Multiple image encryption using an aperture-modulated optical system

A multiple image cryptosystem based on different apertures in an optical set-up under a holographic arrangement is proposed. The system is a security architecture that uses different pupil aperture mask in the encoding lens to encrypt different images. Based on this approach multiple encryption is achieved by changing the pupil aperture arrangement of the optical system among exposures. In addition to the classical speckle phase mask, the geometrical parameters characterizing the apertures are introduced to increase the system security. Even when an illegal user steals the speckle phase mask, the system cannot be broken into without the correct pupil geometrical parameters. The experimental set-up is based on a volume photorefractive BSO crystal as storing device. Information retrieval is done via a phase conjugation operation. We also have to stress that the multiple storage under this scheme, is only possible with the help of the aperture mask. Simulation and experimental results are further introduced to verify the proposed method.     

Triple Encrypted Holographic Storage and Digital Holographic System

We propose a triple encrypted holographic memory containing a digital holographic system. The original image is encrypted using double random phase encryption and stored in a LiNbO3：Fe crystal with shift-multiplexing. Both the reference beams of the memory and the digital holographic system are random phase encoded. We theoretically and experimentally demonstrate the encryption and decryption of multiple images and the results show high quality and good fault tolerance. The total key length of this system is larger than 4.7×10^33.     

Multiplexing encrypted data by using polarized light

We investigate the feasibility of multiplexing, employing polarized light, a set of security encrypted data. The encryption approach is based on the double random pure-phase enciphering method. Phase conjugation operation is conducted in the reconstruction stage with the aid of a photorefractive crystal which stores the encrypted information. When storing each encrypted image, a polarization change is introduced in the system. This induces decorrelation on the speckle patterns inside the storing medium. We apply this approach for multiple image encryption. We show experimental results that confirm our approach.     

Code retrieval via undercover multiplexing

The purpose of this research is to develop an undercover multiplexing technique to give additional protection for optical information encryption. We employ the double random phase mask as our basic optical encryption system. The holographic storage medium of choice is a photorefractive crystal. To achieve the multiplexing we use the aperture size of the pupil in the optical system, as it governs the speckle size. We introduce such variation in order to produce a decorrelation between two consecutively stored speckle patterns. Each stored speckle pattern is associated to an input encrypted image, thus producing a multiplexing of the encrypted information. We implement this operation without altering the setup architecture and the random phase masks. This multiplexing is our undercover operation to encipher a true code behind a fake code. Under this approach, the user can only recover the bulk information stored in the volume hologram. However, he cannot recover the true code without the additional information on the pupil size key, even if accessed in position of the original decoding mask.     

Double image encryption based on iterative fractional Fourier transform

We present an image encryption algorithm to simultaneously encrypt two images into a single one as the amplitudes of fractional Fourier transform with different orders. From the encrypted image we can get two original images independently by fractional Fourier transforms with two different fractional orders. This algorithm can be independent of additional random phases as the encryption/decryption keys. Numerical results are given to analyze the capability of this proposed method. A possible extension to multi-image encryption with a fractional order multiplexing scheme has also been given.     

Signal and reference wave dually encrypted holographic memory with shift multiplexing

We propose a secure holographic storage system with signal and reference waves dually encrypted for shift multiplexing. Two random phase masks are used to encrypt the images in the input and the Fourier planes. The reference beam is phase encoded by a fiber optic faceplate. The encrypted data is stored in a LiNbO₃:Fe crystal and decrypted during the readout process. We experimentally demonstrate encryption and decryption of multiple images and the results show high quality and good fault tolerance.     

Encrypted optical memory system using three-dimensional keys in the Fresnel domain

An encrypted optical memory system using double random phase codes in the Fresnel domain is proposed. In this system, two random phase codes and their positions form three-dimensional keys for encryption of images and are used as keys to recover the original data. The third dimension is the positions of the codes, which can have as many as three degrees of freedom. Original images encrypted by use of the two phase codes located in the Fresnel domain are stored holographically in a photorefractive material. We demonstrate in preliminary experiments encryption and decryption of optical memory in a LiNbO(3) :Fe photorefractive crystal by use of angular multiplexing.     

