Profilometry of Sloped Plane Surfaces by Wavelength Scanning Interferometry

The feasibility of surface shape measurement by wavelength scanning interferometry was investigated by applying it to plane surfaces with various slope angles. We derived the surface height from the peak position of the Fourier transform of the interference signals arising from wavelength scanning of a dye laser at each pixel of a CCD camera, and succeeded in measuring both diffusely reflecting surfaces and machine-milled ones having slope angles up to 45°. Study of the influence of the slope angle on the standard deviations of the measured height showed that the standard deviation increases with increase of the angle of both surfaces. The increase in diffusely reflecting surfaces could be explained in terms of speckle decorrelation caused by wavelength change.     

Relation between statistical properties of surface roughness and the averaged speckle intensity in the diffraction field

A theoretical and experimental investigation is made on the relation between the statistical properties of a rough surface and the averaged speckle intensity in the diffraction field. The theoretical analysis is performed in some detail over a wide range of the random phase variation for various illuminated objects. The result gives an interpretation for the behavior of the averaged speckle intensity obtained experimentally for various states of rough surfaces.     

空间平均的角度散斑相关粗糙度测量模拟研究

角度散斑相关是一种不受表面粗糙度轮廓的间距特性影响的粗糙度幅度参量测量方法,它的数学模型通常建立在集平均的基础上。通过模拟计算随机粗糙表面的远场散斑场,以散斑图面上的空间平均代替常规的集平均来计算角度散斑相关系数,并应用集平均的数学模型反演粗糙度参量。结果证实了这种空间平均角度散斑相关粗糙度测量方法的有效性,在同一表面只需对少数个区域进行测量并对测得的粗糙度参量取平均,即可获得足够的测量精度。对于Rq大于2.0μm的表面,测量相对误差小于15%。根据最佳测量条件,该方法适用于大粗糙度表面。     

Spacetime correlation functions of dynamic speckles produced by a series of moving phase screens

Spacetime correlation functions of the time-varying speckle intensity have been evaluated for the case where speckle patterns are produced in the Fresnel diffraction region by light propagating through a series of moving random-phase screens. The correlation functions are given by a set of recursion formulae which are useful for numerical computations. Three statistical quantities relating to the motion of speckle patterns are derived to examine the relationship between the velocity distribution of the phase screens and the temporal behaviour of resultant speckle patterns. It is found that the velocity differences between the phase screens have a strong effect on both the decorrelation of speckle patterns and the fluctuating speed of the speckle intensity.     

Application of improved Speckle contouring technique to surface roughness measurements

One of the well known drawbacks in Electronic Speckle Pattern Interferometry (ESPI) is the poor fringe density due to electronic and speckle noise and decreasing fringe visibility with increasing speckle decorrelation. As recently reported we suggested improving the fringe density and enlarging the measurement range by the incremental addition of phase images. The technique has already been successfully applied to in-plane and out-of-plane displacement field measurements of carbon-fibre reinforced composites. This paper demonstrates how the technique can be used to improve the sensitivity and to extend the measurement range for speckle contouring applications. The angular correlation of the speckle phase images is used to get the desired 3D information of the investigated object surface. It is demonstrated how the angular speckle contouring techinque can easily be automated with respect, for example, to possible industrial applications. Roughness measurements are carried out on milled Rugo test surfaces. All measurements are performed without the usual vibration isolation, and of course, without the treatment of the surface with fine, white powder for contrast enhancement, which would falsify the results.     

变孔径像面散斑平均光强标定随机表面的理论与实验

采用随机表面的高斯相关模型和统计光学原理,推导出弱散射体在4f系统中的像面上光强的表达式.在此基础上提出了均方偏差粗糙度和横向相关长度的标定方法,该方法用理论结果对实验测量的像面散斑平均光强随滤波孔半径的关系曲线进行拟合,同时测量出被测样品表面的两个统计量.实验上制作了高斯相关随机表面样品,对其表面参数进行了测量,与AFM所测结果符合得较好,这表明该方法具有较高的精度. 关键词： 弱散射体 像面散斑 平均光强     

Spacetime correlation functions of dynamic speckles produced by a series of moving phase screens

Abstract

Spacetime correlation functions of the time-varying speckle intensity have been evaluated for the case where speckle patterns are produced in the Fresnel diffraction region by light propagating through a series of moving random-phase screens. The correlation functions are given by a set of recursion formulae which are useful for numerical computations. Three statistical quantities relating to the motion of speckle patterns are derived to examine the relationship between the velocity distribution of the phase screens and the temporal behaviour of resultant speckle patterns. It is found that the velocity differences between the phase screens have a strong effect on both the decorrelation of speckle patterns and the fluctuating speed of the speckle intensity.     

