Study on Properties of Intensity Profiles Scattered from the Self-Affine Fractal Random Surfaces: an Approximate Theory and Simulations

We study the properties of the intensity profiles scattered from the self-affine fractal random surfaces.We use the mathematical decay function to approximate the duple negative exponent function in the rigorous theory of scattering,by letting them have the same maximum value and half-width,and the expression for the half-widths of the intensity profiles in the whole range of the perpendicular wave vector component is obtained.The previous results in the two extreme cases are included in the results of this paper.In the simulational verification,we propose a method for the generation of self-affine fractal random surfaces,using the square-root of Fourier transform of the correlation function of the surface height.The simulated results conform well with the theory.

Analysis and applications of a frequency selective surface via a random distribution method

A novel frequency selective surface （FSS） for reducing radar cross section （RCS） is proposed in this paper. This FSS is based on the random distribution method, so it can be called random surface. In this paper, the stacked patches serving as periodic elements are employed for RCS reduction. Previous work has demonstrated the efficiency by utilizing the microstrip patches, especially for the reflectarray. First, the relevant theory of the method is described. Then a sample of a three-layer variable-sized stacked patch random surface with a dimension of 260 mm x 260 mm is simulated, fabricated, and measured in order to demonstrate the validity of the proposed design. For the normal incidence, the 8-dB RCS reduction can be achieved both by the simulation and the measurement in 8 GHz-13 GHz. The oblique incidence of 30° is also investigated, in which the 7-dB RCS reduction can be obtained in a frequency range of 8 GHz-14 GHz.

The autocorrelation of speckles in deep Fresnel diffraction region and characterizations of random self-affine fractal surfaces

This paper studies the correlation properties of the speckles in the deep Fresnel diffraction region produced by the scattering of rough self-affine fractal surfaces. The autocorrelation function of the speckle intensities is formulated by the combination of the light scattering theory of Kirchhoff approximation and the principles of speckle statistics. We propose a method for extracting the three surface parameters, i.e. the roughness w, the lateral correlation length ξ and the roughness exponent α, from the autocorrelation functions of speckles. This method is verified by simulating the speckle intensities and calculating the speckle autocorrelation function. We also find the phenomenon that for rough surfaces with α= 1, the structure of the speckles resembles that of the surface heights, which results from the effect of the peak and the valley parts of the surface, acting as micro-lenses converging and diverging the light waves.

Modeling bidirectional reflection distribution function of microscale random rough surfaces

The radiative properties of three different materials surfaces with one-dimensional microscale random roughness were obtained with the finite difference time domain method(FDTD) and near-to-far-field transformation.The surface height conforms to the Gaussian probability density function distribution.Various computational modeling issues that affect the accuracy of the predicted properties were discussed.The results show that,for perfect electric conductor(PEC) surfaces,as the surface roughness increases,the magnitude of the spike reduces and eventually the spike disappears,and also as the ratio of root mean square roughness to the surface correlation distance increases,the retroreflection becomes evident.The predicted values of FDTD solutions are in good agreement with the ray tracing and integral equation solutions.The overall trend of bidirectional reflection distribution function(BRDF) of PEC surfaces and silicon surfaces is the same,but the silicon's is much less than the former's.The BRDF difference from two polarization modes for the gold surfaces is little for smaller wavelength,but it is much larger for the longer wavelength and the FDTD simulation results agree well with the measured data.In terms of PEC surfaces,as the incident angle increases,the reflectivity becomes more specular.

A Stochastic Gradient Descent Method for Computational Design of Random Rough Surfaces in Solar Cells

In this work,we develop a stochastic gradient descent method for the computational optimal design of random rough surfaces in thin-film solar cells.We formulate the design problems as random PDE-constrained optimization problems and seek the optimal statistical parameters for the random surfaces.The optimizations at fixed frequency as well as at multiple frequencies and multiple incident angles are investigated.To evaluate the gradient of the objective function,we derive the shape derivatives for the interfaces and apply the adjoint state method to perform the computation.The stochastic gradient descent method evaluates the gradient of the objective function only at a few samples for each iteration,which reduces the computational cost significantly.Various numerical experiments are conducted to illustrate the efficiency of the method and significant increases of the absorptance for the optimal random structures.We also examine the convergence of the stochastic gradient descent algorithm theoretically and prove that the numerical method is convergent under certain assumptions for the random interfaces.

Critical Slope and Plasticity

Limit analysis based on upper bound theorem into slope stability is presented. A rotational failure mechanism (log spiral) passing through the toe in an inclined slope is assumed for getting the critical height. The proposed limit analysis, although on the kinematical admissible velocity field, always satisfies the equilibrium of forces acting on sliced rigid blocks. And the most critical slip surface can be searched by random technique. A new solution scheme is also developed for rapid searching critical slip surface. It is also applicable to a variety of slope models. The method is shown having a high accuracy compared with limit solution for simple slope.

A THREE-DIMENSIONAL RANDOM DISPERSION MODEL WITHIN SURFACE LAYER

Taking advantage of the relation of lateral Lagrangian time scale T_(LY) with the stability and height, we establish a three-dimensional random dispersion model and simulate the dispersing process of a ground source within the surface layer. The results calculated show that under the condition of stable stratifica- tion our model is obviously better improved than those obtained by assuming T_(LY) to be constant, while under unstable condition, not much improved.