Lu-Zhong Cai

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.

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.

Experimental demonstrations of the digital correction of complex wave errors caused by arbitrary phase-shift errors in phase-shifting interferometry

In previous papers we proposed a digital method of correcting both amplitude and phase distortions caused by arbitrary phase-shift errors in standard four-frame phase-shifting interferometry (PSI), then extended it to the most generalized PSI, and showed the validity of this technique by computer simulations. Here some new simulations and a series of optical experiments with a plane wave, a spherical wave, and a piece of glass as objects are reported. The experimental results have further proved the correctness of our theoretical analysis and confirmed that our method is able to suppress double-frequency fringes in the retrieved amplitude map and the distortions in the phase map that are introduced by phase-shift errors such as to effectively eliminate the wave ripples and wall-like structures that are present in the unwrapped phase map owing to these errors. In addition, our technique can reduce the density of invalid pixels, which are barriers in phase unwrapping. Therefore the accuracy of both amplitude and phase measurements can be considerably improved.

Phase shift selection for two-step generalized phase-shifting interferometry

A phase shift selection method is proposed to design algorithms immune against phase shift errors in two-step generalized phase-shifting interferometry. A general formula for wavefront reconstruction error is derived, and its specific expressions for two common errors are also given. Calculation results suggest that the proper range of phase shift for general application is about from 0.5 to 2.0 rad for both the fixed and linear phase shift errors. Computer simulations have demonstrated the effectiveness of this phase shift selection method by decreasing the wave reconstruction errors to one-fifth.

Zero phase delay induced by wavefront modulation in photonic crystals

A new mechanism for generation of efficient zero phase delay of electromagnetic wave propagation based on wavefront modulation is investigated in this paper. Both numerical simulations and experiment have demonstrated the zero phase delay behaviors of wave propagation in a two-dimensional triangular photonic crystal. The zero phase delay propagation, independent of the propagating distance, is attributed to an invariable wavefront modulation of photonic crystal in the direction of wave propagation, where the phase velocity is perpendicular to the group velocity with parallel wavefronts (or phasefronts) extending along the direction of energy flow. This effect can be extended to the three-dimensional cases or other artificially engineered materials, and may open a new route to obtain perfect zero-phase-delay propagation for electromagnetic wave instead of using zero-index or zero-averaged-index materials and have significant potential in many applications.

Detection and correction of wavefront errors caused by slight reference tilt in two-step phase-shifting digital holography.

A simple and convenient method, without the need for any additional optical devices and measurements, is suggested to improve the quality of the reconstructed object wavefront in two-step phase-shifting digital holography by decreasing the errors caused by reference beam tilt, which often occurs in practice and subsequently introduces phase distortion in the reconstructed wave. The effects of reference beam tilt in two-step generalized interferometry is analyzed theoretically, showing that this tilt incurs no error either on the extracted phase shift or on the retrieved real object wave amplitude on the recording plane, but causes great deformation of the recovered object wavefront. A corresponding error detection and correction approach is proposed, and the formulas to calculate the tilt angle and correct the wavefront are deduced. A series of computer simulations to find and remove the wavefront errors caused by reference beam tilt demonstrate the effectiveness of this method.

Band gap analysis and holographic design of 3-fold hybrid triangular photonic crystals of irregular columns with large full band gaps

A new kind of two-dimensional 3-fold photonic crystal (PhC) conforming to the hybrid triangular configuration formed by holographic lithography (HL) is proposed, and the relation between its photonic band gap properties and its specific holographic design is systematically investigated. This structure can be conveniently produced using a multiple-beam dual-exposure technique. In addition to its high complete relative band gap, namely a 22.1% gap/mid-gap ratio for the dielectric constant contrast 13.6:1 in optimized design, it has very large tolerance on the system parameters and fabrication conditions and requires a quite low dielectric constant contrast to open complete band gaps. This study reveals that the band gaps of PhCs made by HL may be widened by introducing irregularity in the columns and lowering the symmetry of the structure. Light propagation in this structure is also simulated. The results show that a transverse electric (TE) or transverse magnetic (TM) band gap can be obtained in this structure even with a very low dielectric constant contrast (e.g. 2.56:1), and this fact makes it very suitable for low-index waveguides.

Six-fold hybrid photonic crystal formed holographically with full band gap for low refractive index

A novel kind of two-dimensional (2D) photonic crystals conforming to the 6-fold hybrid triangular configuration formed by holographic lithography is proposed. The relations between their photonic band gap properties and their specific holographic designs for the normal structures are systematically investigated. Computations show that this normal structure has complete band gaps over wide ranges of system parameters, and the minimum dielectric constant required to open a complete band gap with Δω/ω>1% is as low as 3.8, which is the lowest compared with the results of 2D periodic photonic crystals ever reported. The latter fact is also verified by light propagation simulation in waveguide. This work may make holographic photonic crystals promising for application in the range of optical devices and provide a guideline for their design and experimental fabrication.

Analysis of structure and band gap evolution of photonic crystals formed holographically by symmetric umbrella configuration with varying apex angles

A theoretical investigation of the possible three-dimensional photonic crystal structures that can be created by holographic interference using the symmetric umbrella configuration of four plane waves is made. The irreducible Brillouin zones and the photonic band gap (PBG) properties of the possible resulting crystal lattices when the apex angle is varied from 10° to nearly 180° are investigated. Our calculations indicate that a complete PBG can exist in the resulting structure in a very wide range of the apex angle, from 33° to 135° except a narrow region at 49° to 55°. The study has also shown that a larger band gap may be obtained in a structure that slightly deviates from the standard cubic lattice and that the optimum exposure threshold or optimum filling ratio of the dielectric material is roughly a step-like function of apex angle. These results may give a general outlook on this method and relax some requirements in experiments.

Anomalous refractive effects in photonic crystals formed by holographic lithography

Anomalous refractive effects of PhCs formed by holographic lithography can be modulated more easily than regular PhCs. The unique features extend the possibly guiding ability of holographic PCW and promising potential in optical application.