Reconstruction Of Rough Surface Research Articles

Reconstruction of rough surfaces from a single receiver at grazing angle

AbstractThis article develops a method for recovering a one‐dimensional rough surface profile from scattered wave field, using a single receiver and repeated measurements when the surface is moving with respect to source and receiver. This extends a previously introduced marching method utilizing low grazing angles, and addresses the key issue of the requirement for many simultaneous receivers. The algorithm recovers the surface height below the receiver point step‐by‐step as the surface is moved, using the parabolic wave integral equations. Numerical examples of reconstructed surfaces demonstrate that the method is robust in both Dirichlet and Neumann boundary conditions, and with respect to different roughness characteristics and measurement noise.

Deep learning based ultrasonic reconstruction of rough surface morphology

This paper introduces a methodology to recover the morphology of a complex rough surface from ultrasonic pulse echo measurements with an array of equidistant sensors using the one dimensional convolution neural network (1DCNN). The neural network is trained by the datasets simulated from high-fidelity finite element simulations for surfaces with a range of roughness parameters and is tested on both numerical and real experimental data. To assess the performance of our proposed method, the rough surface reconstruction results from the deep learning approach are compared with those obtained from conventional ultrasonic array imaging methods. Unlike array imaging-based methods that require a large number of sensors (e.g., 128, 64 or 32), the deep learning-based method uses pulse echo signals and can achieve accurate results with much fewer sensors. The developed deep learning approach has the potential to enable low-cost, accurate, and real-time reconstruction of complex surface profiles.

Anisotropic 3D rough surface reconstruction model based on fractal method and its application in contact characteristics

Anisotropic 3D rough surface reconstruction model based on fractal method and its application in contact characteristics

Data-driven reconstruction of rough surfaces from acoustic scattering

This work investigates the use of data-driven approaches for reconstructing rough surfaces from scattered sound. The proposed methods stand as alternatives to matrix inversion, which requires a linearisation of the dependence on the surface parameters. Here, a large dataset was formed from different surface realisations alongside the corresponding scattered acoustic field, estimated through the Kirchhoff Approximation. Limiting this work to the reconstruction of a static surface, K-Nearest Neighbours, Random Forests, and a stochastic approach are compared to recover a parameterisation of surfaces using the scattered acoustical pressure as input. The models are then validated against a laboratory experiment alongside methods highlighted in Dolcetti et. al., JSV, 2021. The models are tested at a frequency that best fits the lab uncertainties, then tested on a broad frequency range. This scheme provides relatively accurate results in comparison to the approaches tested. Estimation errors as well as robustness in the presence of noise are discussed.

Steady-state and dynamic performances of journal bearing based on rough surface reconstruction technology

Steady-state and dynamic performances of journal bearing based on rough surface reconstruction technology

Fractal Characterization on Anisotropy and Fractal Reconstruction of Rough Surface of Granite Under Orthogonal Shear

The anisotropy of three orthogonal surfaces is studied based on the fractal description of profiles and its statistical evaluation. Under shear tests, three granite cubes are prepared for the generation of orthogonal rough surfaces and the morphology reconstruction is based on laser scanning. Four roughness descriptors of asperity height, inclination angle, line length and surface area are proposed for investigating the anisotropy, which is dependent on the skewed normal distribution. The compared distribution of four descriptors for parallel and perpendicular profiles is deeply analysed for the coupled effect of orthogonal roughness. The surface roughness is described by fractal dimension based on the set product of orthogonal fractal profiles. The result shows that the fractal reconstruction describes the anisotropy effectively and the four descriptors show high precision for fractal dimension calculation. Moreover, on the asperity scale, three behaviours of compression–shear, pure shear and tension–shear show different distribution and contribution for roughness determination. With the increasing covering length, the proportion distribution shows the compression–shear dominates the macrobehaviour, which is just dependent on the two other behaviours on the asperity scale. Finally, the separation distribution of proportion line for compression–shear and tension–shear is obtained. The linear relationship with shear strength shows good adaptability for four roughness descriptors to analyse the anisotropy.

Rough surface reconstruction from phaseless single frequency data at grazing angles

We develop a method for the reconstruction of a perfectly reflecting rough surface from phaseless measurements of a field arising from single frequency scattering at grazing angles. Formulations are given for both Dirichlet and Neumann boundary conditions, and numerical experiments are presented in which close agreement is found with the exact solution. The approach is a marching method based on the parabolic integral equation, which recovers the surface progressively in range, and is iterated a small number of times to produce the final result. It is found that the approach is robust with respect to spatially localized perturbations and to measurement noise.

Recovery of rough surface in ducting medium from grazing angle scattered wave

A method is developed for rough surface reconstruction using fields scattered at grazing angles in a medium with a linearly varying refractive index and Neumann boundary condition. This regime represents a ducting medium, bounded by a perfectly conducting surface with a TM incident field or an acoustically hard surface. This significantly extends the iterated marching method, based upon the parabolic integral equation for forward-scattered field components [Chen and Spivack, J. Opt. Soc. Am. A 35, 504–513 (2018)]. The approach, which uses a fixed frequency, is able to accurately recover multiscale surfaces and is found to be robust with respect to measurement noise and localized perturbations.

