Y. R. Wang

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.

All fourteen Bravais lattices can be formed by interference of four noncoplanar beams

The interference of four noncoplanar beams (IFNB) is analyzed. It is shown that all 14 Bravais lattices can be formed by a holographic method of IFNB. The relationship among the three basis vectors of the lattice that are to be produced, the required wavelength, and the geometric arrangement of the four beams is derived. This analysis may lay the foundation for fabrication of three-dimensional photonic crystals by holographic lithography.

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.

Formation of three-dimensional periodic microstructures by interference of four noncoplanar beams

A newly reported method of making three-dimensional microstructures or photonic crystals by holographic lithography has some obvious advantages over other techniques with the same purpose. A systematic and comprehensive analysis of interference of four noncoplanar beams (IFNB) is provided. It shows that all 14 Bravais lattices can be formed by means of IFNB and gives explicit relationships between each lattice and the corresponding recording geometry. The concept of pattern contrast is extended to the case of IFNB, and it is indicated that a uniform contrast for each interference term can be obtained by properly choosing the beam ratio and polarization. A calculation algorithm is then developed to optimize the direction of polarization of each beam to ensure maximum uniform contrast. These results, verified by computer simulations, may lay a theoretical foundation for fabrication of photonic crystals with the approach of IFNB.

Formation of a microfiber bundle by interference of three noncoplanar beams.

A systematic analysis of interference of three noncoplanar plane waves with identical frequency is provided. This analysis shows that a fiber bundle with spacing of the order of the wavelength, which one may conveniently control by changing the recording geometry, can be formed by this means. The relation between the incident light-wave vectors and the resultant pattern is analyzed. The concept of uniform contrast for an interference pattern is introduced, and the polarization optimization approach for each beam that ensures maximum uniform contrast for each beam is also given.

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.

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.

Direct phase shift extraction and wavefront reconstruction in two-step generalized phase-shifting interferometry

A direct phase shift extraction and wavefront reconstruction method in two-step generalized phase-shifting interferometry (GPSI) with arbitrary unknown phase shift is proposed. In this method the unknown phase shift ? can be extracted by a determinate formula directly without iteration or additional judgment of its correct value from two or more phase shift solutions as necessary before. By an appropriate formula of GPSI the complex object field in the recording plane can be calculated and then the object wavefront in the original object plane obtained. This method is applicable for GPSI of any frame number K?2 and for both the amplitude and phase objects. Computer simulations have shown that the phase shift extraction errors are below 0.01?rad in a wide range of 0.4?rad<?<2.6?rad and the computation time is greatly reduced by a factor of about 20 compared with the previous method. The effectiveness and accuracy of this method are also verified by optical experiments.

Wavefront reconstruction and three-dimensional shape measurement by two-step dc-term-suppressed phase-shifted intensities

A wavefront reconstruction and three-dimensional (3-D) shape measurement method by a two-step phase-shifting algorithm with arbitrary phase shift in (0,pi) is proposed. In this method, only two phase-shifted intensities, with the removal of the dc term by an averaging technique in spatial domain or low-pass filter operation in the frequency domain, are needed, and the other additional measurements are no longer required. The simulation for an irregular wavefront has shown the feasibility, and the optical experiment for a 3-D face mask in the case of a sinusoidal fringe projection system has illustrated the validity of the proposed method.