通过相移条纹图差分测定相移量的方法

提出一种通过两幅相移条纹图相减来确定它们之间相移量的方法,进行了理论分析和实验验证。两幅相移条纹图相减并归一化后,得到的相移差分函数是振幅只与相移量有关的正弦函数,可以通过确定该函数最大极值的方法得到振幅,进而计算出相移量。介绍了极值直接查找法和平均法两种实现最大极值测量的方法。由于不使用傅里叶变换,减少了运算时间,既可以用于高空间频率条纹,也可以用于稀疏平行条纹,以及任意花样的条纹。在衬比度因子确定后,用这种方法就能够直接在空域内确定两幅条纹图之间的相移量,通过大量采样点进行统计计算,使结果达到很高的精度。将所得到的结果与用傅里叶变换方法得到的结果进行了比较,表明两种方法得到的结果具有完全相同的精度。     

Multiple phase-shifted interferograms obtained from a single interferogram with linear carrier

In this paper we propose a new method for phase retrieval in an interferogram with a spatial linear carrier. We demonstrate that from the primary interferogram one can extract multiple interferograms (with lower resolution than the original one) with arbitrary phase-shift amounts between them. Then, by applying well-known phase-shifting algorithms, from these phase-shifted interferograms the phase can be retrieved. The method does not require sophisticated data-processing and is computationally efficient. Numerical simulations and validation experiments are presented.     

Generalized phase-shifting algorithm for dynamic phase measurement in electron-wave interferometry

A generalized phase-shifting algorithm is implemented in the electron-wave interferometry with a transmission electron microscope, based on simultaneous measurement of the initial phases of the interferograms. The initial phase of each interferogram that has inherent linear carrier fringes is calculated using the Fourier co-efiicients of the interferogram itself corresponding to the carrier-frequency. Taking advantage of this phase-shifting method in both spatial resolution and precision, the phase distribution of a biological weak phase object is successfully measured. This promises to be one of the most spectacular application fields for this new technology.     

相移相位测量的全息再现算法及测量误差分析

用全息原理和方法研究相移相位测量,得到了N步整周期相移再现物光波复振幅同步叠加函数(N步相移函数),同时提出一种新的相移相位测量误差分析和最大误差估计方法。N步相移干涉图是以理想平行光为参考光的无衍射同轴全息图,将其与对应的相移参考光相乘后求和得到N步相移函数;在理想情况下,这是一种复振幅分离、测量和物光波复振幅函数同步叠加方法,存在误差时计算出的相位是最小二乘方法的最佳期望结果。利用N步相移函数得到的N 1步相移函数,说明非理想N步相移函数是理想N步相移函数与误差函数之和,可以把相位型误差转化为与振幅和强度相对误差同等的误差来对待,降低了相位测量中误差估计的难度,给出了N步相移算法最大误差的估计方法和公式。     

Polarization phase-shifting Jamin shearing interferometer

The Jamin shearing interferometer is very useful in wavefront testing, especially for the low coherent light. Based on this interferometer, a polarization phase-shifting Jamin shearing interferometer is proposed to improve the performance. In the interferometer, two interference beams are linearly polarized and a polarization phase shifter is applied to realize the phase shifting. Different types of configurations of the interferometer are given. With phase-shifting interferograms, the precision of the interferometer can be improved. The interferometer is kept as an equal optical path system and its shearing amount remains changeable with simple structure and easy operation. In experiments, phase-shifting interferograms are obtained by rotating the analyzer. The usefulness of the interferometer is verified.     

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.     

Three-step self-calibrating generalized phase-shifting interferometry

An accurate and fast three-step self-calibrating generalized phase-shifting interferomertry (SGPSI) is proposed. In this approach, two new phase-shifting signals are constructed by the difference interferograms normalization and noise suppressing, then the unknown phase shift between the two difference phase-shifting signals is estimated quickly through searching the minimum coefficient of variation of the modulation amplitude, a limited number of pixels are selected to participate in the search process to further save time, and finally the phase is reconstructed through the searched phase shift. Through the reconstruction of phase map by the simulation and experiment, and the comparison with several mature algorithms, the good performance of the proposed algorithm is proved, and it eliminates the limitation of requiring more than three phase-shifting interferograms for high-precision SGPSI. We expect this method to be widely used in the future.     

Simple phase extraction in x-ray differential phase contrast imaging

A fast and simple method to extract phase-contrast images from interferograms is proposed, and its effectiveness is demonstrated through simulation and experiment. For x-ray differential phase contrast imaging, a strong attenuation signal acts as an overwhelming background intensity that obscures the weak phase signal so that no obvious phase-gradient information is detectable in the raw image. By subtracting one interferogram from another, chosen at particular intervals,the phase signal can be isolated and magnified.     

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.     

基于区域生长理论的波面解包算法研究

在移相干涉技术的相位计算中,周期函数arctan的相位值分布在[-π,π]之间,相位值分布的跃变形成了被压包后的波面。理想无噪声和边界形状规则的压包波面可以直接通过条纹扫描法进行解包。例如当被测物边界形状不规则和存在噪声(灰尘脏点)时,会导致干涉图上出现无效区域,必须采用不依赖于边界形状,能自动绕过无效区域的算法。采用区域生长法对这类干涉图进行了解包。通过编程计算表明,这种解包算法能解决光学检测中的几乎所有的干涉图处理问题。     

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.     

