The diffraction characteristics of orthogonal gratings with variable duty cycles and phase modulation depths are analyzed by using a spatial light modulator. The calculation methods of the transmission function, far-field diffraction light field, and diffraction efficiency of orthogonal gratings are deduced in theory. Meanwhile, the influences of the duty cycle and phase modulation depth on the diffraction characteristics of the orthogonal grating are discussed. The simulation and experimental results verify the correctness of the theoretical derivation. This method can be widely used in the fields of an optical vortex array, laser parallel processing, optical computing, optical communication, and optoelectronic hybrid processing.
In this paper, a phase error compensation method based on a probability distribution function (PDF) is proposed to improve the accuracy of phase extraction, which is helpful for three-dimensional (3D) reconstruction. First, the relationship between the gamma and the gray values is established to segment the projection regions. Then a new method based on a PDF is designed to represent the variation degree of phase error, which fits the precoded gamma value in the minimum range of the phase error. After that, the error compensation method is applied to the self-built system and packaged independently from the 3D reconstruction system to unwrap phases with high precision. The experimental results show that the proposed method can reduce the standard deviation of the phase error by 46.9% compared without phase error compensation, and decrease the standard deviation of the phase error by 30% compared with the whole precoding. Generally, our method can effectively avoid overcompensation or under-compensation caused by single global gamma precoding correction, and better reduce the phase error and improve the 3D reconstruction accuracy in the fringe projection system.
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