Forward/Inverse problem modeling for defect detection based on Coplanar Capacitance Scanning Imaging technology

Coplanar Capacitance Scanning Imaging (CCSI) is an emerging non-destructive testing (NDT) technique with significant potential for detecting internal defects in insulating materials. Traditional CCSI is primarily used to confirm defect presence, but exhibits limited effectiveness in high-precision imaging of complex boundary defects, severely restricting its engineering applications. This paper proposes a Sensitivity Convolution Mapping Framework (SCMF) to achieve integrated modeling of the forward and inverse problems in CCSI. During the forward problem stage, this method establishes a convolution relationship between dielectric distribution, electric field distribution, and capacitance signals by combining scanning parameters such as electrode size and step size. For the inverse problem, a linear mapping between dielectric distribution and capacitance signals is established through the sensitivity mapping matrix, transforming the dielectric distribution solution into the problem of solving a system of linear equations. SCMF corresponds to the physical scanning process in modeling while theoretically ensuring the full-rank property of the constructed linear system, mathematically guaranteeing the stability of inverse problem solutions. Experimental results demonstrate that SCMF achieves high-precision reconstruction and visualization of complex defect geometries while exhibiting strong generalization capabilities across different electrode configurations and back-end inversion algorithms. This research provides a universal theoretical framework for advancing the application of CCSI in high-precision non-destructive testing.