Multiple scatter of vector electromagnetic waves from rough metal surfaces with infinite slopes using the Kirchhoff approximation

One of the most popular methods for calculating the scattering of light from rough surfaces is the Kirchhoff approximation. A recent modification of the Kirchhoff approximation allows calculation of the scattering of electromagnetic radiation from rough surfaces with very high, or even infinite, slopes, which occurs frequently in, for example, imaging or testing of printed circuits or remote sensing applications. The modification involves a simple change in the way the surface normal is described which removes the explicit dependence of the resulting integral equations on the surface slope, and changing the sampling of the surface, removing the requirement of small slopes for application of the method. In this paper we present the application of the method to vector electromagnetic scattering, using the Stratton-Chu equation, from 2D rough metallic surfaces with infinite slope. The single and double scatter contributions to the total scattered intensity are calculated numerically with this new formulation. Geometrical shadowing is included by using ray tracing directly on the surface. The theoretical basis and preliminary numerical results of the application of this method to vector electromagnetic scattering from simple rough metallic surfaces (plane surfaces with single grooves or with a small number of identical grooves) with infinitely sloped structure are presented.

An efficient geometric modeling method has been proposed for investigation on the properties of the electromagnetic (EM) scattering from two-dimensional (2D) rough surface. In this approach, the plane surface related to the rough surface is firstly modeled by the non-uniform rational B-spline (NURBS) surface through the computer aided geometric design (CAGD). Then the rough surface is reconstructed with the parameters of the plane surface and its height function. The method of moments (MOM) is adopted to solve the electric field integral equation (EFIE) with the rooftop basis function and line matching technique. Moreover, based on the message passing interface (MPI) platform, the parallel MOM algorithm is presented to reduce the simulation time of a single-processor. The conjugate gradient method (CGM) is developed to solve the matrix equation and parallelized with the impedance matrix divided to different processors by lines according to the property of MPI. The validity of this approach is shown by comparing to the flat triangular patch. Some numerical simulations are also exhibited and analyzed.

The aim of this work is to design an off-line system, method and experimental set-up for predicting surface roughness (Ra) of metal surfaces with the help of audio signals. The frictional contact between a metal surface and sharp pencil like scratching tool will produce audio signals which vary based on the roughness of the surface. The samples considered to design and validate the concept are work pieces machined with metal cutting processes such as Turning and Grinding. Several audio signals are generated from various types of metal surfaces produced by these processes after the completion of the machining process away from the machining area in an enclosed chamber. The audio waves are captured with the help of a microphone fixed inside the chamber. These audio signals are processed to generate the surface pattern of the relevant surface. The audio signals are then converted to spectrogram and normalized histogram plots with the help of MATLAB, based on which the roughness of the surfaces is predicted. An experimental set-up is designed which provides a sound-proof environment to capture and record the audio signals. The proposed system, method and set-up are validated with the actual surface roughness of the chosen surfaces measured with the help of a surface roughness measurement instrument.

Titanium alloys are considered as 'metals of future' because of their exceptional properties such as high strength to weight ratio, high specific strength, corrosion resistance etc and there is a crucial need to develop cost effective methods for their machining. The present paper highlights the analysis of variation of objective functions namely, metal removal rate, surface roughness and dimensional deviation depending upon the process parameters of wire electric discharge machining in machining of Ti 6-2-4-2 alloy. Box-Behnken designs are used to plan and analyse the experiments. Mathematical models are developed for metal removal rate, surface roughness and dimensional deviation using regression technique and consequently opted for optimisation of objective functions. As the parametric effect on metal removal rate, surface roughness and dimensional deviation is opposite, the problem is considered a multi objective optimisation problem. Pareto optimal solutions satisfying the conflicting objective functions are obtained using non-dominated sorting algorithm -II. The solutions obtained so can be utilised as machining recommendations to set levels of process parameters to satisfy the set of aforesaid process yield criteria.

In present work, abrasive waterjet machining has been used to machine adhesively bonded titanium-carbon fiber-reinforced plastics-titanium hybrid laminate with varying traverse speed, jet pressure, and stand-off distance. The effect of varying abrasive waterjet machining parameters on cut quality has been quantified by material removal rate, metal composite interface damage factor, taper ratio ( T r), and surface roughness (Ra). Response surface methodology along with central composite design has been used to analyze the influence of process parameters on output responses. Additionally, analysis of variance was performed to identify the significant parameters on the output responses. For better abrasive waterjet cut quality, the optimal values of process parameters obtained were 200 MPa jet pressure, 237.693 mm/min traverse speed, and 1 mm stand-off distance. The corresponding material removal rate, metal composite interface damage factor, taper ratio, and surface roughness are 5.388 mm3/s, 1.41, 1.16, and 3.827 µm, respectively. Furthermore, validation tests have been performed with obtained optimal parameters that deliver satisfactory outcomes with an error of 5.35%, 3.07%, 2.29%, and 0.39% for material removal rate, metal composite interface damage factor, taper ratio, and surface roughness, respectively.

