A mathematical description of the absolute out-of-plane height distribution in 3D shape measurement with an arbitrarily arranged fringe projection profilometry system is presented, and a corresponding algorithm is proposed to determine the parameters required for accurate 3D shape determination in practical applications. The proposed technique requires neither a specific and precise experimental setup nor a manual measurement of geometric parameters, and it yields high measurement accuracies while allowing the system components to be arbitrarily set and positioned. Computer simulations and a real experiment have been conducted to verify the validity of the technique.
A noncontact, fast, accurate, low-cost, broad-range, full-field, easy-to-implement three-dimensional (3D) shape measurement technique is presented. The technique is based on a generalized fringe projection profilometry setup that allows each system component to be arbitrarily positioned. It employs random phase-shifting, multifrequency projection fringes, ultrafast direct phase unwrapping, and inverse self-calibration schemes to perform 3D shape determination with enhanced accuracy in a fast manner. The relative measurement accuracy can reach 1/10,000 or higher, and the acquisition speed is faster than two 3D views per second. The validity and practicability of the proposed technique have been verified by experiments. Because of its superior capability, the proposed 3D shape measurement technique is suitable for numerous applications in a variety of fields.
The out-of-plane shape determination in a generalized fringe projection profilometry is presented. The proposed technique corrects the problems in existing approaches, and it can cope well with the divergent illumination encountered in the generalized profilometry. In addition, the technique can automatically detect the geometric parameters of the experimental setup, which makes the generalized fringe projection profilometry simple and practical. The concept was verified by both computer simulations and actual experiments. The technique can be easily employed for out-of-plane shape measurements with high accuracies.
An atomic force microscope (AFM) head designed for nanometrology is accomplished in this study. It is the sensing component of the nano-measuring machine, a nanometrological instrument with a working range of 50 mm × 50 mm × 2 mm, as well as a part of the metrological system of the instrument. Three reference mirrors are mounted on the head and arranged without Abbe error. Relative displacement of the AFM head and the specimen is measured by interferometers and results are traceable. The optical beam deflection method is used to detect the atomic force. The laser beam is introduced through a single-mode polarization-maintaining optical fibre from an external laser diode. With a compact design, a 100 mm optical lever is realized inside the AFM head that is less than 20 mm in thickness and 200 g in weight. A force–distance curve is obtained using a gauge block in a test. Furthermore, online tests of the measurement of a step scale have been made. According to the calculation and experimental verification, the resolution of our AFM head reaches 0.05 nm.
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