Windowed Fourier assisted two-dimensional Hilbert transform for fringes phase extraction

In this article, two-dimensional windowed Fourier assisted Hilbert transform for fringes phase extraction has been proposed. The mathematical derivations of the filtered fringes image and its Hilbert transformations are presented using windowed Fourier transform. The proposed method has been verified by calculating the wrapped and unwrapped phase of the experimental moire fringes. In comparison to the conventional fringes phase extraction methods, the proposed method is found to be effective.     

基于最小二乘法准则的光学综合孔径观测目标傅里叶信息提取

提出了基于最小二乘法准则提取光学综合孔径观测目标的傅里叶信息,给出了系统的理论推导过程.与其它传统条纹信息提取方法作了比较,指出基于最小二乘法准则提取观测目标信息周期短,速度快,可提取观测目标的傅里叶幅度和相位.实验仿真表明,基于最小二乘法准则提取观测目标信息是可行的.     

Comparison of results of interferometric phase extraction algorithms for three-dimensional flow-field tomography

A comparison of the results of interferometric phase information retrieval and subsequent tomographic reconstruction from deformed wavefront projections by phase unwrapping is presented. In interferogram processing, conventional fringe tracking and Fourier transform methods have been utilized for comparison. With these methods by injecting carrier fringes, the projection data of any axial cross section can be extracted in all projection directions to implement three-dimensional tomographic reconstruction. The results of experiments of a simulated temperature field prove that the phase extraction based on the Fourier transform method produces tomographic reconstruction much superior to the conventional fringe tracking technique.     

基于傅里叶变换的高精度条纹细分方法

针对传统傅里叶变换法在提取条纹图相位中存在的能量泄漏问题,提出了条纹图整周期裁剪的方法,可有效抑制能量泄漏对检相精度的影响,提高傅里叶变换法相位计算的精度。在此基础上,提出了一种基于傅里叶变换时移特性的叠栅条纹细分新方法。与传统傅里叶变换法相比,该方法求取相邻两帧条纹图间的相移,只需经过两次傅里叶变换,不需要截取条纹图的基频再逆变换回空域,因此计算量至少减少了一倍,计算速度大大提高。数值计算结果表明,对两束单色平面波形成的条纹,理想条件下细分精度高达10-12量级;对高斯包络调制的条纹,细分精度至少可达10-3量级。     

Automatic processing of Young''s fringes in speckle photography

A new method for the automatic processing of Young's fringes in speckle photography is described, based on the technique of spatial phase detection. The amount of calculation is reduced, yet accuracy is of an order comparable with that of the Fourier transform method. Furthermore, orientation of fringes is determined as well as fringe spacing.     

X-ray interferometric Fourier holography

An X-ray interferometric Fourier holography was proposed and theoretically investigated. X-ray Interferometric Young fringes and the reconstruction of an object image were investigated by the Fourier transform method. It was shown that on the output surface of the analyzer crystal (the third plate of the interferometer) the interference pattern of two slits gives X-ray interferometric Young fringes. An expression for the period of X-ray interferometric Young fringes was obtained. The subsequent reconstruction of the slit image as an object is conducted by means of the Fourier transform method of intensity distribution on the hologram. Three methods for reconstruction of the function of complex transmission of the object are presented: an analytical one–the approximate method, the iteration method and the step-by-step approach. As examples a recording of X-ray interferometric Fourier hologram and the reconstruction of the function of complex amplitude transmission of a beryllium circular cylinder are given.     

