Model Random Media Research Articles

Reduction of ultrasonic multiple scattering applied to flaw detection with array probes in polycrystalline materials

Flaw detection using ultrasonic evaluation of coarse-grain steels is perturbed by a high structural noise due to scattering. This leads to a decrease of the detection capabilities, particularly at high frequencies and large depths for which multiple scattering dominates. Recent academic studies have shown that the contribution of multiple scattering could be dramatically reduced. These results were obtained on a model random medium made of parallel steel rods immersed in water. The ability to detect a target could be significantly increased using a specific filtering method, based on the full matrix capture (F.M.C.) combined with a smart post-treatment based on random matrix theory, in supplement with the DORT method (i.e., decomposition of the time-reversal operator). Here, the same technique to separate simple and multiple scattering contributions is now applied to a real material. Experimental results were obtained on a nickel-based alloy (Inconel600®) with a thermically-induced coarse grain structure and manufactured flaws (side drilled holes) at different depths. The experimental set-up used a multi-element ultrasonic array. Results are presented and compared to other detection techniques, at various depths and frequencies. Despite a dominant multiple scattering noise, a significant improvement of the detection performances is observed.

Using convex quadratic programming to model random media with Gaussian random fields

Excursion sets of Gaussian random fields (GRFs) have been frequently used in the literature to model two-phase random media with measurable phase autocorrelation functions. The goal of successful modeling is finding the optimal field autocorrelation function that best approximates the prescribed phase autocorrelation function. In this paper, we present a technique which uses convex quadratic programming to find the best admissible field autocorrelation function under a prescribed discretization. Unlike previous methods, this technique efficiently optimizes over all admissible field autocorrelation functions, instead of optimizing only over a predetermined parametrized family. The results from using this technique indicate that the GRF model is significantly more versatile than observed in previous studies. An application to modeling a base-catalyzed tetraethoxysilane aerogel system given small-angle neutron scattering data is also presented.

Exact Controllability for the Time Dependent Transport Equation

Exact Controllability for the Time Dependent Transport Equation

Dynamic effect of weak localization on the light scattering from random media using ultrafast laser technology

Angle and time resolved experiments on the backscattering of light from model random media are presented. Weak localization was observed using 30-fs laser pulses, where this time scale is shorter than the scattering mean free time of the light in the random medium. This observation implies that the coherent peak is due to interference between the scattered light at the point of observation. The time resolved experiment directly shows that the light rays which undergo longer scattering paths contribute to the narrow coherent peak. A proper description of the temporal profile pulses scattered from random media requires the effect of weak localization to be taken into account.

Estimates of wave front distortion from measurements of scattering by model random media and calf liver.

An expression based on a perturbation method is employed to estimate the correlation of path length difference in a plane normal to the direction of wave propagation from measurements of ultrasonic scattering by model random media and calf liver. The expression gives the correlation function of path length difference in terms of an integral of the correlation function of the medium variations or an equivalent integral of the power spectrum of medium variations, both for a scattering angle of zero degrees. Power spectra derived from measurements of average differential scattering cross section over a spatial-frequency window are used to fit analytic functions that extend over all spatial frequencies. The results for the windowed and unwindowed data yield correlation functions and corresponding power spectra that are used to estimate the correlation function of path length difference. The results suggest that the correlation length in calf liver is less than 100 microns and that a root-mean-square path length variation of about 20 microns results from propagation through a 100-mm calf liver path.

Experimental investigation of the scattering of electromagnetic waves from a model random medium of discrete scatterers

The paper describes a new three‐dimensional physical model of a random discrete‐scatterer medium and presents the results of an experimental investigation to determine the suitability of the model in studies aimed at the evaluation of approximate scattering theory. In contrast to previous models in which the scatterer statistics were indirectly controlled by a physical process, the present model allows the statistics to be directly controlled as in a Monte Carlo computer simulation. It also permits considerable flexibility in the type of scatterers used. The experimental model investigated consisted of a layered slab region of polystyrene foam (142 × 16 × 21 cm) in which polyethylene spheres of 1.27 cm diameter were embedded at random positions. These positions were generated by computer from a uniform distribution. The medium was scanned by a narrow 35‐GHz beam and the randomly varying transmitted field was recorded, sampled, and statistically analyzed. The accuracy of the first and second field moments, determined in experiments on the model with two different average densities of the spherical scatterers, is evaluated.