in color fringe profiling impair the accuracy of the 3D shape reconstruction of the object to a certain extent.  
Due to the DLP having a faster refresh rate at lower bit depth, many phase shift profilometry measurement based on binary gratings has been proposed to increase the detection speed of 3D detection. [PERSON] et al. proposed a technique using Ronchi grating to generate sinusoid grating fringe patterns by the method of defocusing binary structured ones [18]. However, it is not easy to calibrate the defocused projector and the depth range measurement of this method is small. [PERSON] et al. demonstrated a nine or more step binary phase-shifting algorithm with a nearly focused projector, which has a significantly large depth range and highly accurate calibration [19], however, the accuracy and efficiency are limited by the wide period of binary grating and multi-phase-shifting steps. [PERSON] et al. compounded the sinusoid fringe into the binary color defocused projected fringe to reduce the nonlinear gamma [20]. However, this method has the limits of a specific defocusing device and the color crosstalk problem remains inevitable. [PERSON] et al. introduced the method of bi-frequency tripolar pulse-width modulation (TPWM) fringe projection and the sinusoid pulse-width modulation (SPWM) fringe projection. By optimizing the PWM properly, this method could eliminate the impact of the dominant undesired harmonics. However, the duty cycle is still 1/2 and the four-step phase-shifting algorithm is needed to reconstruct the object [21; 22]. [PERSON] et al. proposed a one-shot projected fringe profilometry using a 2D fringe-encoded pattern, and the fringe pattern used for phase extraction can be directly utilized for unwrapping, but the accuracy of this method is limited by the FTP algorithm [23]. [PERSON] et al. [24] designed a contrast encoded pattern with a quaternary contrast-encoded scheme for phase-shifting techniques, however, three sinusoid quaternary contrast-encoded pattern are necessary to reconstruct the 3D profile of an object. [PERSON] et al. [25] introduced a quantized phase-coding method to generate more than 36 different three-digit codes to achieve a high measurement accuracy, but the measurement speed was also limited by three fringe pattern projection. [PERSON] et al. proposed an alternative measurement using an aperiodic sinusoidal fringe pattern with intensity profiles instead of phase-shifted purely sinusoidal fringes, where two cameras were used in the measurement system, thus it should be noticed that the array projector is unique, and the speed of the whole system is high [26]. [PERSON] [27] et al. proposed a real-time 3D surface PMP based on color binary gratings, in which three monochromatic binary fringes occupy 1/3 period, respectively, and when arranged periodically, these binary fringes are encoded in red (R), green (G), and blue (B) channels, and the sinusoidal is directly extracted from the encoded binary grating without defocusing projection and using a proper filtering operation in spatial frequency domain. However, a color charge coupled device (CCD) camera must be adopted in this method, which will limit the overall reconstruction rate.  
In this paper, we propose a new real-time 3-D shape measurement method based on single-shot quaternary grating projection.