Measurement of surface roughness using dichromatic speckle

The dependence on the surface roughness of the structural difference of two normalized intensity distributions in a dichromatic speckle pattern is studied theoretically. It is shown that the difference of two speckle intensity distributions increases with increase of the object surface roughness. Using this proportional relationship, a new method for measuring surface roughness is proposed. The effective measuring range can be changed by varying the two wavelengths of the illuminating light. Some computer simulation studies are conducted to verify the theoretical results.     

金属表面非相干线结构光条纹中心提取方法

采用线结构光法测量金属表面形貌时,由于受到金属表面光学特性和散斑噪声的影响,条纹中心的提取误差往往较大。为此,提出了一种非相干线结构光形貌测量方法,避免了散斑噪声的影响。通过分析该方法测量金属表面形貌时的条纹图像特点,提出一种适合非相干线结构光条纹的中心提取方法。该方法首先采用结合积分图像原理的自适应阈值分割算法,对原条纹图像进行分割。采用灰度重心法粗提取原条纹中心坐标,以该坐标为基准向条纹宽度方向延伸,从而确定阈值分割后条纹图的感兴趣区和背景区,并去除背景区的噪声。经中值滤波后,采用几何中心法提取条纹中心。实验结果表明:采用该方法提取粗糙度样块表面非相干光条纹中心的平均误差为1.5 μm,提取齿轮渐开线样板表面非相干光条纹中心的平均误差为0.9 μm,均比其线激光条纹中心的提取误差小。所提方法能实现金属表面非相干线结构光条纹中心的精确提取。     

Study on the reduction of speckle noise in the reconstructed image of digital hologram

As one of the most important 3-D display technique, reduction of speckle noise in the reconstructed image of digital holography should be grounded on the digital hologram itself. Based on the whole process of the recording and reconstruction of digital holography, the optical distributions of recorded object and reconstructed image of digital holography have been studied. It has been proposed that the root formation cause of speckle noise in its reconstructed image is the speckle noise formed on the recorded object surface when illuminated by coherent light because of its optical roughness. A novel approach has been presented to reduce speckle noise in digital holography by changing the interference structure of hologram itself. First, by reducing the speckle noise in the reconstructed image, the distribution of ideal reconstruction light with reduced speckle noise is acquired. Then in turn, taking the ideal reconstruction light with reduced speckle noise as ideal object light, a new hologram can be rebuilt, which can reconstruct the ideal object light. The experimental results are given to confirm the proposed method. Therefore, it offers a brand-new thought and practical way to reduce the speckle noise in the reconstructed image of digital holography.     

粗糙表面对散斑统计特性的影响

为研究高速摄影中激光相干噪声的影响因素,降低激光照明中散斑噪声对高速摄影成像质量的影响,对激光照射表面的粗糙程度与形成的散斑场统计特性之间的关系进行了研究。基于菲涅尔-基尔霍夫衍射原理,分析了高斯光束入射在随机粗糙表面上经反射形成的散斑图样,通过对大量散斑图样的数据统计,得出了激光散斑的信噪比、自相关函数、概率密度函数与入射表面粗糙度之间的变化关系。计算结果表明:粗糙度的增大使散斑场信噪比降低、相干程度减小、概率密度降低,即表面越粗糙散斑噪声越严重。     

Roughness measurement of metallic surfaces based on the laser speckle contrast method

A method of measuring surface roughness of flat lapped, ground and polished metallic surfaces, by the far-field speckle contrast method is presented in this paper. The laser speckle contrast technique depends on the existence of an approximately linear relationship between the speckle contrast and the roughness of the illuminated surface. Initially it was shown that the linear relationship existed up to 0.1 μm Ra (centre-line average) roughness using Helium–Neon light, after which a saturation effect was observed. The effect of varying the incident angle of illumination was investigated with a view to extending the measurement range. The use of high incident angles of illumination has been found to increase the surface roughness range up to 0.4 μm measurement Ra.     

利用散斑图像测量表面粗糙度的计算机模拟及实验

从菲涅耳-基尔霍夫衍射公式出发推导出了粗糙面近场衍射方程。通过对观察面散斑光强统计特性的分析,提出了采用镜射光强分量法测量表面粗糙度的思想。为验证该方法的有效性,首先用计算机模拟产生具有不同统计特性的随机表面,然后对由随机表面产生的散斑场及其光强分布进行计算。计算结果表明,与传统的散斑对比度法相比,散斑镜射光强分量法测量弱粗糙表面粗糙度具有更大的适用范围和更高的测量精度,克服了散斑对比度法易受表面横向相关长度影响的缺点。通过实验对计算机模拟结果进行了验证。     

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.     

