Small-slope expansion for electromagnetic-wave diffraction on a rough surface

Abstract

The diffraction and absorption of the plane electromagnetic wave on a rough surface is considered to find the scattering and emissivity of the surface. For this purpose a system of integral equations for unknown surface fields is derived from Green's formula for the Helmholtz equation. The small-slope approach is used to find a solution, i.e. the solution is determined from an expansion over the roughness spectrum that, in the limit of the large-scale roughness, turns out to be the expansion over the slope spectrum.     

To optimal elasticity of adhesives mimicking gecko foot-hairs

Artificial structure of a plate with elastic fibers interacting with rough fractal surface by Van der Waals forces is simulated numerically to find an optimal relation between the system parameters. The force balance equations are solved numerically for different values of elastic constant and variable surface roughness. An optimal elasticity is found to provide maximum cohesion force between the plate and surface. It is shown that high flexibility of the fibers is not always good to efficiency of the system, artificial adhesives must be made from stiff enough polymers. If the ellasticity is close to an optimum, the force is almost constant at a wide interval of the surface roughness. It is desirable to make system adaptive to wide spectrum of applications.     

Mass operator for wave scattering from a slightly random surface

This paper deals with the mass operator representing multiple-scattering effects in the theory of wave scattering from a slightly random surface. By means of the stochastic-functional approach, a recurrence equation for the mass operator is obtained in the form of an iterative integral. However, its solution oscillates in a non-physical manner against the number of iterations. Next, the recurrence equation may be regarded as a nonlinear integral equation, when the number of iterations goes to infinity. An analytical solution of the nonlinear integral equation is presented for a special case in which the roughness spectrum is the Dirac delta function. Then, the nonlinear integral equation is solved numerically for the Gaussian roughness spectrum by iteration, starting from such an analytical solution. It is shown that only a few iterations are required to obtain the mass operator, even when the correlation distance is small. Effects of the mass operators on the coherent reflection coefficient and the incoherent scattering cross section are calculated and shown in figures.     

Application of an acoustic backscatter technique for characterizing the roughness of porous soil

An acoustic backscatter technique proposed by Oelze et al. [J. Acoust. Soc. Am. 109, 1826-1832 (2001)] was used to characterize the roughness of porous soil surfaces. Roughness estimation errors are minimized when the effective flow resistivity of the porous soil is high, e.g., above 300,000 mks Rayls/m. Four soil plots were constructed by roughening soil with farming implements. Three plots were sealed using Saran powder dissolved in methyl ethyl ketone (MEK) and then covered to prevent further weathering. A fourth plot was left in the open and exposed to rainfall, which also acted to seal the surface and further change the roughness. In sealing the surface the effective flow resistivity of the surface was increased above 300,000 mks Rayls/m, which is typical for weathered agricultural surfaces. The roughness power spectra of the soil surfaces were measured by acoustic backscatter and alternatively by a laser profiler. Regression analysis was used to approximate each roughness power spectrum versus roughness wave number with a best-fit line. The best-fit line was used to calculate the rms height and the correlation length of the rough surface by integrating the approximate roughness power spectrum over a range of roughness wave number values. The range of roughness wave number values defines the roughness length scales used in the statistical calculations. High-roughness wave numbers correspond to smaller length scales of roughness and low-roughness wave numbers correspond to larger length scales of roughness. Over certain ranges of roughness wave number values the statistics from the acoustic backscatter and laser profiler measurements is in good agreement. However, as the low-cutoff roughness wave number is decreased and the high-cutoff roughness wave number is increased, agreement between the laser and acoustic techniques diminishes.     

