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.

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.

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.

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.

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.

Phase-only encryption and watermarking based on phase-shifting interferometry.

Generally, the reconstruction of an object image from its diffraction field requires both the amplitude and the phase information of this field. We systematically investigated the effects of using only the real part, the imaginary part, or the phase information of the diffraction field to reconstruct the original image for both the binary and the gray-level images. We show that the phase information can yield a better result of image retrieval than the real or imaginary part and that the recovered image from the phase information is satisfactory especially for binary input.

Correction of wave-front errors caused by the slight tilt of a reference beam in phase-shifting interferometry.

In standard phase-shifting interferometry the reference beam is supposed to be a plane wave exactly normal to the recording plane. A slight tilt of the reference beam, however, may occur in practice, and it will introduce phase distortion for the reconstructed object wave front. The effects of reference wave tilt on the wave reconstruction are analyzed, and a novel method is proposed to correct the errors caused by this tilt.

Digital image encryption and watermarking by phase-shifting interferometry.

A method for both image encryption and watermarking by three-step phase-shifting interferometry is proposed. The image to be hidden is stored in three interferograms and then can be reconstructed by use of one random phase mask, several specific geometric parameters, and a certain algorithm. To further increase the security of the hidden image and confuse unauthorized receivers, images with the same or different content can be added to the interferograms, and these images will have no or only a small effect on the retrieval of the hidden image, owing to the specific property of this algorithm.

Determination of global phase shifts between interferograms by use of an energy-minimum algorithm.

A new algorithm for precise determination of the global phase shift between two interferograms is introduced. First we calculate the frame difference between the first and the second interferogram; the difference is multiplied by a properly chosen test phase factor, and then we implement a two-dimensional Fourier transform of the frame difference and calculate the energy of the first positive (or negative) diffraction order. An iterative approach is used for the test phase to ensure that the minimum energy is obtained, and then the correct phase shift value is found.

Polarization optimization in the interference of four umbrellalike symmetric beams for making three-dimensional periodic microstructures.

A systematic and comprehensive analysis of the interference of four umbrellalike beams (lFUB) is provided based on the reciprocal space theory. The concept of pattern contrast is extended to the case of the IFUB, and it is indicated that a uniform contrast for all the interference terms can be obtained by properly choosing the beam ratio and the polarization of each beam. Different polarization combinations, including linear light and linear light, circular light and circular light, and linear light and circular light, have been discussed for the purpose of maximum uniform contrast.