X. X. Shen

Two-step phase-shifting interferometry and its application in image encryption

Conventional phase-shifting interferometry (PSI) needs at least three interferograms. A novel algorithm of two-step PSI, with an arbitrary known phase step, by which a complex object field can be reconstructed with only two interferograms is proposed. This algorithm is then applied to an information security system based on double random-phase encoding in the Fresnel domain. The feasibility of this method and its robustness against occlusion and additional noise attacks are verified by computer simulations. This approach can considerably improve the efficiency of data transmission and is very suitable for Internet use.

Security enhancement of double-random phase encryption by amplitude modulation

Conventional double-random phase encoding is vulnerable to a chosen or known plaintext attack owing to the linearity of the system. We introduce a technique to break down this linearity with an undercover amplitude modulation in the encryption scheme. As an additional key, this operation can significantly enhance the security of the system. A series of computer simulations have shown the effectiveness of this method and its resistance against the known plaintext attack. The design and parameter choice of the amplitude modulator is also discussed.

Simple direct extraction of unknown phase shift and wavefront reconstruction in generalized phase-shifting interferometry: algorithm and experiments

An algorithm to extract the arbitrary unknown phase shift and then reconstruct the complex object wave in generalized phase-shifting interferometry (GPSI) without the iteration process and measurement of object wave intensity is proposed. This method can be used for GPSI of any frame number >or=2. Both computer simulations with smooth and diffusing object surfaces and optical experiments have verified the effectiveness of this method over a wide range of phase shifts with very satisfactory results.

Information security system by iterative multiple-phase retrieval and pixel random permutation

A novel information security system based on multiple-phase retrieval by an iterative Fresnel-transform algorithm and pixel random permutation (PRP) technique is proposed. In this method a series of phase masks cascaded in free space are employed and the phase distributions of all the masks are adjusted simultaneously in each iteration. It can achieve faster convergence and better quality of the recovered image compared with double-phase encoding and a similar approach in the spatial-frequency domain with the same number of phase masks and can provide a higher degree of freedom in key space with more geometric parameters as supplementary keys. Furthermore, the security level of this method is greatly improved by the introduction of the PRP technique. The feasibility of this method and its robustness against occlusion and additional noise attacks are verified by computer simulations. The performance of this technique for different numbers of phase masks and quantized phase levels is investigated systematically with the correlation coefficient and mean square error as convergence criterions.

Generalized phase-shifting interferometry with arbitrary unknown phase shifts: Direct wave-front reconstruction by blind phase shift extraction and its experimental verification

A simple wave-front reconstruction method by generalized phase-shifting interferometry (PSI) with arbitrary unknown phase shift between 0 and π for two adjacent frames is proposed. In this method the unknown phase shifts are extracted by a noniterative algorithm with the use of the interferograms and the intensities of object and reference waves, and then the original object field can be further obtained. This method is applicable for generalized PSI of any frame number N (N⩾2) and for both the amplitude and phase objects. Its effectiveness and accuracy are verified by both the computer simulations and optical experiments.

Fast blind extraction of arbitrary unknown phase shifts by an iterative tangent approach in generalized phase-shifting interferometry

A novel fast convergent algorithm to extract arbitrary unknown phase shifts in generalized phase-shifting interferometry (PSI) is proposed and verified by a series of computer simulations. In this algorithm an error function is introduced and then the unknown phase shifts are found by an iterative tangent approach. In combination with the statistical method, this algorithm can give the most exact results in the fewest iteration steps. It can be used for generalized PSI of arbitrary frames for both smooth and diffusing objects and can usually reach the exact phase shifts with only four or five iterations for three- or four-frame PSI.

Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain

A novel hierarchical image encryption system based on cascaded multiple-phase retrieval by an iterative Fresnel-transform algorithm is proposed. In this method a series of phase masks cascaded in free space is employed to retrieve different target hidden images in their corresponding hierarchical levels. It can realize different levels of accessibility to the secret data for different authority levels with the same system, and the higher level authority can get access to more hidden images. This approach can achieve fast convergence and high quality of the recovered images without any recognizable cross-talk noise or distortion, and the security level of this system is further enhanced by the use of a series of supplemental keys such as the orders of cascaded phase masks and the geometrical parameters in addition to all the iterated phase masks as principal keys. The feasibility of this method and its unique features are verified and analysed by computer simulations.

Cross-talk-free double-image encryption and watermarking with amplitude-phase separate modulations

A novel digital method of double-image encryption and watermarking by constructing a complex field with one non-negative image as its amplitude and another as its phase and then encrypting this complex field by means of digital optics, such as phase-shifting interferometry with double-random phase encoding, is proposed. Since no direct addition of the information of two hidden images is employed in the encryption process, each image can be perfectly retrieved without cross-talk caused by the existence of the other. The feasibility of this method and its robustness against occlusion and additional noise from watermarked images with different weighting factors are verified by computer simulations. The signal-to-noise ratio and mean square error of the retrieved images are calculated for different distortions. This technique can considerably improve the efficiency of data transmission, and it is particularly suitable for the image transmission via the Internet.

Digital color image watermarking based on phase-shifting interferometry and neighboring pixel value subtraction algorithm in the discrete-cosine-transform domain

A novel single-channel color-image watermarking with digital-optics means based on phase-shifting interferometry (PSI) and a neighboring pixel value subtraction algorithm in the discrete-cosine-transform (DCT) domain is proposed. The converted two-dimensional indexed image matrix from an original color image is encrypted to four interferograms by a PSI and double random-phase encoding technique. Then the interferograms are embedded in one chosen channel of an enlarged color host image in the DCT domain. The hidden color image can be retrieved by DCT, the improved neighboring pixel value subtraction algorithm, an inverse encryption process, and color image format conversion. The feasibility of this method and its robustness against some types of distortion and attacks from the superposed image with different weighting factors are verified and analyzed by computer simulations. This approach can avoid the cross-talk noise due to direct information superposition, enhance the imperceptibility of hidden data, and improve the efficiency of data transmission.

Correction of wavefront reconstruction errors caused by light source intensity instability in phase-shifting interferometry

In the recording process of phase-shifting interferometry, intensity fluctuation caused by light source instability may occur and then introduce amplitude and phase errors to the reconstructed object wavefront. A simple direct algorithm of digital data processing to correct these errors is proposed and satisfactorily verified by both computer simulations and optical experiments. This method can work without specific knowledge of the source intensity fluctuation, and it reduces both the amplitude and phase errors of the reconstructed wavefront by about two orders of magnitude in computer simulations.