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Fringe projection profilometry (FPP) is a rapidly developing technique which is widely used for industrial manufacture, heritage conservation, and medicine etc. because of its high speed, high precision, non-contact operation, full-field acquisition, and easy information processing. Among the various FFP methods, the squared binary defocused projection method (SBM) has been promptly expanding with several advantages: (1) high projection speed because of 1-bit grayscale fringe; (2) eliminating nonlinear gamma of the projector for the defocusing effect. Nevertheless, the method is not trouble-free. When the fringe stripe is wide, it brings down the fringe contrast and is difficult to control the defocused degree, resulting in a low measurement accuracy. In order to further improve high-speed and high-precision three-dimensional shape measurement, this paper presents a new three-dimensional shape measurement method based on double-frequency fringes projection. This new method needs to project two sets of 1-bit grayscale fringe patterns (low-frequency fringe and high-frequency fringe) onto the object surface under slightly defocused projection mode. The method has the following advantages: (1) high projection speed because of 1-bit grayscale fringe; (2) high measurement precision for selectively removing undesired harmonics. Low-frequency fringe is produced by error-diffusion dithering (Dithering) technique and high-frequency fringe is generated by optimal pulse-width modulation (OPWM) technique. The two kinds of fringe patterns have each superiorities and flaws. The low-frequency fringe has a low measurement accuracy, but the continue phase can be easily retrieved. However, the property of high-frequency fringe and low-frequency fringe is the opposite. The general idea of this method proposed is as follows: Because the both fringes test the same object, the height is the same. The low-frequency fringe can be used to assist the high frequency fringe to retrieve continue phase map, then the three-dimensional shape information of the object can be obtained. Theory analyzes the mathematical principle of error-diffusion dithering technique, optimal pulse-width modulation technique and three-dimensional reconstructed algorithm based on double-frequency fringes projection. A second-hand mouse was used to test the proposed method. The experiment results show that the three-dimensional shape measurement method combining OPWM technique and Dithering technique can achieve fast-speed and high-precision three-dimensional shape measurement.
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