## 1 Introduction  
Due to its advantages of non-contact measurement, high speed and high accuracy, optical 3D shape measurement profilometry has been widely applied in various fields, including but not limited to 3D sensing, machine vision, mechanical engineering, industry monitoring, etc. [1, 2] Several profilometry methods based on structured light projection have been extensively studied. The two most representative technologies are phase-measuring profilometry (PMP) and Fourier transform profilometry (FTP). Originating from laser interferometry, PMP is a temporal domain phase measurement technology [3, 4]. The initial phase is calculated by multiple fringe patterns with a fixed phase difference. To solve the initial phase of the measured object, spatial information of full-field phase-shifting fringe patterns and temporal information in a period are obtained by scanning along the temporal axis. The phase calculation on each pixel is independently performed and the phase value of any point is only related to its intensity distribution. Hence, PMP has the advantages of high measurement accuracy and high resolution and is widely used in the field of 3D optical metrology. Although at least three modulated fringes are required to reconstruct the 3D shape of one measured object, it is usually applied in static scene measurement. Advantages of FTP include the use of a single-shot measurement, full-field analysis and being easy to use, which have resulted in FTP being widely applied in dynamic scene measurement [5; 6; 7]. However, FTP needs to perform operations of spatial Fourier transform, band-pass filtering and spatial inverse Fourier transform on the fringe patterns. The band-passing filtering operation on the fundamental frequency component would lose high-frequency components which contain the detailed information of the measured object, and it would result in unavoidable errors. The reconstructed object looks smoother than the measured object. Therefore, when considering a measured complex object, the measurement accuracy of traditional FTP is not as good as that of PMP. At present, dynamic 3D shape measurement systems based on structured light techniques are limited by the projection speed of digital projectors. Existing digital projectors are mainly silicon-based projection devices--such as LCD or DLP projectors--which have high projection speed, high precision and high flexibility. Although affected by the digital projector's resolution and nonlinearity, complicated nonlinear correction is required for most occasions. In 2011, [PERSON] et al. developed a set of high-speed sinusoidal structured light illumination systems [8]. A series of binary gratings with a fixed phase-shifting interval were placed in a rotating metal wheel. [PERSON] et al. achieved a binary pattern projection at the rate of 200 Hz. However, system error corrections were required to obtain accurate phase shift and the fringe pattern could not be flexibly changed. Additionally, it was also limited by machining accuracy and synchronized control. In 2014, [PERSON] et al. developed an array projector using LED arrays to project binary patterns [9]. Since LEDs can be turned on or off at an ultra-high speed, high-speed projection of aperiodic sinusoidal fringes were obtained by switching the LED array in sequence. [PERSON] et al. achieved a projection frame rate of 3 kHz, and approximately 330 Hz 3D reconstruction rate. However, the production of the projector was complex, and its radiant flux was limited by the power of LED. In 2016, [PERSON] et al. developed a Goes Before Optics (GOBO) projector with high-power and high-speed projection [10]. They achieved a high radiant flux of 250 W, and a 3D frame of 1333 Hz. While, the GOBO wheel's exact rotational position was unknown, two cameras were required for 3D measurement. In 2018, [PERSON]'s experiment was improved by [PERSON] et al. [11; 12] whose measurement system consisted of a mechanical projector and two cameras.