Phase-shifting interferometry with four interferograms using linear polarization modulation and a Ronchi grating displaced by only a small unknown amount

A method to reduce the number of captures needed in phase-shifting interferometry is proposed on the basis of grating interferometry and modulation of linear polarization. The case of four interferograms is considered. A common-path interferometer is used with two windows in the object plane and a Ronchi grating as the pupil, thus forming several replicated images of each window over the image plane. The replicated images, under proper matching conditions, superpose in such a way so that they produce interference patterns. Orders 0 and +1 and −1 and 0 form useful patterns to extract the optical phase differences associated to the windows. A phase of π is introduced between these orders using linear polarizing filters placed in the windows and also in the replicated windows, so two π-shifted patterns can be captured in one shot. An unknown translation is then applied to the grating in order to produce another shift in the each pattern. A second and final shot captures these last patterns. The actual grating displacement and the phase shift can be determined according to the method proposed by Kreis before applying proper phase-shifting techniques to finally calculate the phase difference distribution between windows. Related simulations and experimental results are given.     

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.     

Phase-shifting interferometry based on principal component analysis

An asynchronous phase-shifting method based on principal component analysis (PCA) is presented. No restrictions about the background, modulation, and phase shifts are necessary. The presented method is very fast and needs very low computational requirements, so it can be used with very large images and/or very large image sets. The method is based on obtaining two quadrature signals by the PCA algorithm. We have applied the proposed method to simulated and experimental interferograms, obtaining satisfactory results.     

Polarization phase-shifting interferometer by rotating azo-polymer film with photo-induced optical anisotropy

A new type of phase-shifting interferometer was presented by rotating an azo-polymer film with photo-induced optical anisotropy in the light path of orthogonal polarization interferometry. By changing the angle of the optical axis of the azo-polymer film, four phase-shifted fringe patterns were obtained, from which phase difference between orthogonal polarized light could be calculated. The polarization states and the formation of the interferograms were analyzed theoretically using Jones matrix calculations and the experimental verification of the proposed method was also given. This method has a simple optical configuration which utilizes commercially available polarization devices and anisotropic azo-polymer film of low cost. The phase-shifting interferometer also demonstrates a new application of azo-polymer film.     

Spectrally-resolved white-light interferometry as a profilometry tool

Phase-shifting interferometry and white-light interferometry are reliable techniques for surface analysis in which the optical path difference has to be changed by some transducer to evaluate the phase. We present here a different procedure in which optical path modulation is completely avoided. This technique is based on the spectral analysis of white-light interferograms. By means of a spectroscopic device, a non-visible interferogram is split into its monochromatic components and absolute, unambiguous values of the phase are obtained along the spectral axis. Only one interferogram is required to obtain the profile of one-dimensional surfaces with nanometric resolution.     

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].     

FTIR单边干涉图相位校正技术的研究与改进

基于傅里叶变换红外光谱仪干涉图的单边过零采样和非对称性,对相位校正技术进行研究和改进。针对Mertz乘积法对切趾函数的匹配性要求高,干涉图非对称切趾旁瓣抑制效果差、光谱分辨率低的缺点,综合Mertz法和Forman法的特点提出一种改进的相位校正方法。采用对称化方法将单边干涉图变换为双边干涉图、对称切趾、傅里叶变换重建功率谱,并采用对称化的双边干涉图傅里叶变换求取高分辨率的相位谱,提高相位校正的精度。通过仿真分析了非对称窗函数较对称窗函数有比较宽的主瓣宽度、高的旁瓣幅值,分辨率降低;实验验证该改进的相位校正方法功率谱误差小、计算量少,且光谱分辨率比较高,达到2cm-1。     

Phase-shifting interferometry by wave amplitude modulation

A new method for phase-shifting interferometry based on wave amplitude modulation is proposed and discussed. This proposal is based on the interference of three waves, where two waves attend as two reference waves and the other wave attends as a probe wave. Thereby, three interference terms are obtained, but because a phase difference of π/2 between the two references is kept constant, one of the three terms will be dropped, while the two remaining will be put in quadrature. Under these conditions, the resulting pattern is mathematically modeled by an interferogram of two waves, where an additional phase is given by the amplitude variations of the reference waves. In this Letter, both a theoretical model and some numerical simulations are presented.     

Phase Measurement Algorithm without Phase unwrapping Problem for Phase stepping interferometry

１ＩｎｔｒｏｄｕｃｔｉｏｎＰｈａｓｅｓｔｅｐｐｉｎｇｉｎｔｅｒｆｅｒｏｍｅｔｒｙｈａｓｂｅｅｎｅｘｔｅｎｓｉｖｅｌｙａｐｐｌｉｅｄｉｎｍａｎｙａｓｐｅｃｔｓ．Ｃｏｎｖｅｎｔｉｏｎａｌｐｈａｓｅｕｎｗｒａｐｐｉｎｇｉｓｉｍｐｌｅｍｅｎｔｅｄｂｙｔｈ...