# A Content Hiding Method for Digital Hologram Using Multiple Fresnel Diffraction
## 1 Introduction  
A hologram is a collection of fringe patterns generated by interference between a reference light wave and an object light wave, in which the 3-dimensional object information is stored as differential phase or amplitude from that of the reference wave [1]. Its digital content (digital hologram, DH) can be obtained by acquiring the fringe patterns with digital equipment, such as a CCD camera, or by calculating them by modeling the interference phenomenon which is called a computer-generated hologram (CGH) [2]. Because even a CGH needs a lot of time for calculations, some proposed a faster hardware implementation of a CGH method [3]. A hologram, either analog or digital, obtained either optically or by calculation, is very highly valued because its generation cost is very high and the information it contains is also very intensive [4]. Thus, there is high demanded to protect the ownership and defend against exposure to a person who is not allowed. The usual method to protect the ownership is digital watermarking [5; 6; 7; 8]. Some transformed the watermark data into a Fourier hologram [5] and some others used the Fresnel transform for watermark data [6] to embed it into the host DH. In another work, the watermark data were transformed to a phase-shift CGH and the result was phase-encoded [7]. In [8] various frequency transforms for 2-dimensional images were applied to the host hologram to embed a real watermark data. To hide the DH content itself from exposing its information to the public, a content encryption method is used and there have been many studies on it. However, here only a few representative ones [9; 10; 11; 12; 13] are mentioned. Some proposed methods to encrypt during hologram acquisition. [PERSON] et al. [9] encrypted the host DH by synthesizing the object beam without reflecting from the object and by phase retarding and random phase masking the reference beam in the interfering process. Its encryption key would be the degree of phase retarding and the random phase mask. [PERSON] et al. [10] also used a random phase mask to distort the host DH and the result was Fresnel diffracted for encryption. The secret keys to this method are the random mask key, the diffraction distance, and the wavelength. In [11] a DH was segmented and each segment was encrypted separately by applying extended fractional Fourier transform twice, each of which had phase modification by subtraction and used three parameters. The two sets of parameters were the encryption keys for the corresponding DH segments. The above three works encrypted the whole DH to hide all the information, but some encrypted a part of the data for the same purpose. [PERSON] et al. [12] proposed a scheme to encrypt in the hologram domain and DCT (discrete cosine transform) and DWT (discrete wavelet transform) transform domain by calculating energy. In the hologram domain, only the two highest bit-planes of a DH were encrypted. In the DWT domain some combination of subbands were encrypted, while in the DCT domain only the DC coefficient(s) was encrypted. Among the three, the one in the DCT domain was the best and it insisted that encrypting only 0.0061% of the DH data (the entire DH was used as the unit of DCT) could hide more than 95% of the total energy. However, for some holograms, the reconstructed image after encryption shows some outlines, although they are quite dim. [PERSON] et al. [13] also used a DWT domain named the DWPT (discrete wavelet packet transform) domain. It is a version of DWT for a subband that includes calculating the energy included. It showed that hiding only 30% of energy was enough to hide all of the information, which was 0.032% of the total hologram data. Our method encrypts a part of DH data to hide all of the information that the DH contains. It can work with any kind of DH, no matter how it is acquired, optically or numerically.