Radar Imaging Statistics of Non-Gaussian Rough Surface: A Physics-Based Simulation Study

This paper investigates the radar image statistics of rough surfaces by simulating the scattered signal’s dependence on the surface roughness. Statistically, the roughness characteristics include the height probability density (HPD) and, to the second-order, the power spectral density (PSD). We simulated the radar backscattered signal by computing the far-field scattered field from the rough surface within the antenna beam volume in the context of synthetic aperture radar (SAR) imaging. To account for the non-Gaussian height distribution, we consider microscopic details of the roughness on comparable radar wavelength scales to include specularly, singly, and multiply scatterers. We introduce surface roughness index (RSI) to distinguish the statistical characteristics of rough surfaces with different height distributions. Results suggest that increasing the RMS height does not impact the Gaussian HPD surface but significantly affects the Weibull surface. The results confirm that as the radar frequency increases, or reaches a relatively larger roughness, the surface’s HPD causes significant changes in incoherent scattering due to more frequent multiple scattering contributions. As a result, the speckle move further away from the Rayleigh model. By examining individual RSI, we see that the Gaussian HPD surface is much less sensitive to RMS height than the Weibull HPD surface. We demonstrate that to retrieve the surface parameters (both dielectric and roughness) from the estimated RCS, less accuracy is expected for the non-Gaussian surface than the Gaussian surface under the same conditions. Therefore, results drawn from this study are helpful for system performance evaluations, parameters estimation, and target detection for SAR imaging of a rough surface.

A new technique for modelling phonon scattering processes at rough interfaces and free boundaries of solids

Scattering processes at interfaces and free boundaries of solids strongly affect heat transfer in micro- and nanostructures such as integrated circuits, periodic nanostructures, multilayer thin films, and other nanomaterials. Among many influencing factors, surface roughness due to atomic disorder plays a significant role in the rate of thermal transport. Existing approaches have been developed only for the limiting cases of smooth or completely diffuse surfaces. We have developed a new effective and simple method based on a direct consideration of the scattering of elastic waves from a statistically random profile (using a normal Gaussian surface as an example). This approach, first, allows to generalize common methods for determining the thermal properties of a real random rough surface using simple modifications, and, second, provides a tool for calculating the Kapitza conductance and the effective longitudinal thermal conductivity and studying the influence of roughness on heat transfer.

MODIFIKASI DISTRIBUSI MUATAN BERDASARKAN DISTRIBUSI FERMI-DIRAC DAN APLIKASINYA PADA HUKUM GAUSS

Gauss's law is one of the fundamental laws of physics, especially in the study of electricity. One of the important variable to use Gauss's law is the ability to determine the enclosed charge by the Gaussian surface. Commonly, the definition of the charge distribution of an object is defined by piecewise continuous function. In this paper, a charge distribution model that can accommodate all regions is proposed. The model is constructed based on analogies with the Fermi-Dirac's distribution function. The proposed model contains an exponential function that is related to the radius of an object and is equipped with a parameter to avoid the appearance of a not physical curve. The charge distribution can be used to calculate the enclosed charge by the Gaussian surface and to determine its electrical field. Some of the cases reviewed were spherical solid objects and spherical concentric objects. When compared to the conventional charge distribution, the modified distribution is more straightforward, and it can reduce the computational process algorithm. Therefore this can be used to construct concise and simple computer-based learning media.

A Vector Operation to Extract Second-Order Terrain Derivatives from Digital Elevation Models

Terrain derivatives exhibit surface morphology in various aspects. However, existing spatial change calculation methods for terrain derivatives are based on a mathematical scalar operating system, which may disregard the directional property of the original data to a certain extent. This situation is particularly true in second-order terrain derivatives, in which original data can be terrain derivatives with clear directional properties, such as slope or aspect. Thus, this study proposes a mathematical vector operation method for the calculation of second-order terrain derivatives. Given the examples of the first-order terrain derivatives of slope and aspect, their second-order terrain derivatives are calculated using the proposed vector method. Directional properties are considered and vectorized using the following steps: rotation-type judgment, standardization of initial direction, and vector representation. The proposed vector method is applied to one mathematical Gaussian surface and three different ground landform areas using digital elevation models (DEMs) with 5 and 1 m resolutions. Comparison analysis results between the vector and scalar methods show that the former achieves more reasonable and accurate second-order terrain derivatives than the latter. Moreover, the vector method avoids overexpression or even exaggeration errors. This vector operation concept and its expanded methods can be applied in calculating other terrain derivatives in geomorphometry.

A Model of Mixed Lubrication for the Repeated Sliding Problem Considering the Reloading Characteristic: Application to Ring/Liner Conjunction

Loading, unloading, and reloading of rough surface contacts are common for most friction pairs. However, usually, only loading characteristic is concerned in the modeling of the cyclic loading problem. In this paper, a comprehensive mathematical model of mixed lubrication was developed for the lubricated friction pairs under cyclic loading. The metal contact was calculated by an improved asperity contact model of elastic–plastic with the loading, unloading, and reloading characteristics in consideration. The developed model was applied to the ring/liner conjunction, as its contact problem was the typical cyclic loading problem. Different from the previous studies, assuming the “virgin” topography of the rough surface, the current one accounts for the plastic deformation of surface asperities, occurring during the first few cycles and leading to the significant roughness modification. It appears that considering the reloading characteristics is necessary, whether it is a Gaussian surface contact or a non-Gaussian surface contact.

REFLECTANCE RECONSTRUCTION OF HYPERSPECTRAL IMAGE BASED ON GAUSSIAN SURFACE FITTING

Different from the field of remote sensing, artificial lights are often utilized as the energy source for spectral imaging in the ground hyperspectral applications. The kind of double-spot light source is widely adopted in some large scale ground hyperspectral applications. However, it is hard to reach a satisfied lighting without difference in light intensity in many cases although the lamps are tuned carefully. Therefore, a reflectance calibration of hyperspectral imaging based on the data of diffuse reflectance standard and Gaussian surface fitting is proposed in this paper. The purpose is to improve the reconstruction accuracy of hyperspectral reflectance image by minimized the error caused by the uneven illumination of artificial light source. The method has a higher accuracy than traditional one according to the experiment results.