpolation (ONEDI). Simulation and experimental results show that VRF-PMP can reconstruct the 3-D shape of rail effectively without a physical reference plane plate. This paper provides a new suggestion for actual detection by PMP.