Spatial coherence in the high-frequency limit

Two expressions for the spatial coherence of acoustic signals scattered by a randomly rough pressure-release surface using composite-roughness theory are presented. One model is the conventional result, obtained by splitting the surface spectrum. The second model includes diffractive corrections which in principle remove the first model's dependence on choice of spectral cut-off wavenumber. We find that both models produce outcomes that do not differ significantly from one another, particularly for very high frequencies, for any reasonable choice of spectral wavenumber cut-off. Thus, for the purpose of coherence computations, the diffractive corrections are unnecessary in the high frequency/roughness regime. We show, as well, that in this regime the composite roughness models agree with Kirchhoff integral formulations for the coherence.     

铜薄膜等离子改性及表面增强拉曼光谱的研究

表面增强拉曼光谱(surface-enhanced Raman spectroscopy, SERS)技术是一种基于探测吸附于金属基底表面分子振动光谱的快速无损检测方法,目前广泛应用于表面吸附、电化学催化、传感器、生物医学检测和痕量的检测与分析等领域。本实验采用直流磁控溅射技术在BK7玻璃基底上沉积一层厚度为50 nm的金属铜薄膜,在Ar离子轰击作用下获得不同表面粗糙度的金属铜薄膜样品,从而制备具有不同表面增强拉曼光谱活性的金属基底。实验样品分别通过X射线衍射仪（XRD）、原子力显微镜（AFM）、分光光度计、拉曼光谱仪表征其结构、表面形貌及光学性质。测试结果表明铜膜在Ar离子束轰击前后,样品X射线衍射谱的峰值强度没有发生变化,说明其晶相结构未发生改变;随着离子束能量的增加,薄膜表面粗糙度改变,光学散射强度随着表面粗糙度的增加而增强;离子束薄膜表面改性后,以罗丹明B(Rh B)为探针分子,表征薄膜样品表面增强拉曼的活性,通过对比不同样品表面Rh B的拉曼光谱,发现其光谱强度随金属铜薄膜样品表面粗糙度的增加而增强。     

Negative dependence of surface magnetocrystalline anisotropy energy on film thickness in Co_(33)Fe_(67) alloy

In this work, the magnetocrystalline anisotropy energy(MAE) on the surface of Fe_(33)Co_(67) alloy film is extracted from x-ray magnetic linear dichroism(XMLD) experiments. The result indicates that the surface MAE value is negatively correlated with thickness. Through spectrum calculations and analysis, we find that besides the thickness effect, another principal possible cause may be the shape anisotropy resulting from the presence of interface roughness. These two factors lead to different electron structures on the fermi surface with different exchange fields, which produces different spin–orbit interaction anisotropies.     

Shadowing function with single reflection from anisotropic Gaussian rough surface. Application to Gaussian, Lorentzian and sea correlations

In this paper, the monostatic (transmitter and receiver are located at the same place) and bistatic (transmitter and receiver are distinct) statistical shadowing functions from an anisotropic two-dimensional randomly rough surface are presented. This parameter is especially important in the case of grazing angles for computing the bistatic scattering coefficient in optical and microwave frequencies. The objective of this paper is to extend the previous work (Bourlier C, Berginc G and Saillard J 2002 Waves Random Media 12 145-74), valid for a one-dimensional surface, to a two-dimensional anistropic surface by considering a joint Gaussian process of surface slopes and heights separating two points of the surface. The monostatic average (statistical shadowing function average over the statistical variables) shadowing function is then performed in polar coordinates with respect to the incidence angle, the azimuthal direction and the surface height two-dimensional autocorrelation function. In addition, for a bistatic configuration, it depends on the incidence angle and azimuthal direction of the receiver. For Gaussian and Lorentzian correlation profiles and practically important power-type spectra such as the Pierson-Moskowitz sea roughness spectrum, the numerical solution, obtained from generating the surface Gaussian elevations (Monte Carlo method), is compared with the uncorrelated and correlated models. The results show that the correlation underestimates the shadow slightly, whereas the uncorrelated results weakly overpredict the shadow and are close to the numerical solution.     

