## 1 Introduction  
With the development of information technology, how to ensure the security of image information becomes an essential point. In image encryption research, optical information processing technology and digital technology have been widely used in image encryption [1; 2; 3; 4; 5; 6; 7]. [PERSON] and [PERSON] proposed double random phase encoding (DRPE) in 1995, which pioneered the field of optical encryption [8]. However, because of the linear symmetry of DRPE technology [9], it is proved to be vulnerable to the known-plaintext attack [10] and chosen-plaintext attack [11]. To improve security, several nonlinear cryptosystems are proposed to improve the weaknesses of traditional symmetric cryptosystems, such as Fresnel domain [12], cylindrical diffraction transform [13; 14; 15], gyrator transform domain [16], and fractional Mellin transform [17]. However, these image encryption methods are usually applied to encrypt one image, which has made it challenging to meet the growing information needs. Recently, more and more scholars have begun to study multi-image encryption [18; 19; 20; 21; 22; 23].  
Multi-image encryption can be divided into two categories according to the encryption process. One of the multi-image encryption technologies is based on cascading [24; 25; 26]. [PERSON] et al. [27] used cascaded fractional Fourier transform to encrypt multiple images. As the number of images increases, the quality of decryption decreases rapidly. [PERSON] et al. [28] proposed a multiple-image encryption method using the cascaded fractional Fourier transform, which cannot get a decrypted image individually from the ciphertext. Hence, the decryption flexibility is poor, and the number of encryption images is severely limited. The other multi-image encryption technology is based on multiplexing, such as space multiplexing [29], region multiplexing [30], wavelength multiplexing [31; 32], and position multiplexing [33]. For instance, [PERSON] et al. [34] proposed a multi-image cryptosystem based on compressive sensing and the DPRE technique. By this method, the space multiplexing method is also used to integrate multiple-image data. [PERSON] et al. [35] came up with a multi-image encryption by using the position multiplexing. Besides, [PERSON] et al. [36] proposed an asymmetric multi-image encryption using the convolution multiplexing. Due to crosstalk issues, this method can only encrypt up to 12 images. Moreover, [PERSON] et al. [37] present a double image encryption using fractional order multiplexing to combine two initial images. Because of the characteristics of multiplexing technology, it can decrypt images individually, which has high decryption flexibility. In the process of information multiplexing, the information of different images occupies the same channel. However, the traditional multiplexing method will lead to data crosstalk and the limited encryption capacity with the number of images increasing.  
In order to solve the problem, a multi-image encryption using spherical diffraction and filtering diffusion is proposed. Owing to the asymmetric characteristics of spherical diffraction, the proposed encryption can effectively resist the phase retrieval attack. Moreover, each image can be decrypted individually with its private key, which has high decryption flexibility. The most significant advantage of this algorithm is the super-large encryption capacity. The encryption capacity is the product of image resolution and grayscale level, which is super-large of \(2^{8}\times\mathrm{m}\times\mathrm{n}\) in case of \(\mathrm{m}\times\mathrm{n}\) points of an image with \(2^{8}\) grayscale level. Numerical simulation results verify the feasibility and effectiveness of the proposed encryption.  
The rest of this paper is organized as follows. Section 2 introduces the spherical diffraction and filtering diffusion technology. Section 3 presents principle of encryption and decryption. Section 4 shows simulation results. Section 5 draws a conclusion.