Multiple-image encryption by two-step phase-shifting interferometry and spatial multiplexing of smooth compressed signal

A multiple-image encryption method based on two-step phase-shifting interferometry(PSI) and spatial multiplexing of a smooth compressed signal is proposed. In the encoding and encryption process, with the help of four index matrices to store original pixel positions, all the pixels of four secret images are firstly reordered in an ascending order; then, the four reordered images are transformed by five-order Haar wavelet transform and performed sparseness operation. After Arnold transform and pixels sampling operation, one combined image can be grouped with the aid of compressive sensing(CS)and spatial multiplexing techniques. Finally, putting the combined image at the input plane of the PSI encryption scheme,only two interferograms ciphertexts can be obtained. During the decoding and decryption, utilizing all the secret key groups and index matrices keys, all the original secret images can be successfully decrypted by a wave-front retrieval algorithm of two-step PSI, spatial de-multiplexing, inverse Arnold transform, inverse discrete wavelet transform, and pixels reordering operation.     

Full-phase image encryption by two-step phase-shifting interferometry

We have proposed a full-phase image encryption method based on double random-phase encoding in Fresnel domain and pixel random permutation (PRP) technique with the use of two-step phase-shifting interferometry (PSI) we reported recently, and verified the effectiveness of this method and its robustness against occlusion and noise attacks by a series of numerical simulations. Comparing with other similar methods, this approach can decrease the number of the interferograms to be delivered from at least three needed in ordinary PSI to only two, give much better performance of image reconstruction than amplitude-based encryption, and provide much higher security level. This method is usable for both the gray-level images and binary images, and usually the latter will lead to better results.     

Phase Measurement Algorithm without Phase unwrapping Problem for Phase stepping interferometry

１ＩｎｔｒｏｄｕｃｔｉｏｎＰｈａｓｅｓｔｅｐｐｉｎｇｉｎｔｅｒｆｅｒｏｍｅｔｒｙｈａｓｂｅｅｎｅｘｔｅｎｓｉｖｅｌｙａｐｐｌｉｅｄｉｎｍａｎｙａｓｐｅｃｔｓ．Ｃｏｎｖｅｎｔｉｏｎａｌｐｈａｓｅｕｎｗｒａｐｐｉｎｇｉｓｉｍｐｌｅｍｅｎｔｅｄｂｙｔｈ...     

基于主元分析的随机相移算法

将统计理论中的主元分析应用到干涉条纹分析中,提出一种基于主元分析的随机相移算法。该算法先将多帧条纹数据分解成不相关的主元成分,然后从主元成分中提取2维相位信息。数值模拟结果表明:该算法不需要迭代运算就能从4帧完全随机相移干涉图中有效提取相位信息,运算时间少,精度高。实验结果表明主元分析相移算法比现有迭代相移算法更适合于随机相移干涉图分析。     

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.     

Experimental requirement of the error-compensating five-frame interferogram-collecting sequence used in phase-shifting interferometry

Digital phase-shifting interferometry (PSI), a technique widely used in optical testing, requires interferograms collected at optical phase differences separated by a definite phase step. The five-frame interferogram-collecting sequence suggested by Hariharan et al. [Appl. Opt. 26, 2504 (1987)] is extremely effective in significantly reducing the errors in height profiles derived using PSI that are caused by phase-step errors. In this Letter, we report on a class of five-frame sequence that, owing to its mathematical equivalence with the one suggested by Hariharan et al. and its ease of execution, is more commonly used but is much less effective in reducing the height profile errors caused by phase-step errors.     

An effective method in calibrating nonlinear errors for phase-shifting interferometry

In phase measurement or digital holography for phase-shifting interferometry, the key role is the variation of reference light wave and recover algorithm based on interferograms and reference phase, so the calculation result is directly affected by phase-shift accuracy. However, because of the errors of nonlinear and other random factors, it is difficult to control the actual phase-shifting amount accurately. In this paper, we aim to propose an efficient method for phase-shifting interferometry which does not require accurate initial estimation of phase-shift amounts, only a few pixels with several randomly shifted interferograms are sufficient for accurate extraction of phase information. This method has reduced the dependence of reference phase, and can obtain phase-shifting amount directly without using complex revised algorithm for correcting phase-shifting nonlinear errors.     