This paper presents a theory of scattering from very rough metallic and dielectric surfaces using the first- and second-order Kirchhoff approximations (KA) modified with the angular and propagation shadowing. The shadowing functions limit the single and double scattered waves which are illuminated and not shadowed by the surface. The theoretical results are compared with the Monte Carlo simulations showing the range of validity of the theory. The theory is applicable to the range where the RMS height is close to a wavelength and the RMS slope is close to unity, and the second medium is lossy. The second-order scattering includes two waves travelling in opposite directions on the surface, giving a physical explanation of the enhanced backscattering.

Surface-enhanced Raman scattering (SERS) spectroscopy is a popular technique for detecting chemicals in small quantities. Rough metallic surfaces with nanofeatures are some of the most widespread and commercially successful substrates for efficient SERS measurements. A rough metallic surface creates a high-density random distribution of so-called "hot spots" with local optical field enhancement causing Raman signal to increase. In this Letter, we revisit the classic SERS experiment [Surf. Sci.158, 229 (1985)SUSCAS0039-602810.1016/0039-6028(85)90297-3] with rough metallic surfaces covered by a thin layer of copper phthalocyanine molecules. As a modification to the classic configuration, we apply an adaptive wavefront correction of a laser beam profile. As a result, we demonstrate an increase in brightness of local SERS hot spots and redistribution of Raman signal over the substrate area. We hypothesize that the improvement is due to optimal coupling of the shaped laser beam to the random plasmonic nanoantenna configurations. We show that the proposed adaptive-SERS modification is independent of the exact structure of the surface roughness and topography, works with many rough surfaces, and gives brighter Raman hot spots in comparison with conventional SERS measurements. We prove that the adaptive SERS is a powerful instrument for improving SERS sensitivity.

This paper investigates on electrochemical micromachining of woven fabric masked stainless steel SS304 using 0.5 mm copper tool electrode with sodium nitrate (NaNO3) Electrolyte. Investigation is carried out to express the performance measures of micro hole such as metal removal rate (MRR), taper angle (TA) and surface roughness (SR). The experimental plan is based on taguchi L16 orthogonal array. Various input process parameters such as voltage, duty ratio, rotational speed, feed rate of tool and electrolyte concentration are varied at four levels. Significant contributions by input process parameters for each output responses such as metal removal rate, taper angle and surface roughness are analysed using contour plots. It is evident that significant contribution to metal removal rate mainly depends on rotational Speed and feed rate of tool. Similarly, duty ratio and feed rate of tool are the significant contributors for both taper angle and surface roughness. Multi response optimization are done for the three output responses using VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method to identify the significant process parameter. Performance score of VIKOR and TOPSIS proved that rotational speed of tool, feed rate and duty ratio are important parameters contributing significantly for precision of microfeatures. Both the multi response optimisation methods mutually concluded the best performance is achieved at voltage 21 V, duty ratio 80%, rotational speed of tool 600 rpm, feed rate of tool 0.8 μm s−1 and electrolyte concentration 0.2 M. The confirmation test showed an improvement of performance grade by approximately 0.245.

The effects of surface roughness on the optical properties of metals have been discussed by comparing experimental results of ellipsometry with theoretical results from the homogeneous effective medium model (HEM), the monolayer effective medium model (MEM) and the gradual density layer model (GDL). A gradual increase of |rp/rs|(=p) has been observed with the increase in surface roughness at a higher angle than θB and gradual decrease at lower angle than θB, where θB is the pseudo-Brewster's angle. Though HEM models do not explain the roughness effect on optical properties, MEM model and GDL model show good explanations for the optical effects from rough metal surface, when Δd<<λ.