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。     

双螺旋叠栅条纹检测光束准直性的两种方法

介绍双螺旋叠栅条纹检测光束准直性的基本原理,进一步就双螺旋叠栅条纹的特征参量与被测光束发散角(即光束准直精度)的关系进行分析和推导。在分析双螺旋叠栅条纹进行时,首先采用频域低通滤波提取纯叠栅条纹,然后提取纯叠栅条纹的特征参量。提出两种特征参量的提取方法,一种依次进行傅里叶变换计算相位信息的傅里叶变换方法,另一种是受传统时间相移算法启发而提出的空间相移算法,讨论了在两种方法中极坐标的重采样问题和相应的计算公式,并进行了计算机模拟。结果表明,傅里叶变换方法和空间相移算法实质都是获取叠栅条纹全场趋势的平均值,使最终光束发散角的检测具有很高的精度,对自成像条纹周期的检测误差在±2.8‰以内。     

Dynamic 3-D shape measurement method based on FTP

In this paper, we propose a method for dynamic three-dimensional (3-D) shape measurement based on Fourier transform profilometry. A sequence of dynamic deformed fringe images can be grabbed by a CCD camera and saved on a disk rapidly. By a Fourier transform, filtering and inverse Fourier transform, a sequence of phase-maps can be obtained. By unwrapping these phase maps in 3-D phase space, we can obtain the shape of the dynamic object at different times. In this paper we also propose the algorithm of a phase difference between two deformed fringes, and the 3-D phase unwrapping method based on the phase difference algorithm. The computer simulation and experiment results show that this method can efficiently deal with the dynamic 3-D shape measurement.     

Limitation of carrier fringe methods in digital photoelasticity

The carrier fringes method has been proposed in digital photoelasticity in combination with techniques such as Fourier transform and phase shifting method, without considering the influence of the isoclinics on the isochromatic patterns analysis. Unlike other optical methods as moiré and holographic interferometry, in photoelasticity the light intensity emerging from a circular polariscope is related to both the isochromatic retardation and the isoclinic parameter. As it is shown by the theoretical analysis, owing to the misalignment between the principal stresses in the model and in the carrier, the computed retardation is affected by an error which is the same for all photoelastic methods based on the use of carrier fringes. Consequently, the photoelastic analysis carried out by methods that use carrier fringes cannot be applied as a full-field technique. In detail, numerical simulations show that the retardation error is comparable (less than 0.05 fringe orders) with that of other photoelastic methods provided that the misalignment between the principal stresses in the model and in the carrier is less than 30°. On the contrary, in the model zones where the misalignment is higher than 30°, the retardation measurement can be affected by non negligible errors (up to 0.25 fringe orders).     

Parameter estimation of optical fringes with quadratic phase using the fractional Fourier transform

Optical fringes with a quadratic phase are often encountered in optical metrology. Parameter estimation of such fringes plays an important role in interferometric measurements. A novel method is proposed for accurate and direct parameter estimation using the fractional Fourier transform (FRFT), even in the presence of noise and obstacles. We take Newton׳s rings fringe patterns and electronic speckle pattern interferometry (ESPI) interferograms as classic examples of optical fringes that have a quadratic phase and present simulation and experimental results demonstrating the performance of the proposed method.     

Multi-STFT for adaptive SCPS phase determination

This paper presents a fast and reliable approach for phase modulo 2π-calculation from a single fringe pattern. It calculates correct phase values even for very complex and variable shape gradients based on a locally variable fringe period determined for the entire image. In the paper, a new two-step method for wrapped phase calculation is proposed. It is performed through the use of a method based on a multiple local fast Fourier transform for estimation of a local fringes period map and a 5-point spatial carrier phase shifting (SCPS) formula for phase modulo 2π-calculation. The described approach is verified by a correct demodulation of a real fringe pattern taken by a 3D-shape measurement system.     

傅里叶变换轮廓术中频谱泄漏的讨论

讨论了频谱泄漏对傅里叶变换轮廓术测量精度的影响。由于用傅里叶变换轮廓术进行三维面形测量时 ,测得的变形光场是空间有限函数 ,故离散傅里叶变换时先要进行周期拓展 ,如果拓展周期选择不当 ,拓展后的条纹将不连续 ,对之进行傅里叶变换会产生频谱泄漏。文章从理论上推导了拓展周期与变形结构光场频谱泄漏之间的关系 ,给出了由泄漏引起的视场边缘误差的计算模型和定量分析。提出采用条纹外插以减小泄漏误差的方法 ,计算机模拟及初步实验证实了该方法的有效性。     