Granularity growth of laser speckle and its application to surface inspection

A process of granularity growth in partially developed speckle patterns produced in the near field of wavy object surfaces illuminated using a laser has been experimentally studied by investigating the probability density function and average contrast of their intensity variations. These parameters have been measured as a function of the distance from the object surface to the detector for four typical sample objects having different surface qualities. It has been found that the variation in average speckle contrast with receiving distance is strongly dependent on the surface quality of the objects. The saturated value of the speckle contrast, found from the graph of its dependence on receiving distance, is also related to the maximum height of irregularities in the surface.     

Speckle decorrelation influence on measurements quality in vortex metrology

We study speckle decorrelation effects in connection with conventional vortex metrology techniques. Our proposal is based on processing speckled images recorded by using two different experimental set-ups. In both schemes two laterally displaced patterns are generated: one scheme allows for obtaining undecorrelated speckle distributions and the other for decorrelated ones. Vortex networks associated with speckle patterns are analyzed by employing the usual tools developed for vortex metrology. For each recorded image, a 2D pseudo-phase map is generated on the basis of the Reisz transform. Then the vortices are located, and parameterized in terms of their topological charge, eccentricity, vorticity and angles between the zero crossing lines from the real and the imaginary parts of the analytical signal. After tracking the homologous vortices onto the maps, the histograms corresponding to the coordinate displacements are analyzed. We show that histograms interpretation is prone to failure due to its high sensitivity to decorrelation. Experimental evidences are presented to support the restrictions imposed by decorrelation of actual speckles due to uniform in-plane displacements.     

Computed speckle decorrelation (CSD) for the study of fatigue damage

A video-based laser speckle technique has been developed for noncontact analysis of fatigue in situ and at speeds approaching video frame rates. This technique, computed speckle decorrelation (CSD), makes use of the speckle decorrelation associated with surface deformation. It is a method of full field inspection which both locates fatigue damage sites and measures damage severity. In its current application, CSD has been used to study the fatigue deformation progression in reverse bending fatigue of a cylindrically notched aluminum specimen. However, film based studies have shown the usefulness of laser speckle decorrelation to analyze fatigue deformation of thick graphite/epoxy composite materials as well. With the development of the CSD method it will now be possible to examine in greater detail the progression of fatigue damage in these materials, allowing a much faster and more quantitative analysis than was previously available.     

Statistical Properties of Laser Speckles Generated from Far Rough Surfaces

The statistical properties of speckle patterns generated from far rough surfaces, under illumination of a Gaussian beam, are investigated. The surface roughness dependence of the first- and second-order moments of intensity is theoretically investigated, and their analytical expressions have been derived and presented. The analysis indicates that the mean intensity distribution on the receiver plane is closely related to the ratio of the lateral correlation length to the surface root mean square (rms) height. On the other hand, the speckle size and the correlation degree of the speckle intensities are found to be independent of the parameter characterizing the roughness of a surface, and are only determined by the laser beam waist.     

The autocorrelation of speckles in deep Fresnel diffraction region and characterizations of random self-affine fractal surfaces

This paper studies the correlation properties of the speckles in the deep Fresnel diffraction region produced by the scattering of rough self-affine fractal surfaces. The autocorrelation function of the speckle intensities is formulated by the combination of the light scattering theory of Kirchhoff approximation and the principles of speckle statistics. We propose a method for extracting the three surface parameters, i.e. the roughness w, the lateral correlation length ξ and the roughness exponent α, from the autocorrelation functions of speckles. This method is verified by simulating the speckle intensities and calculating the speckle autocorrelation function. We also find the phenomenon that for rough surfaces with α= 1, the structure of the speckles resembles that of the surface heights, which results from the effect of the peak and the valley parts of the surface, acting as micro-lenses converging and diverging the light waves.     

Measurement of surface roughness properties using speckle patterns with non-gaussian statistics

The surface roughness properties (i.e. the rms surface roughness and the correlation length) of strong diffuse objects are investigated by using the speckle patterns which obeys the non-gaussian statistics. The intimate linear relation is found to exist between the rms surface roughness of objects and the maximum contrast obtained from the varying curves of the average image speckle contrast as a function of the point spread of an optical imaging system. The correlation length of surface roughness of objects is related to the averaged intensity distribution of speckle patterns produced at the far-field diffraction plane. It now becomes clear that the rms roughness and the correlation length of strong diffuse objects are determined, respectively, from the maximum speckle contrast at the image plane and the averaged speckle intensity distribution at the far-field diffraction plane.     

