A New Method for Measuring Scattering of Light from Optical Surfaces with Random Roughness

In this letter we report a new method for measuring light scattered from optically rough surfaces. By collecting scattered light in a given solid angle, the measurement system does not require a detection unit with an extremely large dynamic range. This in turn significantly simplifies the system configuration. Measurements of scattering close to specular reflection (the so-called small angle or near-specular scattering) also can be completed without any difficulty. Unlike in the common angle resolved scattering (ARS) measurement system, in this system a linear movement instead of rotation is adopted to scan scattered light. In this way, the angular resolution of scattering measurements is independent of the resolution of the translation stages and may be adjusted.     

表面上方微粒及微粗糙度偏振光散射特性

为了区分由表面上方微粒和表面微粗糙度两种散射机理引起的散射光,利用偏振双向反射分布函数,并借助于由,■,■组成的正交右手基组表示了入射电场和散射电场。从理论上给出了两种不同散射机理在不同偏振状态下的双向反射分布函数与入射面外方位角之间的变化关系,并通过对这两种散射机理下的偏振双向反射分布函数的比较发现,利用p偏振入射产生的p偏振散射光(BRDFpp)可以将表面上方微粒和表面微粗糙度两种散射机理区分开来。     

基于偏振门的动态光散射颗粒测量法的研究

为了解决动态光散射纳米颗粒测量技术无法测量高浓度颗粒粒径的难题,提出了一种基于偏振门的动态光散射测量法。从动态光散射和Mie理论出发,理论分析了在高浓度溶液下多重散射效应对散射光偏振态和颗粒粒度测量结果的影响。根据散射光偏振特点,结合偏振门检测技术,改进了传统的动态光散射光学系统。实验研究了在低浓度和高浓度溶液时,不同偏振角度下的散射光强和粒度测量值,完善了散射光的偏振理论。采用90°偏振门检偏,通过各种浓度下的实验,证明了方法的可行性。该方法较之目前同类方法具有原理和结构简单,系统易于维护的特点。     

The modified Beckmann–Kirchhoff scattering theory for surface characteristics in-process measurement

This paper focuses on how the scattering theory can be applied to the analysis of the surface characteristics in an in-process optical measurement. The mean scattered intensity distributions from a surface without and with the additional layers are presented based on the modified Beckmann–Kirchhoff scattering theory. The results show that the introduction of the additional layers only affects rough surfaces. The light scattered from a rough surface under the additional layers seems to be scattered from a bare rough surface with a different surface parameter in the small angle approximation. The experiment is conducted with pixel gray value measurement along the main direction of light scattering stripe to verify the theoretical analysis. The experimental curves can well fit the proposed model, which testifies the correction of the modified Beckmann–Kirchhoff scattering theory.     

An angular cutoff composite model for investigation on electromagnetic scattering from two-dimensional rough sea surfaces

Based on the local configuration angle division to select the corresponding method for electromagnetic scattering calculation from rough sea surface,this paper presents an angular cutoff composite model:when the local scattered angle is in the specular region that is given by an approximately 20 degrees cone around the specular direction,the Kirchhoff approximation is applied to evaluate the specular reflection,which dominates the total scattering in this region;the small perturbation method is employed to handle the diffuse reflection which is predominant as the local scattered angle is situated out of the specular region.Numerical results are compared with those of experimental and theoretical models in several configurations as a function of incident angle,wind speed,wind direction.The comparison of numerical results of other experimental and theoretical models in several configurations shows that the new composite model is robust to give accurate numerical evaluations for the sea surface scattering.     

Multiple scattering of plasmons at rough surfaces

We investigated the polarization and angle dependence of the scattered light intensity of surface plasma oscillations (SPO) propagating along rough silver surfaces. The rough silver films were prepared using the methods of pre-evaporating CaF₂ and silver on heated substrates. The scattered light intensity of both systems is explained by surface scattering effects. Differences of the light intensities between the rough silver films prepared by the two methods mainly were observed in “restlight intensities”, which cannot be described by first-order scattering theories. We explain these differences by higher order scattering effects.     

Effect of wall scattering on SNR in off-axis differential-type laser Doppler velocimetry

Though various properties and applications of laser Doppler velocimetry have been extensively studied in the past decade, there is little discussion on the effect of light scattering from the surface of a cell on Doppler beat signals or on methods of reducing it. In this paper, the effect of light scattering from the surface of the cell is treated as a background noise and is studied theoretically and experimentally on the detecting process of Doppler beat signals in off-axis differential-type laser Doppler velocimetry. Laser Doppler velocimetry of an off-axis type is verified to be effective for measurement of the flow velocity in the vicinity of a scattering wall. The effect of the light scattered from the wall surface on the signal-to-noise ratio (SNR) of Doppler beat signals is discussed in detail. The minimum distance, which is close to the wall and at which good Doppler beat signals can be obtained, is defined and determined quantitatively. This minimum distance is found to be strongly affected by the off-axis angle of the detecting optical system.     