Carrier squeezing interferometry: suppressing phase errors from the inaccurate phase shift

The carrier squeezing interferometry algorithm is proposed to retrieve the phase from interferograms with phase shift errors. A linear carrier is introduced in the interferograms, and the image data is rearranged by the squeezing interferometry technology. In the spectrum of the rearranged image, the error lobe and the phase lobe are separated so the error-free phase can be retrieved by filtering. The simulated interferograms with phase shift errors are computed, and the precisions are better than 8.4×10(-4)λ. Its validation is verified by experiments, where a mean precision of 0.0040λ is obtained.     

Discussions about FFT-based two-step phase-shifting algorithm

An FFT-based two-step phase-shifting (TPS) algorithm is described in detail and implemented by use of experimental interferograms. This algorithm has been proposed to solve the TPS problem with random phase shift except π. By comparison with the visibility-function-based TPS algorithm, it proves that the FFT-based algorithm has obvious advantages in phase extracting. Meanwhile, we present a π-phase-shift supplement to the TPS algorithm, which combines the two interferograms and demodulates the phase map by locating the extrema of the combined fringes after removing the respective backgrounds. So combining this method and FFT-based one, one could really implement the TPS with random phase shift. Whereafter, we systematically compare the TPS with single-interferogram analysis algorithm and conventional three-step phase-shifting one. The results demonstrate that the FFT-based TPS algorithm has a satisfactory accuracy. At last, based on the polarizing interferometry, a schematic setup of two-channel TPS interferometer with random phase shift is suggested to implement the simultaneous collection of interferograms.     

Four-step spatial phase-shifting shearing interferometry from moiré configuration by triple gratings

A spatial phase-shifting shearing interferometry is presented in this paper. The whole optical configuration is simple and consists of three Ronchi gratings. Four phase-shifted shearing interferograms can be obtained simultaneously. The explicit intensity distributions of shearing interferograms are given and a corresponding four-step spatial phase-shifting algorithm is proposed to extract phase information from the new interferometry. This spatial phase-shifting configuration is applied to extract phase projection of a propane flame and a mathematical error analysis is presented.     

Advanced iterative algorithm for phase extraction of randomly phase-shifted interferograms

An advanced random phase-shifting algorithm to extract phase distributions from randomly phase-shifted interferograms is proposed. The algorithm is based on a least-squares iterative procedure, but it copes with the limitation of the existing iterative algorithms by separating a frame-to-frame iteration from a pixel-to-pixel iteration. The algorithm provides stable convergence and accurate phase extraction with as few as three interferograms, even when the phase shifts are completely random. The algorithm is simple, fast, and fully automatic. A computer simulation is conducted to prove the concept.     

长干涉腔波长移相计算的自适应相位筛选法

波长移相干涉仪可用于大口径光学元件的测试。其移相量需经过标定方可采用定步长移相算法计算相位分布。在长腔长测试条件下,由于激光器的波长调谐驱动源的精度有限,采用定步长移相算法求解相位分布的精度不高。在分析干涉腔长和波面计算误差的基础上,提出了一种自适应相位筛选计算方法。根据电压-相位标定曲线采集多组周期干涉图,对干涉图中的光强值进行均匀分布抽样后,对其进行随机移相计算,求取每帧干涉图精确的步进移相量,从中筛选出移相量为π/2的四帧干涉图,利用四步移相计算公式求得精确的相位分布。实验结果表明,在波长移相干涉仪中运用该方法,可以很好地解决长腔长测试条件下的相位计算问题,与未进行筛选的计算结果比较,其测试精度得到了显著提高。     

Phase Retrieval of Phase-Shifting Interferometry with Iterative Least-Squares Fitting Algorithm: Experiments

We report our experimental results of phase-shifting interferometry with an iterative least-squares fitting technique to estimate both the wave front phases and the phase shifts. The method allows phase retrieval from phase-shifting interferograms even though the calibration data of the phase shifter is unknown. The algorithm is used to analyze two sets of experimental interferograms. One records by moving a piezoelectric transducer shifter randomly and therefore has embedded random phase shifter errors, and the other samples the interference movie recorded by a video recorder while driving a stepping motor and therefore has embedded random intensity noises. The results are comparable with that of the conventional M-frame algorithm. Investigation of the effects of the intensity noises and phase shift errors shows the algorithm to perform well in both. Problems such as convergence, unique solution and reliability are also discussed.     

