Single-shot profilometry of rough surfaces using hyperspectral interferometry

The combination of white light interferometry with hyperspectral imaging ("hyperspectral interferometry") is a recently proposed technique for single-shot measurement of 3D surface profiles. We consider for the first time its application to speckled wavefronts from optically rough surfaces. The intensity versus wavenumber signal at each pixel provides unambiguous range information despite the speckle-induced random phase shifts. Experimental results with samples undergoing controlled rigid body translation demonstrate a measurement repeatability of 460 nm for a bandwidth of approximately 30 nm. Potential applications include roughness measurement and coordinate measurement machine probes where rapid data acquisition in noncooperative environments is essential.     

Evaluation of nanoscale roughness measurements on a plasma treated SU-8 polymer surface by atomic force microscopy

A comparison between roughness data obtained with an atomic force microscope (AFM) on different surfaces requires reliable roughness parameters. In order to specify the appropriate parameters for nanoscale roughness measurements, we compared the root mean square (rms) roughness and the relative surface area (sdr) as function of varying scan size, speed and pixel size. By using oxygen plasma (24 kJ) treated SU-8 with an average rms roughness of 2.6 ± 0.5 nm as reference surface, the repeatability of the method was evaluated for dynamic (tapping) and contact mode. The evaluation of AFM images indicated a decrease of the effective tip radius after a few measurements. This degradation of the tip lowers the resolution of the image and can affect roughness measurements.     

Simple method for measurement of surface roughness using spectral interferometry

The phenomenon that correlation between two beams, in a two-beam interferometer, modifies the spectral characteristics of the light field, is used to estimate the average of the roughness of the surfaces. In the case of intensity interferometer, the path difference between the two arms of the interferometer should be less than the coherence length of the light and the light should be quasi-monochromatic. However, the advantage of spectral interferometer is that the light need not be quasi-monochromatic and the path difference could be much more than the coherence length of light. It is found that more the path difference between the two arms of the interferometer, accurate are the measurements of the roughness of the surfaces. This study shows that spectral interferometry enables one to measure average roughness of the surfaces in the subscales of optical wavelengths.     

Roughness measurement of metals using a modified binary speckle image and adaptive optics

This paper proposes an integrated roughness measurement system that is based on adaptive optics (AO) and binary analysis of speckle pattern images. The aim of this study was to demonstrate the necessity for AO compensation in regions containing both heat and fluid flow turbulences. A speckle image was obtained by projecting a laser beam onto the specimen surface, and the laser pattern image reflected from the surface was binarized to experimentally correlate the intensity with the surface roughness. In the absence of the AO correction scheme, induced turbulences can severely increase the residual rms error from 0.14 to 1.4 μm. After a real-time closed-loop AO correction, we can reduce the wavefront root mean square (rms) error to 0.12 μm, which not only compensates for the aberration error from induced disturbances but also improves the overall performance of the optical system. In addition, an AO system having different gains was investigated, and a threshold gain value was found to be able to steadily compensate for the wavefront errors in less than 2 s. Measurement results of five steel samples having roughness ranging from 0.2 to 3.125 μm (0.3λ and 5λ, where λ is the diode laser wavelength) demonstrate an excellent correlation between the intensity distribution of binary images and average roughness with a correlation coefficient of 0.9982. Furthermore, the proposed AO-assisted system is in good agreement with the stylus method and less than 9.73% error values can be consistently obtained.     

Investigation of the performance of an SPR-based optical fiber sensor using finite-difference time domain

Finite-difference time domain (FDTD) method was used to investigate the performance of surface plasmon resonance (SPR)-based optical fiber sensors. The results show that the performance of the fiber sensor can be optimized by choosing a proper combination of metal layer thickness of 40–60 nm and residual cladding thickness of 400–500 nm. Furthermore, the roughness effect of the gold surface layering the fiber sensor is significant in rough surfaces when sigma rms is greater than 5 nm or correlation length is lower than 100 nm.     

Profile of WYKO Corporation

WYKO Corporation is a company which produces optical measurement equipment. It specializes in phase-measuring interferometry systems for a wide variety of applications from measuring microsurface roughness to contouring large surfaces. This paper outlines the history of WYKO and then describes some of the research and development projects now in progress. These projects include multiple-wavelength profiling, holographic interferometry, projected-fringe contouring, and aspheric surface testing.     