粗糙度对岩石热红外光谱解混影响的实验研究

现有的岩石热红外光谱解混,大多针对颗粒岩石,无法满足自然界块状岩石高精度光谱解混的要求。研究将粗糙度作为影响光谱发射率与解混精度的考虑因素,研究块状岩石的热红外光谱解混问题。以自然岩石表面形态为依据,设计了三个粗糙度等级;顾及到岩石的结构情况,采用矿物块体拼接的方法模拟制作了3种块状岩石;通过相同和不同粗糙度的解混实验,来研究自然界块状岩石的表面粗糙度对岩石光谱特征和光谱解混的影响规律。结果表明,当矿物端元与岩石在相同粗糙度下光谱线性解混时,效果较好;而在不同粗糙度下解混时,60个解混结果中有48.3%误差超过5%,最大达到25.3%。基于此,建议在实际岩矿高光谱定量遥感中,应该充分考虑粗糙度对光谱解混的影响。     

Measurements of roughness noise

Experiments have been performed on the roughness noise produced by a two-dimensional turbulent wall jet boundary layer flowing over short fetches of sandpaper roughness. A range of rough surface sizes were studied from hydrodynamically smooth through fully rough. Velocity measurements were made to document the form of the wall jet boundary layer and the influence of the roughness upon it. Acoustic measurements showed background noise levels to be very low so that the sound produced by the rough surfaces could be clearly detected with signal to noise ratios as large as 20 dB. Even hydrodynamically smooth roughness was found to produce noise, conclusively indicating the presence of scattering as a source mechanism. Variations of the roughness noise spectra with flow speed and roughness size are found to be inconsistent with any simple parameter scaling. Boundary layer wall pressure fluctuation measurements made within the roughness fetches reveal a spectral form quite different than the roughness noise, and fluctuation levels some 50-70 dB higher. Despite these differences the wall pressure and roughness noise are found to be very simply related, at least at lower frequencies (<6 kHz). The roughness noise spectrum varies closely as the product of the wall pressure spectrum, the frequency squared, and the mean-square roughness height. This is the scaling predicted by scattering theory and implies a major simplification to the problem of roughness noise prediction for stochastic surfaces.     

Noise of a turbulent boundary layer flow over smooth and rough plates at low mach numbers

The spectral levels of the quadrupole noise generated by a boundary layer flow over a smooth surface are calculated. Explicit dependences of the noise levels on the Reynolds number are obtained for the low-frequency and high-frequency ranges. It is shown that the logarithmic zone of the velocity profile is responsible for the region of the quadrupole noise spectrum with a hyperbolic dependence on frequency. A method of calculating the dipole noise of a boundary layer flow over a rough surface is developed. The method is based on the use of the combined probability density for the turbulent velocity fluctuations and the random dimensions of protuberances of the rough surface. The two constants involved in this theory are determined from a special experiment. It is shown that the surface roughness noticeably increases the radiation levels of a boundary layer flow in a certain frequency range.     

HF ground wave propagation over a curved rough sea surface

For a vertically polarized line source, in the context of HF (3–30?MHz) ground wave propagation over a curved rough sea surface, this paper presents different asymptotic and rigorous methods to compute the attenuation function. When the Earth's curvature is taken into account, the attenuation function is expressed as a series, in which the roots of a differential equation, depending on the Airy function, must be calculated. In addition, from Taylor series expansions, different closed-form expressions can be obtained. For a smooth sea surface, the purpose of this paper is to compare these different formulations with fast rigorous numerical methods, such as the BMIA-CAG (Banded-Matrix-Iterative Approach CAnonical-Grid) and FB-SA (Forward-Backward Spectral-Acceleration) methods, based on the method of moments and originally developed for rough surfaces. These methods are especially efficient to solve a problem with huge unknowns, which is required to predict the ground wave propagation over a long surface. In addition, from a partial fraction expansion of the attenuation function in the Laplace domain, the Bremmer asymptotic expansion is extended to any order by including the surface roughness.     

