基于分数傅里叶域信号处理的迈克尔逊干涉法测量波长北大核心CSCD

建立了迈克尔逊干涉法测量波长所得条纹图的数学模型,揭示了其线性调频信号(chirp信号)特性,提出了基于分数傅里叶变换信号处理方法对迈克尔逊干涉条纹进行处理,实现了激光波长测量。实验结果表明:该测量方法具有可行性,对于波长范围为400~635 nm的激光,波长测量的平均相对误差约为0.39%。在干涉条纹图被高斯白噪声污损情况下,波长测量的平均相对误差仍然小于1%。     

基于三角形收缩法改进的分数傅里叶变换估计牛顿环参数北大核心CSCD

针对分数傅里叶变换用于牛顿环参数估计时速度较慢的问题,通过分析牛顿环条纹图分数傅里叶域幅值最大值与相应旋转角的分布规律,提出基于三角形收缩法改进的分数傅里叶变换进行牛顿环参数估计的方法。实验结果表明:该方法具有可行性,对于图像尺寸小于640×640 pixels的条纹图,处理所需时间<1 s,随着图像尺寸增加,条纹图中包含的条纹数目增加,曲率半径估计值相对误差降低,而处理时间仍可满足工程实际需求。以处理1080×1080 pixels的图像为例,估计值相对误差为0.001%,处理时间为3.31 s。该方法估计720×720 pixels高斯噪声污损的牛顿环干涉条纹图像平均用时1.28 s,约为传统分数傅里叶变换用时的1/700。     

基于时域傅里叶变换的波长移相算法

基于傅里叶变换的波长移相算法，是基于时域傅里叶变换和差分技术来实现干涉图处理。这种算法主要用于实现较粗糙轮廓或台阶件的光学检测。介绍了该算法的中心思想，指出了已有的Takeda算法的缺点，提出了改进算法。叙述了新算法的实现过程并进行了误差分析，最后给出了实验结果。     

提高计算全息图再现质量的迭代傅里叶变换算法

提出了迭代傅里叶变换算法设计了计算全息图的新方法。采用迭傅里叶变换算法，计算配置与目标相关的迭代位相，使物波频谱具有限带宽和平滑性。实验结果表明，迭代傅里味算法求适当的位相参数，使计息图再现象上的斑纹被明显抑制，提高了信噪比和衍射效率。     

静态光谱分析检测及其软件实现

 在激光光谱分析中静态干涉法比传统机械扫描的稳定性好、实时性高,因此设计了一种基于静态傅里叶干涉具空间扫描型光谱分析算法,并在Visual Studio平台下采用C#编写了光谱分析软件.实验采用532,660,780,850,980 nm的多种激光器,经斜楔角度0.1°的静态傅里叶干涉具,得到干涉条纹,由CameraLink公司的M2CL型线阵CCD探测器采集干涉条纹,经光谱分析算法得到光谱信息.通过将本算法得到的光谱数据与采用Q8344A型光谱仪经Labview分析得到的光谱数据作对比,计算得到相似度大于95%,并给出误差及灵敏度分析.     

一种激光探测与波长测定装置的研究

介绍了一种主要用于夜间的激光探测与波长测定装置，它是基于激光在光学劈尖上产生干涉条纹的特点、通过傅里叶变换测定条纹间距来计算激光波长的，测试结果表明该装置在背景光微弱的情况下，性能令人满意，具有一定的实用性。     

基于小波变换的傅里叶加密印刷水印算法研究

在研究傅里叶加密全息技术、数字水印技术和小波理论的基础上,提出了一种基于小波变换的傅里叶加密印刷水印算法。利用该算法重建水印,有效地抑制了载体图像的低频分量对水印产生的噪声的影响;使能量分布在图像的所有像素上,具有良好的抗裁切能力;算法采用密钥加强了水印的安全性。实验表明:嵌入水印的图像一次印刷可检测,二次扫描印刷提取的水印脆弱,可以抵抗基本的图像处理操作。     

畸变测量中应用窗口傅里叶变换载频条纹分析

为了测量光学成像系统的径向畸变,提出了基于伸缩窗口傅里叶变换空间载频条纹相位分析的测量新方法.畸变分布测量转化为调制相位测量.首先,将纵向朗奇基准光栅作为模板,通过成像系统成为变形光栅即畸变像.接着采用伸缩窗口傅里叶变换提取畸变载频光栅条纹中心无畸变点的基频和相位信息,获得理想无畸变像的基频成分,然后对变形载频光栅条纹进行频谱分析,滤波提取基频信息、逆傅里叶变换、相位解包,提取径向调制相位分布,计算畸变图像的径向位置畸变分布.最后利用该径向位置畸变分布规律和双线性插值灰度重建对畸变图像进行校正.详细的理论分析和实验结果证明,该方法是可行的.     