Consistency of the Surface Roughness Determined from Soft-X-Ray Reflectance and Surface Profiles Measured Using a Scanning Tunnelling Microscope: Coherence Length of the Soft X-Rays

There exists serious inconsistency between the rms surface roughness determined from the Debye-Waller factor for the soft-x-ray reflectance analysis and that measured with an optical surface profiler. We have measured the surface profile of evaporated films using a scanning tunnelling microscope, and reproduce the profile with the Fourier components whose spatial wavelength is shorter than the coherence length of the incident soft x-rays in the reflectance measurement. The rms surface roughness derived from the high-pass filtered profile agrees well with that determined using the reflectance measurement. This result explains straightforwardly the photon-energy dependence of the surface roughness estimated by the soft-x-ray reflectance method.     

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。     

Ion beam smoothing of indium-containing III-V compound semiconductors

2 has been used for smoothing of rough InAs, InP, and InSb surfaces, prepared by argon ion beam etching (IBE). The evolution of the surface roughness and morphology has been studied by atomic force microscopy (AFM) as a function of the N₂ RIBE process parameters (ion beam energy, ion beam angle of incidence, and ion dose). A drastic improvement of the surface roughness has been observed for ion beam angles near normal incidence and larger than 70° with increasing ion doses. By using this technique, the initial root-mean-square (rms) roughness of, e.g., InSb of about 40 nm could be decreased to about 1 nm. Received: 20 March 1998/Accepted: 24 March 1998     

平面调制靶的正弦波曲面超精密加工与表征

采用超精密车削技术加工微尺度正弦波调制曲面微结构,解决了尖刃金刚石刀具刃磨和刀具对中等关键技术,研究了进给量、背吃刀量和主轴转速等主要切削参数对铜模板表面粗糙度的影响规律。加工出波长为（20～150）m0.5 m﹑峰谷高度差为（0.2～20）m0.1 m的带正弦波调制曲面。采用原子力显微镜对模板表面轮廓扫描,在20 m20 m的范围内,其表面粗糙度均方根值小于10 nm。将正弦波调制曲面测量结果与理论轮廓进行比较,采用最小二乘寻优算法评定轮廓误差。完成了曲面轮廓的功率谱表征,利用加工的曲面微结构制备了平面调制靶,实现正弦波调制曲面轮廓的精确转移。     

Scattering from unidirectional ground steel surfaces in the specular direction

Scattering in the specular direction from unidirectional ground steel surfaces having random roughness is studied theoretically and experimentally. The grooves were oriented perpendicular and parallel to the plane of incidence and were illuminated by a light beam that was smaller than the sample size. Expressions for scattering from a one-dimensional rough surface in the specular direction were derived for the both orientations of the grooves. For the same groove orientations, scattering (λ = 0.633 μm) from the ground surfaces was measured in the specular direction at angles of incidence from 6° to 82°. The measured rms roughnesses of the surfaces were 0.096 μm, 0.143 μm, 0.311 μm, and 0.501 μm, respectively. The measured scattering was independent of the orientation of the grooves for the two smoother surfaces and depended on the groove orientation for the other surfaces. Calculations using the derived expressions taking into account the experimental results show that the scattering is independent of the orientation of the grooves if the rms roughness is no larger than ∼0.16 μm.     

Optimum frequency selection in multifrequency interferometry

We describe a novel technique for measurement of absolute order of interference in multifrequency interferometry. An optimization criterion is introduced that leads to frequency selection formulations that are optimized with respect to the minimum number of frequencies required for achieving the maximum target dynamic range. The method is generalized to N frequencies and gives a definition of measurement reliability. We demonstrate the technique by means of coherent fringe projection for nonintrusive, full-field profilometry. Experimental data for three frequencies are presented.     

An emittance measurement device for a space-charge dominated electron beam

Beam emittance is one of the most important parameters for electron sources. To investigate the beam emittance of the 3.5-cell DC-SC photocathode injector developed at Peking University, a multi-slit emittance measurement device has been designed and manufactured. The designed slit width, mask thickness and beamlet drift length are 100 μ m, 3 mm and 430 mm respectively. It is suitable for the electron beam with energy of about 5 MeV and the average current less than 0.1 mA. The preliminary measurement result of the rms emittance of the electron beam produced by the DC-SC injector is about 5-7 mm·mrad.     