Particle Manipulation by Ultrasonic Standing Wave Fields to complement dynamic light scattering experiments

Dynamic light scattering is a widely used technique for the sizing of colloidal suspensions. It is capable of measuring particles across the size range from approximately 1 nm to several microns. However the larger particle sizes tend to pose problems for the interpretation of the scattered light signal either by virtue of their light scattering efficiency relative to the smaller species present or the departure of the scattered light signal from Gaussian statistics. Rapid removal of such particles in-situ could extend the use of dynamic light scattering particularly in on-line analysis or laboratory automated measurement. In this paper a method is demonstrated for the in-situ removal of larger particles in suspension by means of ultrasonic standing waves and concurrent dynamic light scattering measurement. The theory behind ultrasonic particle manipulation and its effect on the motion of the particles is discussed. Data from a scattering cell designed to incorporate the ultrasonic technology is presented showing that dynamic light scattering measurements may be carried out under such conditions. Varying the energy density of the ultrasonic field allows particles greater than a defined cut-off diameter to be removed from the measurement region. Theory shows that the minimum cut-off size may be as small as 100 nm. Results presented here demonstrate complete removal at a lower diameter threshold of approximately 2000 nm.     

Experimental investigation of a modified Beckmann-Kirchhoff scattering theory for the in-process optical measurement of surface quality

An experimental investigation of a modified Beckmann-Kirchhoff scattering theory applied in an in-process optical measurement of surface quality is described. The proposed theory describes the scattered light intensity distribution from a surface with the additional layers, and can be employed to analyze the surface characteristics in in-process measurement. Based on light scattering principle and machine vision method, the surface roughness is extracted to testify the correction of the modified Beckmann-Kirchhoff scattering theory. The experimental apparatus consists of a collimated laser diode, a beam splitter, a screen, a measuring lens and a camera. Test specimens with different surface roughness are studied. The results obtained demonstrate the feasibility of in-process optical measurement of surface quality using the modified model.     

X-ray scattering from a randomly rough surface

Abstract

On the basis of the method of reduced Rayleigh equations we present a simple and reciprocal theory of the coherent and incoherent scattering of x-rays from one- and two-dimensional randomly rough surfaces, that appears to be free from the limitations of earlier theories of such scattering based on the Born and distorted-wave Born approximations. In our approach, the reduced Rayleigh equation for the scattering amplitude(s) is solved perturbatively, with the small parameter of the theory η(ω) = 1 - ε(ω), where ε(ω) is the dielectric function of the scattering medium. The magnitude of η(ω) for x-rays is in the range from 10^?6 to 10^?3, depending on the wavelength of the x-rays. The contributions to the mean differential reflection coefficient from the coherent and incoherent components of the scattered x-rays are calculated through terms of second order in η(ω). The resulting expressions are valid to all orders in the surface profile function. The results for the incoherent scattering display a Yoneda peak when the scattering angle equals the critical angle for total internal reflection from the vacuum-scattering medium interface for a fixed angle of incidence, and when the angle of incidence equals the critical angle for total internal reflection for a fixed scattering angle. The approach used here may also be useful in theoretical studies of the scattering of electromagnetic waves from randomly rough dielectric-dielectric interfaces, when the difference between the dielectric constants on the two sides of the interface is small.     

微小颗粒的光散射数值模拟

简单介绍了以经典Mie理论为基础的光散射测量技术在颗粒直径和颗粒浓度测量中广泛的应用。分别以Mie理论和离散偶极子近似理论(DDA)为基础, 用数值计算方法分析了球型颗粒的光散射特性，给出了微小颗粒对平行入射光散射的强度函数和散射偏振度的数值计算方法。得到了强度函数和偏振度随相关物理参量变化的三维图，为微小颗粒散射研究提供了一种三维视图。计算结果表明：当尺度参量x＜4时，2种方法所得结果差异不大；随尺度参量增大，2种方法所得结果出现较大差异。与经典Mie理论相比，由于离散偶极子近似理论可以解决各种形状的颗粒散射问题，其应用前景更广泛。     

Apparent and real roughness

Some works have studied the light scattering from a rough surface immersed in a liquid, where the light scattered from the immersed rough surface was assumed to be equivalent to that scattered from a fictitious rough surface with a different texture. This work deals with this kind of problems analyzing the light scattered by a reflecting strong scatterer and the light scattered by a rough surface immersed in a transparent liquid. The general Kirchhoff solution for scattering from a rough surface has been used.It is shown that under certain conditions, the mean scattered intensity (MSI) from a surface immersed in a liquid can be quasi-indistinguishable from that scattered from a non-immersed surface with an “equivalent texture”. An expression relating the equivalent texture and the immersed surface texture was obtained.The results of this work allow to evaluate the characteristics of any surface immersed in a liquid with a known refractive index.     