基于四元数傅里叶变换的彩色图像数字水印算法

目的提高彩色图像数字水印的抗攻击性能,包括缩放、旋转、平移、噪声攻击等。方法基于坐标变换和四元数傅里叶变换提出一种彩色图像数字水印算法。介绍彩色图像四元数表示形式及其双侧傅里叶变换,并分析笛卡尔坐标和极对数坐标之间的变换关系。选择四元数傅里叶变换后实部的中低频部分作为嵌入区域;为提高算法的抗几何攻击能力,给出笛卡尔坐标系和对数极坐标系之间对应点的位置关系;详细论述水印嵌入和提取的流程。结果针对噪声、滤波、剪切等攻击进行了实验研究,结果表明所述算法可以提高提取信息的准确率和水印的抗攻击能力。结论该算法在保证水印隐蔽性的同时能够抵抗一定程度的攻击,满足版权保护和数字防伪的需要。     

利用傅里叶变换的干扰信号分析

本文采用傅里叶变换对干扰信号进行了分析。首先讨论了正弦干扰信号和脉冲干扰信号的传统计算模式，然后采用傅里叶变换方法对脉冲干扰信号进行分解。最后对两种分析方法进行了综合比较。结果表明采用傅里叶变换可以扩大分析的频率范围，并且处理简单准确。     

Speckle interferometry by using virtual speckle pattern based on Carré algorithm

Dynamic deformation measurement with a large deformation is effectively performed by using virtual speckle patterns. The virtual speckle pattern has been generally produced by using the operation based on Fourier transform. However, it takes a long calculating time to produce a virtual speckle pattern, because the method requires Fourier transform operation at each pixel of CCD. In the proposed method, virtual speckle patterns are produced by Carré algorithm without any operation by Fourier transform. The method is applied to the in-plane deformation measurement in this paper. As the results, it is confirmed that the calculating cost of virtual speckle patterns is improved remarkably, and that the measurement accuracy of the new method is also equal to the ordinary methods. It is also confirmed that the proposed method will expand the use of the speckle interferometry based on virtual speckle pattern technology.     

Three-dimensional phase step profilometry with a multicore optical fiber

This paper demonstrates the feasibility of using phase stepping and a multicore optical fiber to calculate an object's depth profile. An interference pattern is projected by an optical fiber onto the object. The distorted interference pattern containing the object information is captured by a CCD camera and processed using a phase step interferometry method. The phase step method is less computationally intensive compared to two-dimensional Fourier transform profilometry and provides more accuracy when measuring objects of high frequency spatial variations.     

Simultaneous measurement of out-of-plane displacement and slope using a multiaperture DSPI system and fast Fourier transform

The simultaneous quantitative measurement of out-of-plane displacement and slope using the fast Fourier transform method with a single three-aperture digital speckle pattern interferometry (DSPI) arrangement is demonstrated. The method coherently combines two sheared object waves with a smooth reference wave at the CCD placed at the image plane of an imaging lens with a three-aperture mask placed in front of it. The apertures also introduce multiple spatial carrier fringes within the speckle. A fast Fourier transform of the image generates seven distinct diffraction halos in the spectrum. By selecting the appropriate halos, one can directly obtain two independent out-of-plane displacement phase maps and a slope phase map from the two speckle images, one before and the second after loading the object. It is also demonstrated that by subtracting the out-of-plane displacement phase maps one can generate the same slope phase map. Experimental results are presented for a circular diaphragm clamped along the edges and loaded at the center.     

Fourier transform interferometer alignment method

A rapid and convenient method has been developed to facilitate the alignment of the image-plane components of point-diffraction interferometers, including the phase-shifting point-diffraction interferometer. In real time, the Fourier transform of the detected image is used to calculate a pseudoimage of the electric field in the image plane of the test optic where thecritical alignment o f variousoptical components is performed. Reconstruction of the pseudoimage is similar to off-axis, Fourier transform holography. Intermediate steps in the alignment procedure are described. Fine alignment is aided by the introduction and optimization of a global-contrast parameter that is easily calculated from the Fourier transform. Additional applications include the alignment of image-plane apertures in general optical systems, the rapid identification of patterned image-plane alignment marks, and the probing of important image-plane field properties.     