Improved evaluation of electronic speckle pattern interferograms by photogrammetric image analysis

Electronic speckle pattern interferometry (ESPI) is a well-established tool for non-destructive testing. It allows the quantitative determination of surface deformations and micro-movements with a sub-micrometer resolution. In the case of objects which are extended in depth, however, the evaluation and interpretation of the resulting correlation fringe patterns can be affected by perspective image distortions as well as by a varying image size. In this paper a method for combination of ESPI with a photogrammetric 3D coordinate measurement is presented. In this way, interferogram data are precisely allocated in 3D-space. Furthermore, it is possible to take into account a spatially varying sensitivity vector. The utilizability of the method is demonstrated by a deformation measurement on a stone sculpture.     

相移全息干涉计量的统计分析

本文从统计光学的角度对相移全息干涉计量原理进行了详细的分析,指明由于变形过程中面内位移引起的散斑消相关效应的存在,使相位测量产生随机误差,误差的大小由面内位移量的大小决定,且这种误差不随相移计量过程中采样次数的增加而减小。提出了几种提高相位测量精度的有效方法,给出了相应的实验结果。     

Experiments on the space and wavelength dependence of speckle

A comprehensive series of speckle experiments is described for opal glass diffusers ranging in thickness from 10 to 500 μm. Wavelength decorrelation measurements are made using a cw dye laser source; and accurate square-law detection is provided by the use of an optic-fiber, photomultiplier combination rather than film. For this diffuser set intensity distribution functions, polarized and unpolarized, are plotted. Second-order correlation functions are presented for different apertures, relating diffuser motion and probe motion. Remote texture determination using contrast ratio and frequency decorrelation is illustrated.     

Statistical properties of the phase difference between two interfering speckle fields in speckle interferometry

The statistical properties of the phase difference between the two interfering partially correlated and partially developed speckle fields were studied experimentally as a function of the intensity correlation coefficient. The gaussian statistics are assumed for the formation of speckle fields in the diffraction region and the correlation coefficient between the two speckle intensities is used to evaluate the phase difference. The standard deviation of the phase difference can be uniquely determined in the fully developed speckle field from the correlation coefficient of the two speckle intensities. However, it was found in the partially developed speckle field that the standard deviation of the phase difference between the two speckle fields cannot be uniquely determined from the correlation coefficient of the two speckle intensities.     

地面对激光雷达信号散射的统计研究

从理论角度研究了利用高斯光束照射远场目标时,激光散斑的统计特性.导出了散射光场的自相关函数和光强度的二阶矩的解析表达式,计算了激光散斑的面积.研究表明:在接收面上,光强的分布与目标表面高度的相关长度和均方根高度密切相关,激光散斑面积和散斑光强的相关系数只与激光束腰的尺度有关,与目标的均方根高度和相关长度无关. 关键词： 激光散斑 自相关函数 高斯分布 协方差     

Statistical properties of the sum of partially-developed,correlated speckle patterns

General formulas for the average contrast and probability density function of the sum ofN partially-developed, correlated speckle patterns have been theoretically derived. These two parameters characterizing the statistical properties of added speckle patterns have been actually evaluated for the sum of two partially-developed, correlated speckle patterns and shown in figures as a function of the surface roughness of illuminated objects, the wavelength difference of two illuminating lights, and the number of scattering cells within the illuminated area of objects.     

Holography, speckle, and computers

Surveys are presented on automatic and quantitative deformation measurements using CCDs and computers in holographic interferometry and speckle metrology for diffusely reflecting surfaces. For delivering relationships between object deformation and observed quantities, we discuss formations of fringes and signals observed in these methods in terms of correlation functions of spatially randomly varying complex amplitude of light. Dependencies of the observed patterns on object deformation and optical systems are discussed. Physical meanings of the derived relationships are explained in terms of the dynamic behaviors of speckles resulting from surface deformation. Automatic measurements are described in chronological orders. They include analysis of fringe patterns resulting from photographic recording of specklegrams, video recording and analysis of speckle patterns used in electronic speckle pattern interferometry as well as direct digital correlation techniques, and digital holography that uses both digital recording and reconstruction of holograms.