Roughness Approximation Research Articles

Modeling the effect of random roughness on synthetic aperture sonar image statistics.

A model has been developed to predict the effect of random seafloor roughness on synthetic aperture sonar (SAS) image statistics, based on the composite roughness approximation-a physical scattering model. The continuous variation in scattering strength produced by a random slope field is treated as an intensity scaling on the image speckle produced by the coherent SAS imaging process. Changes in image statistics caused by roughness are quantified in terms of the scintillation index (SI). Factors influencing the SI include the seafloor slope variance, geo-acoustic properties of the seafloor, the probability density function describing the speckle, and the signal-to-noise ratio. Example model-data comparisons are shown for SAS images taken at three different sites using three different high-frequency SAS systems. Agreement between the modeled and measured SI show that it is possible to link range-dependent image statistics to measurable geo-acoustic properties, providing the foundation necessary for solving problems related to the detection of targets using high-frequency imaging sonars, including performance prediction or adaptation of automated detection algorithms. Additionally, this work illustrates the possible use of SAS systems for remote sensing of roughness parameters such as root mean square slope or height.

The entropy of rough neutrosophic multisets

The entropy of rough neutrosophic multisets is introduced to measure the fuzziness degree of rough multisets information. The entropy is defined in two ways, which is the entropy of rough neutrosophic multisets generalize from existing entropy of single value neutrosophic set and the rough neutrosophic multisets entropy based on roughness approximation. The definition is derived from being satisfied in the following conditions required for rough neutrosophic multisets entropy. Note that the entropy will be null when the set is crisp, while maximum if the set is a completely rough neutrosophic multiset. Moreover, the rough neutrosophic multisets entropy and its complement are equal. Also, if the degree of lower and upper approximation for truth membership, indeterminacy membership, and falsity membership of each element decrease, then the sum will decrease. Therefore, this set becomes fuzzier, causing the entropy to increase.

Resolution dependence of rough surface scattering using a power law roughness spectrum.

Contemporary high-resolution sonar systems use broadband pulses and long arrays to achieve high resolution. It is important to understand effects that high-resolution sonar systems might have on quantitative measures of the scattered field due to the seafloor. A quantity called the broadband scattering cross section is defined, appropriate for high-resolution measurements. The dependence of the broadband scattering cross section, σbb, and the scintillation index, SI, on resolution was investigated for one-dimensional rough surfaces with power-law spectra and backscattering geometries. Using integral equations and Fourier synthesis, no resolution dependence of σbb was found. The incoherently averaged frequency-domain scattering cross section has negligible bandwidth dependence. SI increases as resolution increases, grazing angle decreases, and spectral strength increases. This trend is confirmed for center frequencies of 100 and 10 kHz, as well as for power-law spectral exponents of 1.5, 2, and 2.5. The hypothesis that local tilting at the scale of the acoustic resolution is responsible for intensity fluctuations was examined using a representative model for the effect of slopes (inspired by the composite roughness approximation). It was found that slopes are responsible in part for the fluctuations, but other effects, such as multiple scattering and shadowing may also play a role.

Stochastic modelling of three-dimensional particle rebound from isotropic rough wall surface

This paper describes an extension of the two-dimensional approach to particle-rough wall collision modelling (Sommerfeld and Huber, 1999; Konan et al., 2009) to the case of three-dimensional particle rebound from an isotropic rough wall surface. The virtual three-dimensional rough wall is represented as a Gaussian correlated surface. Normal vector angle statistical distributions are investigated in detail for such virtual rough walls, and a statistical modelling approach for these angles is proposed and validated in the frame of the low roughness approximation. Next, deterministic simulations of fully elastic particle collisions with the three-dimensional virtual wall roughness structure are carried out for various particle incident angles. It is shown that the rebound angle, in the bouncing plane of the particle, obeys the distribution given by the two-dimensional modelling approach. However, the three-dimensional structure induces a transverse deviation bouncing angle that obeys a Gaussian distribution with a standard deviation that increases with increase in incident angle. A statistical modelling approach for the virtual wall normal vector seen by any particle for a given incident angle is proposed and validated from deterministic simulation results. The probability that particles make only one rebound is in agreement with the two-dimensional multiple-collision model assumption. A new stochastic procedure for particle-isotropic rough wall interactions in a Lagrangian framework is developed and verified by comparisons with deterministic simulations and available experimental results.

Studies of the influence of deep subwavelength surface roughness on fields of plasmonic thin film based on Lippmann–Schwinger equation in the spectral domain

In this paper, we consider a line source over a plasmonic thin film with surface roughness. Using layered medium Green’s functions, we derive the Lippmann–Schwinger equation in the spectral domain with scattering potentials for the case of surface roughness over a layered medium. Because of deep subwavelength surface roughness, the scattering potentials are next approximated by the small potential approximation, so that the solutions of fields in the spectral domain can be readily computed. Numerical results are illustrated for the surface fields on the rough surface and the fields in the image plane. For periodic roughness, small periods, on the order of 0.1λ, and small heights, on the order of 0.01λ, are used. For the case of random roughness, we choose the correlation length to be much smaller than a wavelength, on the order of 0.1λ, and height on the order of 0.01λ. The results of the fields on the rough surface in the spectral domain show that subwavelength roughness creates fields with wave vector components that are many times larger than the free-space wavenumber (∼10k0 or larger). In the spatial domain, the imaging is enhanced by the deep subwavelength roughness. Results of the small roughness approximation are in good agreement with that of exact potential and that of the method of moments.