基于杂散光抑制要求的光学表面粗糙度控制方法研究

光学表面加工误差引起的散射是影响光学系统成像性能的重要因素.描述表面总散射能量的均方根粗糙度是评定光学表面粗糙度的通用指标,但因其未能体现散射能量的空间分布,在表征光学表面散射对具体光学系统杂散光性能影响时存在准确度不足的局限.本文基于全积分散射及双向散射分布函数理论,针对杂散光抑制要求提出一种光学表面粗糙度控制的新方法.首先通过分析确定光学表面纹理中影响系统杂散光的空间频率范围,然后度量该频率带限范围内的表面均方根粗糙度,作为控制光学表面粗糙度的指标.以太阳磁场望远镜(MFT)为例进行方法验证,确定主镜表面纹理有效频率范围为0—18 mm~(-1),分析了主镜表面带限均方根粗糙度对MFT杂散光性能的影响.结果表明,带限均方根粗糙度与MFT杂散光性能之间的关系稳定性能大幅提高,由此验证了采用带限均方根粗糙度描述光学表面粗糙度,能更为准确地控制其对具体光学系统杂散光性能的影响.     

光散射聚集速率测定中T矩阵方法的应用

聚集速率是评估胶体体系特性及稳定性的关键参数, 静态光散射和动态光散射则是测量聚集速率的两个重要方法. 然而, 用静态光散射和动态光散射测量聚集速率时, 需要知道有关单粒子和双粒子聚集体光散射特性的数据. 为此, 通常需要把动、静两种方法结合, 才能消去这个数据. 以前各种近似理论曾用来解决这个问题, 但因粒子尺寸和形状的限制, 结果并不理想. 而T矩阵方法可以不受粒子大小和形状的限制计算其光散射特性. 本工作用T矩阵方法直接计算静态光散射和动态光散射所必须的粒子散射特性, 并将该法得到的聚集速率与动静态光散射结合法得到的聚集速率进行了比较, 两者结果很接近. 本工作为简化静态光散射和动态光散射测量聚集速率, 扩展其应用范围开辟了新途径. 关键词： T矩阵')" href="#">T矩阵 光散射法 聚集速率     

Depolarized light scattering from interacting brownian spheres

The initial decay time of the spectrum and the integrated intensity of depolarized light scattered from a system of interacting spherical and optically isotropic colloidal particles as a function of scattering angle is calculated in the double scattering approximation. These quantities can be reduced in the short-time regime to the static structure factor of single scattering, as observed in polarized scattering for systems of intermediate concentrations of colloidal particles. The results are applied to charged polysterene spheres in solutions and it is shown by numerical calculations that the presence of interactions can modify the angular dependence of initial decay time and integrated intensity considerably.     

Signal statistics of laser light scattering

After a brief survey of number fluctuations, a topic of current interest in light scattering research, the theory is developed for a particular case of this type. A laser beam of Gaussian cross section illuminates a volume in which there is a fluctuating number of identical particles. For incoherent detection the scattered intensities are additive. The interest centers on the statistics of the total scattered intensity. Starting from the moment generating function, the distribution function of scattered intensity is computed using two different methods. In an experiment designed to test the computed distributions, agreement between theory and measurement is found if the mean particle number within the scattering volume exceeds 3. The experimental procedure is described and some difficulties are explained which so far did not permit application of the theory for particle numbers much below 3.     

Directional surface plasmon scattering from silver films

We discuss the bright hollow cone of scattered light from a silver film due to surface plasmon excitation. The power per solid angle scattered into the cone on the prism side of the metal film is an order of magnitude greater than that scattered on the air side. By photographing the cone, we obtain the spatial surface roughness spectrum of the metal film. Results of these experiments are compared to linear scattering theory.     

基于后向散射模型的蒸汽湿度测量及仿真

为了更加准确地测量出汽轮机末级蒸汽湿度,为锅炉给水量提供依据,促进汽轮机内部除湿技术的发展,采用了后向角散射法的思路设计了湿蒸汽参数测量模型,并对模型所需物理量进行了详细的计算,为后向散射法测量蒸汽湿度的研究提供参考。通过对模型进行仿真模拟以及实验研究,得到了后向散射光光强数据。通过对比仿真模拟数据与实验数据,验证了该模型的可行性与有效性,对光散射法测量蒸汽湿度的实验分析以及工程实践具有重要意义。     

The angle-limited integrated scattering (ALIS) measurement system for in-workshop inspection of the optical polishing process

A simple angle-limited integrated scattering (ALIS) measurement technique is described. The relation between the measured scattering within a limited solid angle (ALIS) and the root-mean-square (RMS) roughness of the surface under test is investigated. The technique is applied to the in-workshop inspection of the optical polishing process.     

Measurement of roughness of two interfaces of a dielectric film by scattering ellipsometry

The polarization of light scattered by oxide films thermally grown on photolithographically generated microrough silicon surfaces was measured as functions of scattering angle. Using the predictions of first-order vector perturbation theory for scattering from interfacial roughness to interpret the results, the roughness of each interface and the correlation function between the two interfaces can be determined. The results show the spatial frequency dependence of the SiO (2)/Si interface smoothening.