基于联合变换相关和相移干涉的图像加密

提出了一种在联合变换相关器结构中引入三步相移干涉和二元置乱技术的图像加密方法.用纯相位空间光调制器同时调制原始图像和两个随机相位掩模,利用三步相移技术分别将图像信息和主密钥加密为全息图,并用CCD在输出面上接收,再利用二元置乱技术置乱图像信息的全息图.在获得置乱密钥和附加密钥的情况下,可以通过一定的算法快速、清晰的重建原始图像.用计算机仿真验证了它的可行性和有效性.     

Generalized phase shifting interferometry based on Lissajous calibration technology

The feasibility and limitation of directly using the Lissajous figure and ellipse fitting technology to correct the phase extraction error in generalized data reduction algorithm (GDRA) for phase extraction of randomly phase-shifted interferograms are analyzed and discussed. By combining Lissajous calibration technology, which represents the transformative process of Lissajous ellipse to circle (ETC), with advanced iterative algorithm (AIA) we propose a novel generalized phase shifting algorithm (GPSA), and here it is abbreviated as ETCI method. The phase distribution and phase shifts that extracted from randomly phase shifted interferograms by use of ETCI are more accurate and the whole process is far faster than AIA. Additionally, proposed method is less sensitive to non-uniform background intensity and modulation amplitude. Numerical simulations are conducted to evaluate the performance of ETCI, and some influential factors are elaborated. The experimental results further indicate proposed method is suitable for truly random phase shifted interferograms.     

含冲击波流场干涉图的图像处理方法研究

本文研究了含冲击波流场干涉图的图像处理方法,它包括干涉条纹的快束细化算法,冲击波波阵面的提取算法和时间序列冲击波波阵面的配准算法.根据这些算法,在PC-VISION 100图像处理机上开发了应用软件.实验结果表明,该方法可用于定量计算冲击波的传播速度和压力分布,增加了流场干涉图的用途.     

Two-step interferometry by a regularized optical flow algorithm

A two-step phase-shifting method, that can demodulate open- and closed-fringed patterns without local sign ambiguity is presented. The proposed method only requires a constant phase-shift between the two interferograms. This phase-shift does not need to be known and can take any value inside the range (0, 2π), excluding the singular case where it corresponds to π. The proposed method is based on determining first the fringe direction map by a regularized optical flow algorithm. After that, we apply the spiral phase transform (SPT) to one of the fringe patterns and we determine its quadrature signal using the previously determined direction. The proposed technique has been applied to simulated and experimental interferograms obtaining satisfactory results. A complete MATLAB software package is provided in [http://goo.gl/Snnz7].     

General Phase-stepping Algorithm Using Lissajous Figures Technique

１ＩｎｔｒｏｄｕｃｔｉｏｎＰｈａｓｅｓｔｅｐｓａｒｅｇｅｎｅｒａｌｙｉｍｐｌｅｍｅｎｔｅｄｂｙｍｏｖｉｎｇｔｈｅｒｅｆｅｒｅｎｃｅｍｉｒｏｒｍｏｕｎｔｅｄｏｎａＰＺＴ（ｐｉｅｚｏｅｌｅｃｔｒｉｃｔｒａｎｓｄｕｃｅｒ）．ＳｉｎｃｅｔｈｅＰＺＴｉｓｎｏｎ...     

General Phase-stepping Algorithm Using Lissajous Figures Technique

A new phase-stepping algorithm is proposed, the algorithm can be implemented without knowing or calculating the phase steps. New phase extraction expressions based on using Lissajous figures and ellipse fitting are derived by introducing a simple difference transform for the intensity of the interferograms. The simulating results indicate that the new algorithm is insensitive to phase-stepping errors and the accuracy of the new algorithm is only limited by the computation truncation errors.     

Wavefront reconstruction by two-step generalized phase-shifting interferometry

A wavefront reconstruction method by two-step generalized phase-shifting interferometry (GPSI) with blind phase shift extraction algorithm is verified by both the computer simulations and optical experiments. This method can retrieve complex object wave field by using two interferograms, the recorded object and reference wave intensities, and an unknown phase shift without additional processing. The simulations with irregular wavefronts have shown the effectiveness and high accuracy of this method for blind phase-shift extraction and wavefront reconstruction over a wide range of phase-shifts, while the optical experiments for both the direct and indirect objects have yielded satisfactory results with a higher resolution of reconstructed image than those reported recently.