A computational and statistical framework for multidimensional domain acoustooptic material interrogation

Abstract

Abstract. We consider an electromagnetic interrogation technique in two and three dimensions for identifying the dielectric parameters (including the permittivity, the conductivity and the relaxation time) of a Debye medium. In this technique, a travelling acoustic pressure wave in the Debye medium is used as a virtual reflector for an interrogating microwave electromagnetic pulse that is generated in free space. The reflections of the microwave pulse from the air-Debye interface and from the acoustic pressure wave are recorded at a remote antenna. The data is used in an inverse problem to estimate the locally pressure dependent dielectric parameters of the Debye medium. We present a time domain formulation that is solved using finite differences (FDTD) in time and in space. Perfectly matched layer (PML) absorbing boundary conditions are used to absorb outgoing waves at the finite boundaries of the computational domain, preventing spurious reflections from reentering the domain.Using the method of least squares for the parameter identification problem, we compare two different algorithms (the gradient based Levenberg-Marquardt method and the gradient free, simplex based Nelder-Mead method) in solving an inverse problem to calculate estimates for two or more dielectric parameters. Finally we use statistical error analysis to construct confidence intervals for all the presented estimates, thereby providing a probabilistic statement about the computational procedure with uncertainty aspects of estimates.

Reflection of Microwave Pulses From Acoustic Waves: Summary of Experimental and Computational Studies

“…In [1], finiteelement simulations for a simple 1D geometry demonstrated computationally that EM reflections from the acoustic pulse are possible. These findings were confirmed with 2D computations in [3]. The results of [1,3] consisting of a theoretical framework as well as computational validation of such an approach provide ample motivation for significant "proof-of-concept" experimental investigations of the proposed methodology.…”

“…These findings were confirmed with 2D computations in [3]. The results of [1,3] consisting of a theoretical framework as well as computational validation of such an approach provide ample motivation for significant "proof-of-concept" experimental investigations of the proposed methodology. These prompted our preliminary experiment on which we report here to look for microwave frequency EM reflections from an acoustic pulse.…”

“…Based upon the above literature search and analysis, we estimate the following values for the coefficients of pressure dependence: κ s = 3.74 × 10 −8 Pa −1 and κ τ = −1.05 × 10 −20 s/Pa, with κ ∞ undetermined. As demonstrated in [3], the acoustic reflection is not sensitive to changes in either κ ∞ or κ τ , but is sensitive to changes in κ s . Based on these observations and the low value of κ τ , we chose the following values for our simulations The computational domain is similar to that of [3] and is defined as follows.…”

“…Following the notation in [3] we represent the pressure dependent parameters s , ∞ , and τ as a mean value plus a perturbation that is proportional to the pressure, with the coefficients of pressure designated as κ s , κ ∞ and κ τ , respectively. Based upon the above literature search and analysis, we estimate the following values for the coefficients of pressure dependence: κ s = 3.74 × 10 −8 Pa −1 and κ τ = −1.05 × 10 −20 s/Pa, with κ ∞ undetermined.…”

“…Thus, material density fluctuations produced by a sound wave induce perturbations in the index of refraction. Previous computational work in [1,3] suggested that it might be possible to detect reflections of microwave frequency EM waves from a slowly (relative to the speed of the EM wave) moving acoustic wave front. These efforts focused on reflections in a Debye medium.…”