Deterministic Phase Encoded Holographic Data Storage Using Lenticular Lens Array

This work presents a novel optical holographic encrypted data storage approach based on a phase encoding multiplexed scheme. In the proposed data storage scheme, patterns to be encrypted are stored holographically in a photorefractive LiNbO₃:Fe crystal using a lenticular lens array (LLA) sheet phase-encoded multiplexing. Experimental results reveal that rotating an LLA placed as a phase modulator in the path of the reference beam is a simple but effective method of increasing the phase addresses for holographic memory in a crystal. Combining this rotational multiplexing with two-axis rotating multiplexing provides further data storage and data encryption capacity.     

A half-blind color image hiding and encryption method in fractional Fourier domains

We have proposed a new technique for digital image encryption and hiding based on fractional Fourier transforms with double random phases. An original hidden image is encrypted two times and the keys are increased to strengthen information protection. Color image hiding and encryption with wavelength multiplexing is proposed by embedding and encryption in R, G and B three channels. The robustness against occlusion attacks and noise attacks are analyzed. And computer simulations are presented with the corresponding results.     

Optical holographic memory using angular-rotationally phase-coded multiplexing in a LiNbO3:Fe crystal

We propose a new holographic memory scheme based on random-phase-coded multiplexing in a photorefractive LiNbO₃:Fe crystal. Experimental results show that rotating a diffuser placed as a random-phase modulator in the path of the reference beam provides a simple yet effective method of increasing the holographic storage capabilities of the crystal. Combining this rotational multiplexing with angular multiplexing offers further data-storage possibilities. The advantage of using post-image versus pre-image phase modulation of the object beam is demonstrated. Received: 15 August 2000 / Published online: 10 January 2001     

Multiple images encryption based on Fourier transform hologram

A new optical encryption method is proposed in this paper to achieve multiple images encryption. We introduce reference waves with different incident angles and random amplitude masks into a Fourier transform hologram configuration to encrypt multiple images. In the encryption procedure, different random amplitude masks (RAMs) which are placed into the reference arm vertically admit the multiplexing capability. When decrypting one of the original images, reference wave with the same incident angle as encrypting the target image is used to illuminate the encrypted hologram with the insertion of random amplitude mask whose transmissivity is reciprocal of that of the encrypting random amplitude mask in the reference arm. We also simulate and analyze the influence of partly wrong decrypting key on the decrypted results. Numerical simulation proves that the proposed encryption method is valid and of high security level.     

Multichanneled puzzle-like encryption

In order to increase data security transmission we propose a multichanneled puzzle-like encryption method. The basic principle relies on the input information decomposition, in the same way as the pieces of a puzzle. Each decomposed part of the input object is encrypted separately in a 4f double random phase mask architecture, by setting the optical parameters in a determined status. Each parameter set defines a channel. In order to retrieve the whole information it is necessary to properly decrypt and compose all channels. Computer simulations that confirm our proposal are presented.     

Securing multiplexed information by in-plane rotation of random phase diffusers constituting a sandwich diffuser placed in the Fourier plane of a double random phase encoding system

We propose the encryption and multiplexing of two-dimensional input images by rotating the constituent diffusers of a sandwich random phase diffuser kept in the Fourier plane of a double random phase encoding system. Successive recording of encrypted images is done by taking the input images one by one. The results of multiplexing in encryption and decryption due to different sets of rotation of one or both of the random constituent phase masks have been presented. The use of an aperture system in addition to the rotation of one or both of the random phase masks enhances the multiplexing capability and security of the system avoiding the generation of cross-talk images at the time of decryption. Simulation results are presented in support of the proposed techniques. The decrypted images obtained from a multiplexed encrypted image have been recorded successfully. Mean square-error (MSE) and signal-to-noise ratio (SNR) values as a function of the number of multiplexed images have been calculated.     

Holographic digital data storage using phase-modulated pixels

We propose and demonstrate the use of phase images for holographic data storage. Use of phase images as input leads to uniform diffraction efficiency of multiplexed data pages. Use of binary phase-based data pages with 0 and π phase changes produces uniform spectral distribution at the Fourier plane. This in turn facilitates better recording of higher spatial frequencies. We experimentally demonstrate a phase-based holographic data storage system using shift multiplexing in a Fe:LiNbO₃ crystal, and use it for associative retrieval. Preliminary studies indicate high discrimination capabilities of phase-based holographic data storage system over the amplitude-based system in a content-addressable memory.     

