## 1 Introduction  
At the present stage, the development of stereoscopic display technology is restricted because of the accommodation-vergence confliction, to which experts have proposed solutions such as the realization of multi-depth images, light field display technology, and computer holography with multilayer waveguide. However, different from multilayer waveguide display and light field display technology, holography reconstructs the optical information image in the space by the plane wave traveling through a spatial light modulator. For multi-depth image projection, it is still affected by information crosstalk, resulting in worsened stereoscopic perception of image and image blur [1] and limiting of the viewing angle [2]. Moreover, in terms of the presentation and watching of multi-view images (including views and depths), defocus information on the non-reconstruction plane would reduce watching quality, which could be regarded as multi-view holography crosstalk [3]. Recent research teams have proposed many corresponding solutions. For instance, [PERSON]'s team changed the single plane Gerchberg-Saxton (GS) algorithm into dynamic compensation GSA and adjusted weighting factors in amplitude-constrained function in each iterative operation to effectively enhance the different-depth image quality in the multi-plane 2D holographic image display [4]. Different from the optimization of pure 2D images, [PERSON]'s team proposed to stack 3D images with multi-layer images. However, the multi-plane information crosstalk worsened in this regard. Thus, they proposed to first process the wavefront preshaping of each piece of information with the Fresnel zone plate and orthogonality of the random vector. Then, they used orthogonality of the random vector to reduce the crosstalk across the images to stack multi-plane information and create three-dimensional information with low information interference [5]. Although this method could enhance the computing speed, more 2D images were required to realize high-resolution 3D images or dynamic information, which required a considerable increase in the size of the computational information.  
In this study, optical encryption technology is applied to solve the problem of multi-depth and multi-view image crosstalk. Optical encryption, with its uniqueness, is broadly highlighted; e.g., high speed, high parallel, and key application flexibility [6; 7; 8; 9; 10]. After [PERSON]'s team first proposed double-random-phase encryption [6] in 1995, a series of optical image encryption methods were proposed, such as the use of Fractional Fourier transform [7], Fresnel transform [8], discrete wavelet transform [9], and phase contrast [10]. The maturity of optical encryption system development is apparent.  
As a result, based on the previously proposed 3D modified Gerchberg-Saxton algorithm [11; 12; 13], optical encryption is included in this study with random phase as the key to reduce out-of-focus image interference and enhance image watching quality. The phase-locked key-encrypted multi-depth or multi-view image information is capable of realizing the display of multi-view holographic contents by switching decryption keys. The proposed phase encryption technology with angle multiplexing enables multi-view watching and effectively removes out-of-focus image crosstalk. The objective evaluation of the proposed algorithm reveals the significant enhancement of overall image quality.