Multiple scattering in the high-frequency limit with second-order shadowing function from 2D anisotropic rough dielectric surfaces: I. Theoretical study

In this paper the first- and second-order Kirchhoff approximation is applied to study the backscattering enhancement phenomenon, which appears when the surface rms slope is greater than 0.5. The formulation is reduced to the geometric optics approximation in which the second-order illumination function is taken into account. This study is developed for a two-dimensional (2D) anisotropic stationary rough dielectric surface and for any surface slope and height distributions assumed to be statistically even. Using the Weyl representation of the Green function (which introduces an absolute value over the surface elevation in the phase term), the incoherent scattering coefficient under the stationary phase assumption is expressed as the sum of three terms. The incoherent scattering coefficient then requires the numerical computation of a ten- dimensional integral. To reduce the number of numerical integrations, the geometric optics approximation is applied, which assumes that the correlation between two adjacent points is very strong. The model is then proportional to two surface slope probabilities, for which the slopes would specularly reflect the beams in the double scattering process. In addition, the slope distributions are related with each other by a propagating function, which accounts for the second-order illumination function. The companion paper is devoted to the simulation of this model and comparisons with an 'exact' numerical method.     

Multiple scattering in the high-frequency limit with second-order shadowing function from 2D anisotropic rough dielectric surfaces: I. Theoretical study

Abstract

In this paper the first- and second-order Kirchhoff approximation is applied to study the backscattering enhancement phenomenon, which appears when the surface rms slope is greater than 0.5. The formulation is reduced to the geometric optics approximation in which the second-order illumination function is taken into account. This study is developed for a two-dimensional (2D) anisotropic stationary rough dielectric surface and for any surface slope and height distributions assumed to be statistically even. Using the Weyl representation of the Green function (which introduces an absolute value over the surface elevation in the phase term), the incoherent scattering coefficient under the stationary phase assumption is expressed as the sum of three terms. The incoherent scattering coefficient then requires the numerical computation of a ten- dimensional integral. To reduce the number of numerical integrations, the geometric optics approximation is applied, which assumes that the correlation between two adjacent points is very strong. The model is then proportional to two surface slope probabilities, for which the slopes would specularly reflect the beams in the double scattering process. In addition, the slope distributions are related with each other by a propagating function, which accounts for the second-order illumination function. The companion paper is devoted to the simulation of this model and comparisons with an ‘exact’ numerical method.     

Phase shifting speckle shearing polarization interferometer using a birefringent wedge

A digital speckle pattern shearing interferometer is presented which utilizes a single birefringent wedge. Two orthogonally polarized images of an object measured are sheared by the wedge, and the bias phase difference between two polarized images is shifted by translating the wedge. The phase shifting technique applied to speckle pattern shearing interferometry makes it possible to analyze a slope and surface strain numerically. The fringe formation in the present interferometer is analyzed with statistical theory. Experimental results are also presented in two cases: (1) measurement of a slope and normal displacement with a single illumination; (2) simultaneous and separate measurement of a slope and surface strain with two symmetrical illuminations.     

Some photoeffects on the semiconductor surface under sub-bandgap illumination

Surface photovoltage as well as surface photoconductivity response on the light intensity under sub-bandgap illumination is treated. The influence of the surface barrier height, the density of surface traps, the bulk electron density as well the temperature on the surface photovoltage (surface photoconductivity) is analysed. The detectability conditions are included. The consequences of detectability conditions are discussed.     

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     

New figuring model based on surface slope profile for grazing‐incidence reflective optics

Surface slope profile is widely used in the metrology of grazing‐incidence reflective optics instead of surface height profile. Nevertheless, the theoretical and experimental model currently used in deterministic optical figuring processes is based on surface height, not on surface slope. This means that the raw slope profile data from metrology need to be converted to height profile to perform the current height‐based figuring processes. The inevitable measurement noise in the raw slope data will introduce significant cumulative error in the resultant height profiles. As a consequence, this conversion will degrade the determinism of the figuring processes, and will have an impact on the ultimate surface figuring results. To overcome this problem, an innovative figuring model is proposed, which directly uses the raw slope profile data instead of the usual height data as input for the deterministic process. In this paper, first the influence of the measurement noise on the resultant height profile is analyzed, and then a new model is presented; finally a demonstration experiment is carried out using a one‐dimensional ion beam figuring process to demonstrate the validity of our approach.     

Shape and slope measurement by source displacement in shearography

Shearography is a full field non-contact optical technique usually used to measure the gradient of the displacement of a surface subjected to thermal or mechanical loading. This paper describes the use of shearography for surface slope and shape measurement. Interferometric speckle patterns obtained before and after displacement of the optical source are correlated to yield correlation fringes which are, in general, a mixture of slope fringes and carrier fringes. This paper contains a full treatment of the sensitivity of slope fringes to the parameters; the illumination and the imaging geometry and the magnitude and the direction of the source displacement. The slope fringes are corrected for distortion, which is due to the necessary off-axis illumination, and are scaled using parameters calculated using a mathematical model. Experimentally generated phase-stepped slope fringes are unwrapped and integrated to recover the object shape.     