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。     

Fractal structure of digital speckle patterns produced by rough surfaces

We report on the fractal analysis of digital speckle patterns experimentally generated using an optical setup to record the light scattered from metallic rough surfaces in the normal direction. Using the differential box counting technique, we have calculated the fractal dimension of digital speckle patterns for six samples with different roughness. Our results show a quadratic dependence between the surface roughness and the fractal dimension of the corresponding digital speckle pattern. As an application a method to determine the surface roughness of metallic surfaces is proposed.     

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.     

Roughness and correlation-length determination of rough-surface objects using the speckle contrast

A method using the speckle contrast for the determination of both the roughness and the correlation length of surface-height variations of a rough-surface object is proposed on the basis of the statistical properties of the Gaussian speckle field in the image region. The expression for the speckle contrast is first theoretically derived in the optical imaging system as a function of the defocus distance and the surface parameters of the object. By solving the equations expressing the speckle contrasts at the image and defocus planes, a unique solution is found to exist for the roughness and the correlation length. In particular, a useful approximate relation that the roughness depends only on the contrast ratio is derived for relatively small values of the roughness. The experiments were performed to confirm the validity of the proposed method. The present method has an advantage of the simplicity in a measuring procedure where the contrasts at only the two points are required to determine the surface parameters.     

Understanding the exposure-time effect on speckle contrast measurements for laser displays

To evaluate the influence of exposure time on speckle noise for laser displays, speckle contrast measurement method was developed observable at a human eye response time using a high-sensitivity camera which has a signal multiplying function. The nonlinearity of camera light sensitivity was calibrated to measure accurate speckle contrasts, and the measuring lower limit noise of speckle contrast was improved by applying spatial-frequency low pass filter to the captured images. Three commercially available laser displays were measured over a wide range of exposure times from tens of milliseconds to several seconds without adjusting the brightness of laser displays. The speckle contrast of raster-scanned mobile projector without any speckle-reduction device was nearly constant over various exposure times. On the contrary to this, in full-frame projection type laser displays equipped with a temporally-averaging speckle-reduction device, some of their speckle contrasts close to the lower limits noise were slightly increased at the shorter exposure time due to the noise. As a result, the exposure-time effect of speckle contrast could not be observed in our measurements, although it is more reasonable to think that the speckle contrasts of laser displays, which are equipped with the temporally-averaging speckle-reduction device, are dependent on the exposure time. This discrepancy may be attributed to the underestimation of temporal averaging factor. We expected that this method is useful for evaluating various laser displays and clarify the relationship between the speckle noise and the exposure time for a further verification of speckle reduction.     

Effect of surface roughness on the statistical distribution of image speckle intensity

An experimental investigation is made of the effect of surface roughness on the statistical distribution of image speckle intensity. A speckle pattern is formed by spatially coherent light at the image plane of an object having some surface roughness and its statistical properties are investigated. It is found that the contrast of the speckle is related to the surface roughness. By this relation, a new technique for the measurement of surface roughness is proposed.     

Computation of surface roughness using optical correlation

The laser speckle photography is used to calculate the average surface roughness from the autocorrelation function of the aluminum diffuse objects. The computed results of surface roughness obtained from the profile shapes of the autocorrelation function of the diffuser show good agreement with the results obtained by the stylus profile meter.      

Correlation between roughness and porosity in rocks

The porosity of rocks is a very important parameter in the determination of the performance of oil wells. Optical methods allow us to study surface roughness and different materials that have surface properties with random characteristics.Therefore, we have extended these applications to porosity analysis. In our method, we have used the speckle produced by the scattered light from a porous rock, illuminated by a laser beam, and found a linear relationship between the decorrelation of the speckle intensity distribution and the porosity magnitude. In this paper we present the results for samples extracted from oil wells in Argentina.     

Surface roughness measurement by speckle contrast under the illumination of light with arbitrary spectral profile

Quantification of surface roughness greater than a micron is desirable for many industrial and biomedical applications. Polychromatic speckle contrast has been shown theoretically to be able to detect such roughness range using an appropriate light source with a Gaussian spectral shape. In this paper, we extend the theory to arbitrary spectral profile by formulating speckle contrast as a function of spectral profile, surface roughness, and the geometry of speckle formation. Under a far-field set-up, the formulation can be simplified and a calibration curve for contrast and roughness can be calculated. We demonstrated the technique using a blue diode laser with a set of 20 metal surface roughness standards in the range 1–73 μm, and found that the method worked well with both Gaussian and non-Gaussian surfaces.     

