# Optical Hyperspectral Image Cryptosystem Based on Affine Transform and Fractional Fourier Transform
## 1 Introduction  
With the rapid development of modern communication technology, information security has attracted more and more attention from researchers around the world. Since [PERSON] and [PERSON] proposed double random phase encoding (DRPE) in 1995 [1], a great number of concerns have been raised for this novel optical security technique. In the past decade, many encryption schemes based on different optical systems have been reported [2; 3; 4; 5; 6; 7; 8]. In particular, multiple-image encryption raises the attention of many researchers in the optical encryption area and many algorithms have been proposed [9; 10; 11; 12; 13]. Referring to [13], the cascaded interference structure and vector stochastic decomposition algorithm are introduced into a multiple-image encryption cryptosystem, in which the silhouette problem in the traditional two-beam interference cryptosystem can be removed successfully. Moreover, the cryptosystem for multispectral and hyperspectral image has also been studied in recent years [14; 15; 16]. In [15], by using the 3D Arnold transform, the hyperspectral image is extended from the spatial domain into the spectrum domain in an optical gyrator domain. The robustness of this cryptosystem is improved since secret data in the spectrum domain is impossible to retrieve from the spatial domain. Recently, an optical encryption algorithm for multiple spectral image was presented [17]. To enhance the security, the hyperspectral image was converted into binary data and improved Chirikov mapping was designed to scramble the intermediate data. The feasibility and robustness of the encryption algorithm was verified. However, the large calculation limited the encryption speed in practical implementation.  
Hyperspectral data contains rich information in both the spatial and spectral domains. With the help of spectral information, researchers are able to identify and distinguish the material of the object in the data. This special characteristic is useful in many military and civilian applications involved in the detection of the target or activity, like military vehicles or vehicle tracks [18]. Besides, the ability of differentiating materials in recycling waste has made spectral information become a research focus in the field of laboratory measurements in medical diagnosis and chemical imaging [19]. In this paper, we propose an optical cryptosystem for hyperspectral data in fractional Fourier transform (FrFT) domain. Firstly, the original hyperspectral cube is divided into various independent bands before the encryption. Then, an affine transform is designed to scramble each pair of bands in the original data and then these two images become the real and imaginary part of a complex mask. Subsequently, the converted data are encoded and transformed into the optical FrFT transform. The parameters used in FrFT serve as the extra keys of the encryption. Finally, the discrete cosine transform (DCT) is considered to improve the security of the keys. One of the novelties of the proposed scheme is that we expand the ordinary image into hyperspectral image cryptosystem, which encrypts both the spatial and spectrum information synchronously. Moreover, compared to the encryption schemed presented in [17], the proposed method reduces the calculation and storage space of the encrypted data. Besides, the optical setup of FrFT is more simple and feasible compared to the gyrator transform.  
The rest of the paper is summarized as follows. In Section 2, the intact cryptosystem is introduced in detail. Various numerical experiment results are given to test the validity of the scheme in Section 3. In the final section, the discussion and conclusions are given.