Shaping of nanostructured surface in femtosecond laser ablation of thin films

We report that the nanostructured surface of diamondlike carbon films can be shaped so as to have a sawlike pattern with obliquely incident p-polarized femtosecond laser pulses. The nanoscale surface shape was observed as functions of incident angle, superimposed number and fluence of laser pulses and characterized with height and slope angle of the inclined surface. It is shown that the inclined shape is formed with the non-uniform spatial distribution of the local field enhanced on the nanostructured surface.     

Photostimulated diffusion of atoms adsorbed on a solid surface

A new light-induced effect—surface photodiffusion—is found in the processes of transfer on a solid surface. The essence of the effect is that the energy of electronic excitation of an adsorbed atom is transformed into that of its motion over the surface. It is shown that, under nonuniform illumination of the surface, the adsorbed atoms are moved away from the illuminated region, with the atomic concentration at the boundary between the illuminated and dark regions exceeding the equilibrium value. The dark and photoinduced diffusion coefficients are measured, and the value of the diffusion barrier height is estimated.     

Spontaneous nano pattern formation under pulsed exposure: relaxation kinetics study

Formation of spontaneous surface relief grating under pulsed exposure on the surface of an azo polymer film has been investigated. We did experiments in different repetition rates and pulse widths by use an electro mechanical chopper and a diode-pumped solid-state laser with wavelength of 532?nm as pump beam. Incidence of pump beam, has been set normal to the surface of azo-polymer film. Spontaneous surface relief grating with grating pitch of ~1,250?nm was formed. For low repetition rate, relaxation due to cis-trans isomerization becomes dominant and growth rate becomes slower. A threshold for spontaneous pattern formation was found. In addition to an increase in the diffraction intensity during illumination, anomalous variation of diffraction intensity by switching on and off the laser was observed. By switching off the recording beam sharp enhancement occurred. By switching on the recording beam, after a sharp decrease in the intensity of diffracted beam, it increased further under illumination. Anomalous variations, strongly depends on polarization of the probe beam and the irradiation time for the formation of spontaneous SRG. Sharp enhancement has been attributed to cis-trans thermal isomerization and sharp decrease has been attributed to isomeration in whole surface under illumination.     

Stroboscopic digital speckle pattern interferometry for vibration analysis of microsystem

In this paper, vibration measurement and analysis of microsystems, such as micro-electro-mechanical systems (MEMS) by using stroboscopic digital speckle pattern interferometry (DSPI) is presented. Because of the speckle interferometry, the technique is suited for samples which have a rough surface or whose surfaces can be sprayed into a scattering surface. A laser speckle microinterferometer incorporated with optoelectronic devices for a stroboscopic illumination and a synchronization of the signals between excitation and stroboscopic illumination is described and demonstrated. The system can measure both out-of-plane and in-plane displacement under either a static or dynamic loading. The fundamental is explained and some applications are demonstrated.     

原子力显微镜探针耦合变形下的微观扫描力研究

原子力显微镜(AFM)的微探针系统是典型的微机械构件，它在接触扫描过程处于耦合变形状态.采用数值模拟方法探究恒力模式下探针耦合变形对微观扫描力信号、微观形貌信号的影响.研究表明，AFM的恒力模式扫描中，法向扫描力并不是恒定大小，与轴向扫描力存在耦合作用，在粗糙峰峰值增加阶段，二力均增加；在粗糙峰峰值减小阶段，二力均减小；该耦合作用随形貌坡度、针尖长度等增加而加强.微观形貌的测试信号和横向扫描侧向力信号受探针耦合变形影响较小，但侧向力与形貌斜率密切相关，且其极值点与形貌极值点存在位置偏差，这些结果均与原子力 关键词： 原子力显微镜 探针悬臂梁 耦合变形 扫描力     

基于双自由曲面的LED大角度光学透镜设计

针对直下式LED背光源的均匀照明系统,采用双自由曲面组合,设计了一种大角度光学透镜结构。通过近光源面的自由曲面将光发散成的c/cos3(θ)型光场分布,再利用远光源面实现目标面的均匀分布。这样可以在短距离条件下实现大面积的均匀照明,相对于传统的单自由曲面设计,有效地避免了全反射的发生,提高了照明区域的面积。采用光线追迹软件对所设计的结构进行仿真,通过对模拟结果的分析,在灯箱厚度为15mm时,单透镜均匀照明面积可以达到60mm。采用正三角阵列分布,整个目标面均匀度达到87.5%。相对于传统的大功率器件的直下式光源方式,提高了照明的均匀度,同时大大减少了箱体的厚度。     

Microdeflectometry--a novel tool to acquire three-dimensional microtopography with nanometer height resolution

We introduce "microdeflectometry," a novel technique for measuring the microtopography of specular surfaces. The primary data are the local slope of the surface under test. Measuring the slope instead of the height implies high information efficiency and extreme sensitivity to local shape irregularities. The lateral resolution can be better than 1 microm, whereas the resulting height resolution is in the range of 1nm. Microdeflectometry can be supplemented by methods to expand the depth of field, with the potential to provide quantitative 3D imaging with scanning-electron-microscope-like features.     

