Near-field microwave non-destructive testing for defect shape and material identification

Abstract

We propose a near-field approach to microwave non-destructive detection and evaluation of defects, which is based on electromagnetic (EM) numerical modeling of the forward problem and on an adjoint-variable approach to the calculation of the response Jacobians of the forward model. The measured response of the structure under test is matched to that of the forward model. The inverse least square problem is solved iteratively by an optimizer. The approach features high computational efficiency due to the use of adjoint-based response sensitivities, which are developed here to handle materials with complex permittivity. It allows the recovery of both shape and material parameters of the defect. Examples of defects in lossy media are considered. The numerical EM analysis is carried out with a frequency-domain solver based on the transmission line method. The initial discretization grid is preserved throughout the optimization iterations.

Keywords:

• Electromagnetic modeling
• Inverse problems
• Non-destructive testing
• Optimization
• Sensitivity analysis

Notes

All matrices and vectors are in bold italics.

We define the gradient operator as a row operator (Haug et al. 1986).

When F represents a real function, equation (7) is where R returns the real value of the complex quantity in the brackets.

For a real-valued response F, the semi-analytical formula (10) is .

The subscripts R and I denote the real and imaginary parts of the complex quantity, respectively.