Rapid determination of surface roughness of polycrystalline silicon following frontside and backside excimer laser irradiation

Excimer-laser crystallization (ELC) is the most commonly employed technology for fabricating low-temperature polycrystalline silicon (LTPS). Investigations on the surface roughness of polycrystalline silicon (poly-Si) thin films have become an important issue because the surface roughness of poly-Si thin films is widely believed to be related to its electrical characteristics. In this study, we develop a simple optical measurement system for rapid surface roughness measurements of poly-Si thin films fabricated by frontside ELC and backside ELC. We find that the incident angle of 20° is a good candidate for measuring the surface roughness of poly-Si thin films. The surface roughness of polycrystalline silicon thin films can be determined rapidly from the reflected peak power density measured by the optical system developed using the prediction equation. The maximum measurement error rate of the optical measurement system developed is less than 9.71%. The savings in measurement time of the surface roughness of poly-Si thin films is up to 83%. The method of backside ELC is suggested for batch production of low-temperature polycrystalline silicon thin-film transistors due to the lower surface roughness of poly-Si films and higher laser-beam utilization efficiency.     

等离子体光栅靶的表面粗糙度对高次谐波产生的影响

极紫外光和软X射线由于其波长和脉冲持续时间极短,可用于超快物理过程和物质微观结构的探测.最近几年,研究人员发现激光和等离子体相互作用可以产生持续时间极短(阿秒)且相干性较好的高次谐波辐射,其波长可接近甚至达到水窗波段.然而,实验研究指出,理论上应出现的一些谐波在实验中并没有出现.本文针对超短超强激光与非理想条件下的等离子体光栅靶相互作用产生高次谐波的物理过程进行了理论分析和粒子模拟.研究结果表明,等离子体光栅的周期性结构对于高次谐波的频谱和辐射角分布存在显著调制效果.光栅靶表面粗糙度直接影响光栅的光学调制效果,改变高次谐波的频谱分布和辐射角分布.理想光栅条件下,满足光栅匹配条件的特定阶数谐波明显获得增强,且辐射张角集中在平行靶面的方向.靶表面粗糙度的出现,导致光栅匹配条件失效,高次谐波能量向各阶分散且辐射张角逐渐偏离靶表面方向.研究结果较好地解释了实验中观测到的谐波频谱分布,为进一步的研究提供了一定参考.     

Numerical, analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement

This paper Presents numerical simulations, theoretical analysis, and millimeter wave experiments for scattering from one-dimensional very rough surfaces. First, numerical simulations are used to investigate the effects of roughness spectrum, height variation, interface medium, polarization, and incident angle on the backscattering enhancement. The enhanced backscattering due to rough surface scattering is divided into two cases; the RMS height close to a wavelength and RMS slope close to unity, and RMS height much smaller than a wavelength with surface wave contributions. Results also show that the enhancement is sensitive to the roughness spectrum. Next, a theory based on the first- and second-order Kirchhoff approximation modified with angular and propagation shadowing is developed. The theoretical solutions provide a physical explanation of backscattering enhancement and agree well with the numerical results. In addition to the scattering of a monochromatic wave, the analytical results of the broadening and lateral spreading of a pulsed beam wave scattering from rough surfaces are also discussed. Finally, the existence of backscattering enhancement from one-dimensional very rough conducting surfaces with exact Gaussian statistics and Gaussian roughness spectrum is verified by a millimeter-wave experiment. Experimental results which show enhanced backscattering for both TE and TM polarizations for different angles of incidence are presented.     

Surface studies of niobium chemically polished under conditions for superconducting radio frequency (SRF) cavity production

The performance of niobium superconducting radiofrequency (SRF) accelerator cavities is strongly impacted by the topmost several nanometers of the active (interior) surface, especially as influenced by the final surface conditioning treatments. We examined the effect of the most commonly employed treatment, buffered chemical polishing (BCP), on polycrystalline niobium sheet over a range of realistic solution flow rates using electron back scatter diffraction (EBSD), stylus profilometry, atomic force microscopy, laboratory XPS and synchrotron (variable photon energy) XPS, seeking to collect statistically significant datasets. We found that the predominant general surface orientation is (1 0 0), but others are also present and at the atomic-level details of surface plane orientation are more complex. The post-etch surface exhibits micron-scale roughness, whose extent does not change with treatment conditions. The outermost surface consists of a few-nm thick layer of niobium pentoxide, whose thickness increases with solution flow rate to a maximum of 1.3-1.4 times that resulting from static solution. The standard deviation of the roughness measurements is ±30% and that of the surface composition is ±5%.     