Optical velocimetry: a method using two shifted speckle patterns

A new optical method for measuring the lateral velocity of a diffuse object is presented. The speckle pattern, originated by the surface under coherent illumination, is imaged into a linear photodiode array. The scanning time of the array is selected to detect two slightly shifted speckle patterns. By processing the intensity distributions, the velocity of the surface is derived. Some experimental results are shown.     

基于叠层衍射成像的二元光学元件检测研究

本文提出了一种基于叠层衍射成像(ptychography)的二元光学元件的检测方法,该方法可实现对二元光学元件表面微观轮廓的检测以及特征尺寸的标定.相比于传统的二元光学元件检测方法,其使用无透镜成像技术,简化了系统结构并可适用于特殊环境下的检测.该方法可直接通过采集多幅衍射图,利用叠层衍射成像迭代算法可精确地复原大尺寸待测元件的表面微观轮廓,提高大尺寸器件的检测效率.本文模拟仿真了台阶高度与噪声大小对纯相位台阶板复原结果的影响,并在光学实验中选取计算全息板为样品,复原样品的表面微观轮廓信息以及得到台阶高度.以白光干涉仪检测结果为标准,该方法在精度要求不太高的前提下,可获得令人满意的成像质量.     

Impact of polarized illumination on high NA imaging in ArF immersion lithography at 45 nm node

Immersion lithography has been considered as the mainstream technology to extend the feasibility of optical lithography to further technology nodes. Using proper polarized illumination in an immersion lithographic tool is a powerful means to enhance the image quality and process capability for high numerical aperture (NA) imaging. In this paper, the impact of polarized illumination on high NA imaging in ArF immersion lithography for 45 nm dense lines and semi-dense lines is studied by PROLITH simulation. The normalized image log slope (NILS) and exposure defocus (ED) window are simulated under various polarized illumination modes, and the impact of polarized illumination on image quality and process latitude is analyzed.     

A monostatic illumination function with surface reflections from one-dimensional rough surfaces

When solving scattering or emissivity problems for rough surfaces, the shadowing effect is often taken into account. Furthermore, for rough surfaces with large root mean square slope, surface reflections of the incidence or emission ray should not be neglected, especially at large observation angles. In this paper, a model of the monostatic statistical illumination function for one-dimensional rough surfaces with single surface reflection is developed, which is based on the Smith illumination function. A Monte Carlo ray-tracing algorithm is used to evaluate the accuracy of the present model. It is shown that, when neglecting the correlation between heights and slopes of the surface, the present model agrees quite well with the Monte Carlo result. Moreover, the result is improved if the correlation between heights and slopes is taken into account. For practical purposes, an empirical factor is introduced to improve the performance of the uncorrelated first-order illumination function to avoid computing the correlated one, which takes a long computation time. Besides, the first-order illumination function is significant at large observation angles, which could be promising to overcome problems in models of surface infrared emissivity where underestimation occurs compared with experimental measurements.     

Digital correlation of grainy shadow images for surface profile measurement

An optical method, combining the projection of a structured light pattern with the digital correlation technique, is discussed in this paper. This method allows measurement of full-field profile on object surface of about 20 mm square size. Tests on a rotated plane surface have been performed in order to quantify the method capabilities. It is shown that this technique leads to an accuracy of about 1 μm for a spatial resolution of around half a millimeter. Profile measurements of a micro-engraved object and at the crack tip of a polymer sample are also presented. Results give proof that this technique remains efficient even in presence of important height slope.     

Surface Shape Measurement by Phase-Shifting Digital Holography

Surface contouring by phase-shifting digital holography is proposed that provides surface height from a change of reconstructed phase due to tilting of the object illumination. After phase-unwrapping it directly delivers surface shape. Its sensitivity depends on the tilting angle as well as on the initial incident angle. Although the sensitivity is the same as in the conventional fringe projection, a simpler setup is used without imaging lens and measurement depth is increased due to numerical focusing. We also performed noise suppression by employing nonlinear image-data compression technique that considers amplitude values and attained standard height deviation less than 30 #x03BC;m from a flat surface.