Generalization of Carré equation

The present work offers new equations for phase evaluation in measurements. Several phase shifting equations with an arbitrary but constant phase shift between captured intensity signs are proposed. The equations are similarly derived as the so-called Carré equation. The idea is to develop a generalization of Carré equation that is not restricted to four images. Errors and random noise in the images cannot be eliminated, but the uncertainty due to their effects can be reduced by increasing the number of observations. An experimental analysis of the mistakes of the technique was made, as well as a detailed analysis of mistakes of the measurement. The advantages of the proposed equation are its precision in the measures taken, speed of processing and the immunity to noise in signs and images.     

Digital encryption with undercover multiplexing by scaling the encoding mask

We introduce the technique to get the undercover multiplexing of a set of encrypted data. We base the general encryption approach on the double-random phase encoding method. We made the encoding phase masks with scaled versions of a master speckle pattern. A fake object is encrypted using a master mask made with the master speckle pattern. Each subsequent object to be hidden is associated to a suitable different scaled version of the original master mask. We apply the term suitable referring to avoid a possible cross-talk in the final decrypted images. All encrypted data are multiplexed to form a single message. This operation enables the true information undercover. We openly send this undercover message along with the master mask. Via separated private channels, we send the information on the actual scaling for each encrypting mask to the authorized users. Unauthorized users attempting to recover the information by using the master mask alone, get the fake object. During decryption of the multiplexed message, we only reconstruct the object that matches the predetermined scaled version of the master mask used to encode it. We show results that confirm our approach.     

1000幅数字图像的晶体体全息存储与恢复

利用Ｆｅ：ＬｉＮｂＯ３光折变晶体和角度多重方法，在晶体人的一个公共体积内实现了１０００多幅数字图像的存储与重建。由于同时采用差分编码与纠错编码，因而系统抗噪能力细，误码率低。整个同计算机控制，自动化程度高。     

Color holographic display based on azo-dye-doped liquid crystal (Invited Paper)

A multiplexed holographic display video has been achieved by using a passive azo-dye-doped liquid crystal （LC） cell. Holograms formed in this cell can be refreshed in the order of several milliseconds. By angular multiplexing technique, dynamically multiplexed holographic videos are realized. Moreover, the reconstructed RGB images are merged into a color image, which illustrates the possibility of a color holographic three-dimensional （3D） display by holographic multiplexing of the LC cell.     

Deterministic phase encoding encryption in single shot digital holography

We demonstrate a deterministic phase-encoded encryption system based on the digital holography and adopted a lenticular lens array (LLA) sheet as a phase modulator. In the proposed scheme the holographic patterns of encrypted images are captured digitally by a digital CCD. This work also adopt a novel, simple and effective technique that is used to suppress numerically the major blurring caused by the zero-order image in the numerical reconstruction. The decryption key is acquired as a digital hologram, called the key hologram. Therefore, the retrieval of the original information can be achieved by multiplying the encrypted hologram with a numerical generated phase-encoded wave. The storage and transmission of all holograms can be carried out by all-digital means. Simulation and experimental results demonstrate that the proposed approach can be operated in single procedure only and represent the satisfactory decrypted image. Finally, rotating and shifting the LLA is applied to investigate the tolerance of decryption to demonstrate the feasibility in the holographic encryption, as well as can also be used to provide the higher security.     

Two-time scale subordination in physical processes with long-term memory

We describe dynamical processes in continuous media with a long-term memory. Our consideration is based on a stochastic subordination idea and concerns two physical examples in detail. First we study a temporal evolution of the species concentration in a trapping reaction in which a diffusing reactant is surrounded by a sea of randomly moving traps. The analysis uses the random-variable formalism of anomalous diffusive processes. We find that the empirical trapping-reaction law, according to which the reactant concentration decreases in time as a product of an exponential and a stretched exponential function, can be explained by a two-time scale subordination of random processes. Another example is connected with a state equation for continuous media with memory. If the pressure and the density of a medium are subordinated in two different random processes, then the ordinary state equation becomes fractional with two-time scales. This allows one to arrive at the Bagley-Torvik type of state equation.