Measuring surface pressure with far field acoustics

This paper presents measurements of the wavenumber frequency spectrum of wall pressure fluctuations under a turbulent boundary layer made using sound radiated from hydrodynamically smooth ridges in the surface. The measurements also serve as a test of the scattering theory of roughness noise. The radiated sound reveals a cut through the full three-dimensional wavenumber frequency spectrum of the wall pressure at the wavenumber of the surface. Since ridges can be made with very small wavelengths, this technique can be used to probe the structure of the wall pressure spectrum on scales far smaller than those that can be reached using conventional wall-mounted transducers. Furthermore, the method reveals the wavenumber frequency spectrum directly, without the need for multi-point measurements or the spatial Fourier transforming of data. Measured spectra bear a close similarity to Corcos’ and Chase's model forms, and confirm the applicability of the theory of roughness noise and its prediction of roughness noise directivity.     

非接触式可见光-近红外光谱法快速预测天然高分子材料表面粗糙度的研究

利用触针式轮廓法测量了天然高分子材料木材的表面粗糙度,并对可见光-近红外光谱与实测表面粗糙度参数之间的相关性进行研究,探讨了非接触式光谱法快速预测天然高分子材料表面粗糙度的可行性。结果表明：（1）样品三个切面的可见光-近红外光谱（400～2 500 nm）均可预测样品表面粗糙度,实测值与预测值相关系数可达0.92,其中利用样品横切面光谱所建的模型效果最好;（2）在分段光谱400～780 nm,780～1 100 nm,1 100～2 500 nm,780～2 500 nm,400～2 500 nm范围内,所建模型表面粗糙度参数的实测值与预测值相关系数可达0.80以上,显著相关,其中400～2 500 nm区域所建模型效果最好;（3）光谱预处理并不能提高模型预测效果,建议利用可见光-近红外光谱预测天然高分子材料表面粗糙度时采用原始光谱数据。     

Theory of emission spectra from metal films irradiated by low energy electrons near normal incidence

The emission spectrum produced by low energy electrons incident on a rough metal surface has been calculated for a roughness auto-correlation function containing a prominent peak at a high wave vector. For low energy electrons near normal incidence, the high wavevector peak dominates the roughness coupled surface plasmon radiation (RCSPR) process. The calculation yields estimates of the ratio of RCSPR to transition radiation, the dependence of emission intensity on electron energy and the shape and position of the RCSPR peak. The most interesting result is that the high-wavevector roughness can split the RCSPR radiation into peaks lying above and below the asymptotic surface plasma frequency. The results are compared with data from Ag in the following paper.     

Analysis of skin surface roughness by visual assessment and surface measurement

In this study, we analyze the surface roughness of human skin using human visual assessment and statistical features of three-dimensional shape data and goniometric reflectance data. We use eight skin replicas taken from the cheeks of women. First, we perform human visual assessment to obtain the roughness rankings. Second, we measure three roughness parameters by currently used methods. These parameters show no significant correlation with the roughness rankings. Third, we measure the skin surface shape to calculate surface normal vectors. We show that the surface normal distribution of the skin is isotropic and Gaussian, and the standard deviation has a good correlation with the roughness rankings. Finally, we analyze the goniometric reflectance data to approximate the surface reflection using the Oren-Nayar model. We find that the standard deviation estimated using this model corresponds to the roughness rankings. Thus, this parameter can be effectively used for describing skin roughness.