用像差逐项优化法装调离轴三反射镜光学系统

在对复杂光学系统粗装调完成之后 ,利用自准干涉检验的办法 ,采集光学系统各视场的干涉图 ,然后用干涉条纹分析软件算出整个系统波前误差 ,其量值用泽尼克系数来表示 ,通过泽尼克系数与系统的波像差的关系 ,判断要调整的目标值 ,即当前在光学系统中占主导地位的波前误差 ,对主导误差优化 ,得到系统的失调量 ,由光学设计软件确定其正确后 ,进行一次精密装调。然后进行多次这样的计算机迭代和优化 ,直到光学系统达到最好的调整状态。运用此方法来装调大口径 ,长焦距离轴三反射镜系统 ,在波长λ等于 6 32 .8nm时 ,该离轴三反射镜系统中心视场波像差均方根值达到了 0 .0 94λ ,+1°视场和 - 1°视场的均方根值分别为 0 .10 6λ和 0 .12 5λ。     

超光滑光学表面粗糙度的测定

讨论了如何确定及消除光学轮廓仪的系统误差,进而测定超光滑光学表面粗糙度的方法及结果。在Ｚｙｇｏ Ｍａｘｉｍ ３Ｄ５７００ 表面轮廓仪上使用２－５ ×和２０ ×Ｍｉｒａｕ 物镜测量ｒｍｓ 在０－３ｎｍ 左右的超光滑硅片,通过对每个取样区域数据１６ 次相位平均,再对多个取样区域高度数据平均,消除了仪器的系统误差,使超光滑光学表面粗糙度得到精确测量。并使用其它光学轮廓仪对样品做了验证测量。作为比较,在同样条件下测量了０－８ｎｍ 左右的光滑硅片。     

子孔径拼接干涉测量的精度估计方法

作为一种高精度的光学镜面测量方法,子孔径拼接干涉测量的精度指标十分重要,必须对其进行定量估计.提出将子孔径拼接十涉的结果与全口径测试结果进行对比实验,将全口径测试结果作为拼接测量结果的参考真值,讨论了拼接测量精度评价指标及其计算方法.全口径测试与子孔径拼接干涉测量的几何参量并不相同,提出将全口径测试结果与子孔径拼接结果进行最优匹配,其原理与子孔径拼接算法的原理相同.在最优匹配后计算拼接测量精度的评价指标,通过测量实验进行了验证,结果表明最优匹配后的误差指标比未经最优匹配的误差指标减小约48%,证明上述方法是一种定量估计子孔径拼接干涉测量精度的有效方法.     

规则表面形貌的分形和多重分形描述

以6种具有典型特征的生成元构造了6个具有相同rms粗糙度的规则表面,用变分法计算了这些表面的分形维数,结果表明,分形维数可以将具有相同rms粗糙度的表面区分开来,它定量表征了表面的总体形貌。进一步将多重分形的方法应用到对这些表面的分析中,发现多重分形谱可以全面反映表面概率的分布特征。多重分形谱的宽度可以定量表征表面的起伏程度,多重分形谱最大、最小概率子集维数的差别可以统计表面最大、最小概率处的数目比例。 关键词： 粗糙度 分形维数 多重分形谱     

奇异谱分析用于提升双光梳激光测距精度

从含噪数据中提取信号从而提升数据采集系统精度是极为重要的问题.奇异谱分析(singular spectrum analysis,SSA)作为一种无参数频谱估计技术,广泛用于区分系统模型未知情况下的动态系统信号的复杂成分.本文应用SSA方法提取双光梳飞秒激光测距系统中的含噪时间序列的距离信息,数值仿真显示SSA方法可以从含有有色噪声的信号中提取距离信号.实验中,SSA方法成功地从含有量子噪声的测距信号中提取出激光与目标之间的距离信息,提取后的信号有13倍的精度提升.这种方法同样适用于高维信号,如基于飞秒激光测距的高精度、高速率表面形貌测量的图像提取.     

双光路双波长相移干涉显微法测量衍射光学元件形貌

衍射光学元件（ＤＯＥ）表面形貌的测量需要解决因表面结构深度较大和表面不连续给测量带来的困难。本文将双波长测量法的思想推广应用到不连续深结构表面的测量,并提出了一种新型数据处理方法,有效地克服了这些困难。理论分析和测量结果表明,基于这些方法的三维表面形貌测量系统纵向分辨率为０．５ｎｍ,横向分辨率约为０．５μｍ（ＮＡ＝０．４）,在整个纵向测量范围内重复测量精度地１．３ｎｍ,满足了衍射光学元件表面形貌测     

Limits of the hydrodynamic no-slip boundary condition

A controversial point in fluid dynamics is to distinguish the relative importance of surface roughness and fluid-surface intermolecular interactions in determining the boundary condition. Here hydrodynamic forces were compared for flow of Newtonian fluids past surfaces of variable roughness but similar, poorly wetted, surface chemistry. The critical shear stress and shear rate to observe deviations from predictions using the no-slip boundary condition increased nearly exponentially with increasing roughness and diverged at approximately 6 nm rms roughness. We conclude that local intermolecular interactions dominated when the surface was very smooth, but roughness dominated otherwise. This quantifies the limits of both ideas.