Phase-shifting point-diffraction interferometry at 193 nm

Phase-shifting point-diffraction interferometry at the 193-nm wavelength suitable for highly accurate measurement of wave-front aberration is introduced. The interferometer preserves the advantages of the previously described extreme-ultraviolet phase-shifting point-diffraction interferometer but offers higher relative efficiency. Wave-front measurement of an imaging system, operating at the 193-nm wavelength, is reported. Direct measurement of the refractive-index change in a deep-ultraviolet radiation-damaged fused-silica sample is also presented as an application.     

Denoising in digital speckle pattern interferometry using fast discrete curvelet transform

In digital speckle pattern interferometry, the denoising of speckle fringe patterns is of vital importance for quantitative extraction of phase distribution. A filtering method of fast discrete curvelet transform based on weighted average thresholding technique is proposed in this paper for noise removal in speckle fringe patterns. Both computer-simulated and experimental digital speckle pattern interferometry fringe patterns are adopted to evaluate the performance of the proposed filtering method. In addition, a widely used and representative filtering method, windowed Fourier filter, is introduced for making a comparison and validation in the image processing effect, and the parameter of peak signal noise ratio is also used for assessment of denoising effect. It is shown from the filtered results that the filtering method of fast discrete curvelet transform is effecitve to remove speckle noises and simultaneously preserve fringe structure information.     

Improved white-light interferometry on rough surfaces by statistically independent speckle patterns

White-light interferometry (WLI) on rough surfaces is based on interference from individual speckles. The measurement uncertainty of WLI is limited by a random shift of these individual interference patterns. The statistical error in each measurement point depends on the brightness of the corresponding speckle: a dark speckle yields a larger error than a bright speckle. In this paper, a novel method is presented to reduce the measurement uncertainty significantly: by sequentially switching the direction of the illumination, the camera sees several independent speckle patterns in sequence. From each pattern, the brightest speckles are selected to eventually calculate an accurate height map. This height map displays no outliers, and the measured surface roughness is close to the stylus measurements.     

Simultaneous multidimensional deformation measurements using digital holographic moiré

This paper proposes an elegant technique for the simultaneous measurement of in-plane and out-of-plane displacements of a deformed object in digital holographic interferometry. The measurement relies on simultaneously illuminating the object from multiple directions and using a single reference beam to interfere with the scattered object beams on the CCD plane. Numerical reconstruction provides the complex object wave-fields or complex amplitudes corresponding to prior and postdeformation states of the object. These complex amplitudes are used to generate the complex reconstructed interference field whose real part constitutes a moiré interference fringe pattern. Moiré fringes encode information about multiple phases which are extracted by introducing a spatial carrier in one of the object beams and subsequently using a Fourier transform operation. The information about the in-plane and out-of-plane displacements is then ascertained from the estimated multiple phases using sensitivity vectors of the optical configuration.     

Simultaneous measurement of three orthogonal components of displacement by electronic speckle-pattern interferometry and the Fourier transform method

The measurement of three-dimensional displacement by electronic speckle-pattern interferometry with three object beams and one reference beam is presented. Multiple interference fringes corresponding to different sensitivity vectors are recorded in a single interferogram and separated by means of the Fourier transform method to give three components of displacement. The relationship between the ratio of the speckle size to the pixel size of a TV camera and the measurement error is investigated experimentally and compared with the research of others. The optimum condition leading to a minimum measurement error occurs when the speckle size is approximately equal to the pixel size. With this condition satisfied, the measurement error varies from 1.5% to 6.0%.     

Large deformation mechanical testing of biological membranes using speckle interferometry in transmission. II: Finite element modeling

In holography and speckle interferometry the measurement range is generally limited by the greatest number of fringes that can be resolved in a single image. As a result these techniques have been generally confined to small displacement measurement applications. In the case of out-of-plane measurements one can overcome this limitation by simply adding incremental measurements at individual detector pixels. In the case of in-plane measurements, however, summing incremental measurements is not a straightforward procedure since the interference pattern moves laterally across the detector as the material deforms. We describe a modeling technique based on finite elements which solves this problem. In combination with a full field method such as holography or speckle interferometry, it provides a very sensitive measurement technique with dense spatial sampling and large dynamic range. Experimental results of speckle interferometry operating in transmission to measure in-plane displacements of biological membranes are presented, where total material displacements are of the order of millimeters. The results also demonstrate how the finite strain tensor is calculated analytically from the data at any point on the material.