Rough surface reconstruction of real surfaces for numerical simulations of ultrasonic wave scattering

The scattering of waves by rough surfaces plays a significant role in many fields of physical sciences including ultrasonics where failure surfaces are often rough and their accurate identification is critical. The prediction of the strength of scattering can be hampered when the roughness is not adequately characterised and this is a particular issue when the surface roughness is within an order of the incident wavelength. Here we develop a methodology to reconstruct, and accurately represent, rough surfaces using an AutoRegressive (AR) process that then allows for rapid numerical simulations of ultrasonic wave rough surface scattering in three dimensions. Gaussian, exponential and AR surfaces are reconstructed based on real surface data and the statistics of the surfaces are compared with each other. The statistics from the AR surfaces agree well with those from actual rough surfaces, taken from experimental samples, in terms of the heights as well as the gradients, which are the two main factors in accurately predicting the wave scattering intensities. Ultrasonic rough surface scattering is simulated numerically using the Kirchhoff approximation, and comparisons with Gaussian, exponential, AR and real sample surfaces are performed; scattering intensities found using AR surfaces show the best agreement with the real sample surfaces.

Rough surface reconstruction at grazing angles by an iterated marching method.

An iterated marching method is presented for the reconstruction of rough perfectly reflecting one-dimensional (1D) surfaces from scattered data arising from a scalar wave at grazing incidence. This is based on coupled integral equations adapted from an earlier approach using the parabolic equation, relating the scattered field at a plane to the unknown surface. Taking the flat surface as an initial guess, these are solved here using at most three iterations. The method is applied to scattered field data generated from the full Helmholtz equations. This approach improves stability and self-consistency. The reconstructed surface profiles are found to be in good agreement with the exact forms. The sensitivity with respect to random noise is also investigated, and the algorithm is found to exhibit a type of self-regularization.

Reconstruction of scattering properties of rough air-dielectric boundary

The article is devoted to elaboration of the method of reconstruction of rough surface scattering properties. The object with rough surface is made of transparent dielectric material. Typically these properties are described with bi-directional scattering distribution function (BSDF). Direct measurement of such function is either impossible or very expensive. The suggested solution provides physically reasonable method for the rough surface BSDF reconstruction. The method is based on Monte-Carlo ray tracing simulation for BSDF calculation. Optimization technique is further applied to correctly reconstruct the BSDF. The results of the BSDF reconstruction together with measurement results are presented in the article as well.

Investigation on the reconstruction of roughsurface with hybrid method

Based on the Desantos spectral formalism, using the hybrid method that combines the numerical and approximate algorithms, the reconstruction problem for the one-dimensional rough surface is investigated. For the direct problem, the scattering data is obtained by the numerical algorithm—the method of moments (MOM). For the inverse problem, the profile of rough surface with different roughness is reconstructed by two approximate algorithms—the small perturbation approximation (SPA) and the Kirchhoff approximation (KA) combined with the method of moments. Taking the Gaussian rough surface for example, the numerical results of reconstructed rough surface with different roughness are presented for the hybrid method, and the data are compared and analyzed.

A multi-section approach for rough surface reconstruction via the Kirsch–Kress scheme

We study the reconstruction of three-dimensional rough surfaces via a potential approach. Using single-layer potentials for the solution of shape reconstruction problems was first suggested by Kirsch and Kress in the case of bounded obstacles. The basic idea of this method is the reformulation of the inverse problem in an optimization problem, where the field is approximated by a single-layer potential and the unknown surface is simultaneously fitted as a zero curve of the sum of scattered and incident fields. The key difficulty in the inverse rough surface scattering problem is the unboundedness and non-compactness of the scatterer and the non-compactness of the associated single-layer potential. This significantly changes the setup and rigorous analysis of the optimization problem. We suggest a multi-section approach to the field and surface reconstruction problem. First, we carry out the full convergence analysis of the Kirsch–Kress method for rough surfaces in three dimensions using a semi-finite approach. In particular, we show the existence of an optimal surface and the convergence of the method towards a solution of the inverse problem. Then, we provide the convergence analysis for the multi-section method. This extends recent results of Heinemeyer et al (2008 SIAM J. Numer. Anal. 46 (4) 1780–98) from the direct to the inverse problem. Finally, we study reconstructions of a finite section of the unknown scatterer. The numerical results prove the feasibility of the approach.

Imaging of Rough Surfaces Having Impedance Boundary Condition by the Use of Newton Iterative Algorithm

In this letter, an inverse scattering problem for the reconstruction of rough surfaces having standard impedance boundary condition (IBC) is presented. The method presented in this letter is the extension of a method given by Yapar to the case of IBC. The reconstruction is obtained from the scattered field measurements for a plane wave illumination of the inaccessible rough surface. Through a special representation of the scattered field in terms of a Fourier transformation and a Taylor series expansion, the problem is first reduced to a nonlinear operator equation. Then, this nonlinear equation is iteratively solved via the Newton method. Numerical results show that the method produces quite satisfactory results regardless of the values of the impedance.

A Time Domain Algorithm on the Reconstruction of RoughSurfaces

We consider the inverse scattering problem of a perfectly conductingone-dimensional rough surface in the case that the incident field isunnecessary to be time harmonic. Based on our previous investigation ofthe frequency domain algorithm, a new time domain algorithm is proposed,in which we approximate the incident pulse by a finite sum of timeharmonic fields and then apply the frequency domain algorithm for timeharmonic waves. Numerical experiments indicate that the time domainalgorithm shows great accuracy of reconstruction of the surface profileand yields significant improvement than the frequency domain algorithm.

3D Reconstruction of Rough Surfaces by SEM Stereo Imaging

The paper describes the current state of a multidisciplinary research project which aims to apply advanced stereovision methods to the 3D reconstruction of rough surfaces using scanning electron microscopy (SEM) imaging. SEM stereo imaging compares very favourably to atomic force microscopy (AFM) in a medium range corresponding to elevations less than 10 µm and scanned size less than 100 µm. But the interest of the stereoscopic method is that it enables to characterise wider fields with higher elevations.