用伽柏小波作干涉波前重建

在分析傅里叶相位展开法中存在的一阶频谱定位误差的基础上,尤其针对实际工作中非严格均匀参考条纹干涉图的相位展开问题,提出基于伽柏小波的局域匹配滤波方法,构造多通道伽柏滤波器,得到在Ｍａｌｌａｔ极大模意义下的最佳匹配相位。     

Measurement of vibration amplitude by an optical fiber-based moiré interferometer

A projected-fringe fiber-based moiré interferometer is proposed to measure the local amplitude vibration of a diffuse surface. The technique is based on an optical fiber interferometer which projects interference fringes on the object surface. The visibility of these carrier fringes is modulated by a function of local amplitude vibration. Full-field quantitative analysis is performed by analyzing the fringe pattern with a 2-D Fourier transform method. Theoretical details, and experimental results are presented.     

基于分数阶傅里叶变换的模式测控一体化方法

提出了一种基于分数阶傅里叶变换的模式测控一体化方法。利用分数阶傅里叶变换光路对光纤模式耦合态进行空间调制和相位调制,以实现模式的有效分解。与双重傅里叶变换（F2）法以及空间和频谱成像（S2）法相比,采用的分数阶傅里叶变换法,通过改变分数阶参数,控制模式的空间分布以及模式间的叠加状态,更易于分解出高阶模式。基于分数阶傅里叶变换的模式测量方法可在更广泛空间,研究模式的空间和相位叠加以及模式分解,也可退化为F2法和S2法。     

Multiple-surface interference fringes analysis basing on wavelength-modulated phase shifting interferometry

Phase-shifting interferometry is widely used for high-precision surface measurements, but has difficulty in dealing with parallel optical plates. In this paper, an advanced method is proposed to simultaneously measure surface distributions of parallel optical plates from multiple surface interference fringes. The basic theory behind the technique is by applying wavelength-modulated phase shifting interferometry (WMPSI) to get enough frames of multiple surface interference fringes. In the procession of wavelength-modulated phase shifting, the phase variation for one point of the surface is traced and is processed by Fourier transform, and then the frequency spectrum of every surface can be separated from each other. Therefore, it allows extraction of front surface, back surface and thickness variation from multiple surface interference fringes with high precision.     

Optical image encryption based on the multiple-parameter fractional Fourier transform

A novel image encryption algorithm is proposed based on the multiple-parameter fractional Fourier transform, which is a generalized fractional Fourier transform, without the use of phase keys. The image is encrypted simply by performing a multiple-parameter fractional Fourier transform with four keys. Optical implementation is suggested. The method has been compared with existing methods and shows superior robustness to blind decryption.     

基于双边倾斜傅里叶干涉具的激光光谱探测技术研究

为了在不改变静态傅里叶干涉具尺寸的基础上提高光谱分辨率,设计了双边倾斜傅里叶干涉具及等光程条纹展宽的方法。通过计算分析双边倾斜傅里叶干涉具空间产生光程差与传统干涉具光程差的关系,得到在整个干涉具尺寸不变的条件下,光谱分辨率提高到9.1 cm-1,比同尺寸静态傅里叶干涉具提高了近8倍,并且不会因干涉条纹混叠而造成无法采集。采用BK7材料加工制成双边倾斜傅里叶干涉具,用6种不同波长的激光照射分析干涉条纹,实验结果显示干涉条纹会因反射位置增大而导致探测波长较长的激光时中心波长偏大,根据其满足线性变化的规律,拟合可知每1nm的激光波长变化造成0.021 1 nm的增大误差,经过标定后平均误差与传统干涉具接近,同时可以有效地提高静态干涉系统的光谱分辨率。     

基于Hough变换的数字全息干涉条纹检测

提出了一种利用Hough变换在图像中检测模糊直线条纹的有效方法.将Hough变换对随机噪音不敏感的特性与Fourier变换的性质相结合,可实现对图形中有相同周期条纹的检测.该方法不针对单一条纹,只识别相同周期条纹的总体特征,能有效避免条纹部分缺失对检测结果的影响,并能快速检测条纹的准确数量.将该方法应用于数字全息干涉图...