An approach is introduced for the non-parametric reconstruction of the statistical properties of penetrable, isotropic randomly rough surfaces from in-plane, co-polarized light scattering data. Starting from expressions within the Kirchhoff approximation for the light scattered diffusely by a two-dimensional randomly rough surface, an analytic expression for the normalized surface height correlation function is obtained as an integral over the in-plane and co-polarized scattering data with the introduction of only a couple of additional approximations. The inversion approach consists of two main steps. In the first step the surface roughness is estimated. Next, this value is used to obtain the functional form of the surface height correlation function without initially assuming any particular form for this function (non-parametric inversion). The input data used in validating this inversion approach consist of in-plane and co-polarized scattering data obtained for different forms of the correlation function by either computer simulations or by experiments for two-dimensional randomly rough dielectric or metallic surfaces. Good agreement was obtained between the correlation function and surface roughness obtained during the reconstruction and the corresponding quantities assumed when generating the input scattering data; this was the case for both dielectric and metallic surfaces, for both p- and s-polarized light, and for different polar angles of incidence. The proposed inversion approach provides an accurate, efficient, robust and contact-less method based on in-plane and co-polarized scattering data for the non-parametric characterization of the statistical properties of isotropic two-dimensional randomly rough dielectric and metallic surface.

Aiming at the importance of the microcosmic topography of connecting surface and bolt assembling technique to the bolt connection performance, the fractal characteristic of bolt joint rough surface is studied based on the power spectrum of its micro surface profile. Fractal models of 2D and 3D rough surfaces are presented by W-M function and the 2D and 3D bolt joint rough surfaces are reconstructed. Imageware and Pro/e are used to build the bolt connecting model based on the real rough surface presented by W-M function. The preload is imitated by the PREST179 element. The finite element transient analysis is used to imitate the speed and force size of the bolt tightening. The relationship model between tighten speed, preload size and connecting performance whose target is contact stress is presented based on the finite element analysis results. According the model, the single bolt precise assembling technique is obtained.

In this paper, the main focus is to study the effect of process parameters of electrical discharge machining on RENE80 nickel super alloy in terms of metal removal rate, surface roughness and radial overcut. The responses of the parameters are analysed using statistical tools such as signal to noise ratio and analysis of variance. Further, multi-response optimisation of maximising metal removal rate and minimising surface roughness and radial overcut is solved using grey relational analysis. It is found that peak current and pulse on time contribute significantly to multi-response optimisation. The results of confirmation experiments indicate improvements in metal removal rate, surface roughness and radial overcut as 16.03%, 34.66% and 10.17% respectively. The surface topography study is done to reveal the machined surface characteristics. Finally, regression models are prepared for these responses and they are found to be satisfactory.

The present work aimed to carry out the machining of EN-42 spring steel in wire electrical discharge machining with zinc-coated brass wire using distilled water as a dielectric medium. The effect of WS2 powder added in a dielectric medium, on the metal removal rate and surface roughness has been evaluated. With the use of WS2, the conductivity of the dielectric is found to be constantly equal to 10 S/m, which is a very promising feature. WS2 enhances dielectric life, metal removal rate, and surface roughness significantly. The effect of cryogenically treated wire on the metal removal rate and surface roughness during machining has been carried out. Taguchi method and genetic algorithm were used to optimize machining performance measures. Both methods provide optimum parameters and target value. The results of the Taguchi method show more error as compared to the genetic algorithm. The on time can be predicted as the most significant parameter according to the Taguchi method. From the results, it is observed that higher on time shows better metal removal rate and lower on time shows a better surface finish.

The wavelength dependence of both the total back-scatter cross section σT and the depolarized back-scatter cross section σD for rough metallic surfaces of known statistical characteristics has been determined experimentally by comparing data at 0.63-, 3.39- and 10.6 μ wavelengths. The rms height from the mean, h, and the mean scale size l of the two surfaces used in the experiment are: h≈1 μ, l≈10 μ; h≈7 μ, l≈50 μ. At or near normal incidence, results show that the total cross section per beam area σT/A0 is independent of wavelength λ, provided that h/λ is greater than approximately 14. When h/λ≤14, σT/A0 increases rapidly with decreasing h/λ. Previous microwave data suggest that the metallic surface reflects nearly as a perfectly smooth surface without significant scattering losses when h/λ≲1/40. At or near normal incidence the ratio of σD to σT varies as (h/l)4λ/4πδ for all values of h/λ studied, where δ is the skin depth of the metallic surface. For incident angles ψ in the range from 20° to 80° and h/λ&gt;14, both σT/A0 and σD/A0 vary as λ−n where n increases with increasing ψ. n has a value of 0.40 (±0.2) at 4ψ=20° and 0.8 (±0.2) at 80°.

Effect of metallic surface roughness on the speckle pattern formation at diffraction plane