# Asymmetric Encryption of Invisible Structured Light 3D Imaging
## 1 Introduction  
Structured light 3D imaging technology has been studied since the 1950s [1; 2; 3; 4; 5]. [PERSON] et al. proposed phase measurement profilometry to obtain phase information by projecting grating patterns with certain phase differences onto an object [6]. Following decades of continuous development, a variety of structured light 3D imaging technologies have emerged. Structured light 3D imaging technology consists of the point structured light, line structured light method [7; 8; 9], and surface structured light method [10]. Among them, the surface structured light method is used more often and is therefore discussed. [PERSON] et al. proposed an improved stepped phase coded fringe and a new phase unwrapping algorithm based on the order of the shifted fringe [11]. The main idea of this method is to set the width ratio between each step phase of the sinusoidal fringe and phase coded fringe to 1n. The fringe order retrieved from the phase coded fringe can be multiplied by the offset itself to assist the phase unwrapping process. This method can ensure high measurement accuracy and allow the measurement of isolated objects with complex shapes. [PERSON] et al. proposed a new technology, Fourier transform profilometry (FTP), which is suitable for automatic measurement of three-dimensional object shapes [12]. Because FTP does not use moire contour technology, it does not have the drawbacks related to moire terrain. The advantage of FTP is that it can detect the height changes more accurately than moire contour technology, and it is completely free of the unwanted stray moire fringes generated by the high-order harmonic component of the grating pattern. [PERSON] proposed the windowed Fourier transform to measure the phase and phase derivative using the two-dimensional windowed Fourier transform, which can perform better fringe demodulation and fringe pattern filtering [13; 14]. Among other studies, [PERSON] et al. proposed a 3D reconstruction model based on the parallel axis structured light system [15]. Compared with the traditional structured light system, the new system includes a perspective projection unit and a telecentric imagingunit that can recover the height distribution of the object well with high accuracy. [PERSON] et al. proposed a three-dimensional vision system combining structured light and the shadow shape [16]. This method is suitable for objects that have high motion frequencies. For this technique, the projected structured light vision system uses sinusoidal fringe coding to extract the shape from the shadow, which is can obtain the high-definition gradient information of the weak fluctuation of the weld surface. it is worth noting that phase-shifting is a cost-effective method because of its simple equipment and high measurement accuracy. [PERSON] et al. used this method of combining invisible structured light and phase-shifting 3D imaging technology, where two orthogonal polarized beams were projected onto the object surface without interference fringes [17]. The synchronous phase shift detection technology was then used to detect the structured light fringes to obtain the shape information of a three-dimensional object. The results showed that this method can effectively suppress the background light and greatly reduce the measurement error. Various image encryption methods have been developed based on the classical Fourier transform [18]. In the public-private key cryptosystem, each user has a pair of keys: one is published publicly (public key) and the other is stored in a secure location (private key) [19; 20; 21]. [PERSON] et al. proposed a method of transmitting the double random phase encryption key and encrypted image at the same time [22]. This method takes advantage of the fact that only part of the encrypted image can obtain acceptable decryption results in the decryption process with an appropriate encryption strength.