## 1 Introduction  
In the past few decades, the optical three-dimensional (3D) shape measuring method with the structured light projection has an enormous application in face recognition, industrial inspection, and so on [1; 2; 3; 4; 5; 6]. With the improvement of photoelectric device technology, it has an increased performance in some fields, such as modern industry [7] and medical treatment [8]. For measuring static objects, multiple-shot methods [9; 10] have higher measurement accuracy than single-shot methods. However, the image quality will be degraded due to the vibration, environmental noise, and other interferences in the image shooting gap. The single-shot method [11] only needs one image and has less sensitivity to vibration noise. Many single-shot methods are proposed. [PERSON] et al. proposed the method of Fourier transform profilometry (FTP) [12; 13] which can reconstruct the 3D shape by only one image. However, due to the filtering process, its measuring accuracy has some disadvantages in the actual measurement process. [PERSON] et al. proposed a 3D measurement method with orthogonal composite grating aided by fringe contrast and background calibration [14]. The contrast and background of the demodulated deformed fringes can be calibrated by these ratio coefficients to achieve the measurement of 3D shape. [PERSON] et al. proposed a computer-generated Moire Profilometry to get the 3D shape of the objects [15; 16]. [PERSON] et al. proposed a single-shot 3D measurement based on hue-height mapping [17]. This method calculated the phase with the hue information of the color fringe pattern pixels to obtain the height distribution. [PERSON] et al. proposed the method of single-shot color phase measuring profilometry (PMP) [18], a single-shot color grating whose major color components are designed as three sinusoidal fringes having a shiftedphase of \(2\pi/3\). When this color composite grating is used to measure objects, the image sensor captures a corresponding color deformed pattern and sends it to the PC to achieve 3D measurement. It may be introduced some errors by the existences of sensitivity differences and color crosstalk [17; 18; 19; 20; 21; 22; 23] among the tricolor channels in the measuring process, which are manifested in the inconsistency of the intensity of the tricolor components of the color deformed pattern. Many scholars have proposed corresponding correction algorithms to solve these problems of the existences of sensitivity differences and color crosstalk. For example, [PERSON] et al. proposed a function of chroma transfer function (CTF) to improve tricolor measuring accuracy. Because the CTF can well calibrate the color crosstalk and the grayscale imbalance, this method successfully reduces the errors caused by the above issues in the fast phase measuring profilometry [24]. [PERSON] et al. proposed the method based on tricolor camera combined with a tricolor filter for the calibration of color crosstalk coefficients and the compensation of gray scale imbalance problems [25; 26]. However, this method is too complex due to additional cameras and filters. [PERSON] et al. proposed a 3D measurement with the color binary grating [27]. This method may avoid the effect of color crosstalk by projecting the binary grating. However, because its binary grating projection requires filtering, its measuring accuracy is still insufficient compared to the sinusoidal grating projection. A 3D measuring method with single-shot quadrature phase-shifting color composite grating projection is proposed. Three quadrature phase-shifting sinusoidal gratings are encoded into tricolor channels, respectively, to compose a frame of color composite grating. This color composite grating is projected obliquely on the object by DLP to get the corresponding color deformed pattern with a camera. Then, by color separating, this color deformed pattern is demodulated as the corresponding three frames of monochrome deformed patterns with the shifted phase of \(\pi/2\).