3D surface topography from the specular lobe of scattered light

Scattered light from a surface contains a huge amount of information including surface slope, roughness, pattern, texture, etc. In this paper, the relationship between the intensity distribution of scattered light from a surface and the 3D surface topography will be investigated. From the geometrical point of view the intensity distribution of scattered light from a surface may be modelled with three components, the specular spike, specular lobe and diffuse lobe. In the situation when light is scattered from a relatively smooth surface whose roughness is much larger than the wavelength of the incident light, the scattered light intensity distribution will consist of only a diffuse lobe and a specular lobe, which are well described by a combination of the Lambertian and Torrance–Sparrow geometrical models. Based on the light scattering phenomenon, in this paper a scanning method capable of measuring the 3D surface topography with 500 mm scanning width, high scanning speed, and micron resolution is presented. The 3D topography measurement is implemented by using a linear photodiode array to measure scattered light intensity distribution at different angles against the surface normal. Then the specular lobe of the scattered light will be extracted at each scanning point to calculate the surface normal distribution. Sequentially, the 3D surface topography is obtained by using gradient integration techniques.     

激光相干场成像散斑噪声复合去噪方法

噪声是影响激光相干场高分辨成像系统像质的重要因素,激光相干场成像系统既受背景光加性噪声影响,又受激光乘性散斑噪声影响.为解决激光相干场成像系统受激光乘性散斑噪声和背景光加性噪声叠加引起的成像像质退化效应问题,从噪声抑制角度提高激光相干场系统高分辨成像像质,研究建立了激光散斑乘性噪声和背景光加性噪声对大气下行链路激光回波场信号影响干扰模型,并基于该模型提出了一种基于同态滤波和稀疏基追踪级联复合去噪算法.首先基于同态滤波理论将激光乘性散斑噪声转化为加性噪声,再由高通滤波器滤除散斑噪声,最后采用基追踪稀疏理论方法抑制背景光等加性噪声对像质的影响.研究表明,较现有单一去噪方法,该级联复合去噪方法可一次性消除激光乘性散斑噪声和背景加性噪声两种不同性质的噪声,有效改善了激光相干场成像质量.     

Introducing speckle noise maps for Laser Vibrometry

When coherent light scatters from a surface, which is rough on the scale of the wavelength of the light, a speckle pattern is produced. The Laser Vibrometer measures target vibration velocity in the direction of the incident laser beam and typically samples a region of a speckle pattern on its photodetector. Target motions can cause the speckle pattern to change on the photodetector surface, particularly when target motions are non-normal to the direction of the laser beam. This speckle motion modulates the Doppler signal and adds noise to the demodulated output signal. Periodic target motions can cause the speckle noise to become pseudo-random and produce harmonic peaks, with the same fundamental frequency as the genuine target vibrations, which can be indistinguishable from the genuine target vibrations. Typical speckle noise levels are generally considered to be low-level, but they have not so far been adequately quantified. This paper reports preliminary results quantifying speckle noise levels using controlled experimental configurations incorporating periodic in-plane and tilt target motions. Working with commercial Laser Vibrometers, various target surface finishes and treatments are considered and speckle noise maps are produced for each configuration. For a tilting surface, speckle noise has been quantified at approximately 1 μm s^?1/deg s^?1 while, for surfaces with in-plane motion, the sensitivity to speckle noise has been estimated pessimistically at 0.1% of the in-plane velocity. Ultimately, these speckle noise maps will form a valuable practical resource for the Laser Vibrometer user.     

基于激光散斑成像的零件表面粗糙度建模

表面粗糙度是衡量机械表面加工水平的重要参数. 通过构建一套激光散斑成像采集系统, 获取了不同表面加工类型和不同粗糙度值的零件表面激光散斑图像. 应用Tamura纹理特征理论提取图像的纹理粗糙度、对比度、方向度特征, 并分析了这三个特征与表面粗糙度的关系. 发现了纹理粗糙度特征与表面粗糙度的单调关系, 推导出平磨、外磨、研磨三种表面加工工艺的粗糙度值与图像纹理粗糙度特征的数学函数关系, 实现了表面粗糙度的测量. 同时, 利用Tamura纹理特征与加工工艺的依赖关系, 建立了基于贝叶斯网络的工艺识别推理模型, 推理出了零件表面加工工艺. 通过为多种加工类型表面建立粗糙度测量模型, 为粗糙度测量提供了新思路. 实验证明所提的粗糙度测量模型能以较高的准确率识别出零件表面加工类型并测量出其表面粗糙度值.