Multimodal method and conformal mapping for the scattering by a rough surface

The scattering of a wave from a periodic rough surface in two dimensions is considered. The proposed method is based on the use of a conformal mapping and of the multimodal admittance method. The use of the conformal mappings induces a spatially varying refractive index and transforms the boundary condition on the rough surface into a boundary condition on a flat surface. Then, the multimodal admittance method reduces this problem to a Riccati equation for the modal admittance matrix, which is solved numerically with a Magnus–Möbius scheme. The method is shown to converge exponentially with the number of Fourier modes. The method also allows to find geometries having trapped modes, or quasi-trapped modes, at a given frequency, by looking at singularities, or quasi-singularities, of this Riccati equation. Besides, a simple perturbation expansion, based on a small roughness approximation, is developed.

The Sediment Erosion Rate Flume (SERF): A New Testing Device for Measuring Soil Erosion Rate and Shear Stress

Abstract A new apparatus that measures soil erosion in a flume is described. It is designed to measure a bed material’s erosion rate and approximate its corresponding applied shear stress (erosion function). The apparatus, or Sediment Erosion Rate Flume (SERF), is unlike similar devices, in that during an erosion test, sample advancement is computer-controlled through a feedback loop via a series of lasers, ultrasonic depth sensors, and a Servo-stepper motor. Because of this computerized control mechanism, the SERF can be used to measure near-instantaneous erosion rate as opposed to average erosion rate over an elapsed time domain. Also, included with the SERF is a device that can measure shear stress directly for a sample with a certain uniform roughness. Using the SERF, erosion versus time curves were used to estimate erosion rate for both synthetic and natural samples. For synthetic samples, a roughness approximation was conducted to estimate shear stress. Tests with the shear stress sensor appear to indicate that smooth-wall approximations used in previous flume-style erosion rate testing apparatuses under-predict shear stress. However, further analysis of erosion results indicates that the smooth-wall approximation is conservative; and until a direct method for measuring shear stress is discovered, it may be appropriate for devices like this. Using this rationale, erosion functions were estimated for natural samples.

Roughness scattering in X-ray grazing-incidence telescopes

In the framework of the scalar theory of diffraction, we determine the rms width of the angle spread function degraded by surface roughness in reflective grazing-incidence optics of cylindrical symmetry for X-ray astronomy. Our derivation does not rely on the small roughness approximation, is thus valid for arbitrary roughness values, and takes into full consideration the cylindrical symmetry of the mirrors. The dependence of the rms beam width on both the grazing-incidence angles and the radiation wavelength is studied for both single and double reflection optics, the latter being more relevant to X-ray telescopes. When the small roughness approximation is applicable, we also derive an expression for the angle spread function of the optical system in the presence of roughness scattering that provides the correct expression for the rms beam width.

Angle spread function degradation by surface roughness in imaging optics

A formula is derived for the total width of the angle spread function in an imaging optical system, the performance of which is degraded by surface roughness. The derivation is done in the framework of the scalar theory of diffraction, but it does not rely on the small roughness approximation. The contribution of scattering from surface roughness to the total width of the angle spread function is found to depend only on the variance of the roughness slope. It is also shown that the common rule of obtaining the total width of the angle spread function as a square sum of the pure scattering component and the pure specular component is actually incorrect and does not fully account for the contribution of the specular component.

Extended boundary condition method for scattering and emission from natural surfaces modeled by fractals

The extended boundary condition method with the Weierstrass-Mandelbrot fractal function (WM-EBCM) has been recently employed to model and solve the problem of electromagnetic scattering from natural surfaces. In this paper we first of all show, on the basis of theoretical considerations and of numerical examples, that this method can be used also for the evaluation of electromagnetic emission from natural surfaces. In addition, a small roughness approximation of the WM-EBCM solution is presented to highlight the connection between EBCM and SPM, and to avoid matrix ill-conditioning in scattering problems. Achieved results show that the zero-order scattered field is the (deterministic) field reflected by the mean plane, and that the first-order (random) scattered field is directly proportional to surface roughness. Validity limits of the approximated method are discussed and verified by studying the scattered field behavior at different surface roughness conditions.

Roughness in sputtered multilayers analyzed by transmission electron microscopy and X-ray diffuse scattering

Sputtered W/C multilayers with a period of 25 Å have been studied both by cross-section TEM and by X-ray diffuse scattering using 10 keV synchrotron radiation. Fitting to the X-ray data is aided by the TEM images in modeling the roughness and roughness propagation within the Born approximation. We report on a study of the correctness of the often applied small roughness approximation, and we find that is not well justified in the present case. In order to probe short lateral length scales at q y =0.1 Å −1, diffuse scattering data were obtained in an unconventional scattering geometry.