DPO-SDF: Differentiable Physical Optics Method with Signed Distance Field for 3-D Reconstruction of Perfect Electric Conductors

Solving 3-D inverse scattering problems (ISPs) through learning-based approaches is a crucial yet challenging task due to the complex 3-D representation and the difficulty in incorporating domain knowledge. This study presents a differentiable physical optics method with signed distance field (DPO-SDF) for 3-D reconstruction of perfect electric conductors (PEC) from scattered electric fields. The DPO-SDF comprises two key components: the model representation part, which uses a signed distance field (SDF) as the continuous geometric representation of the reconstructed model, and the electromagnetic (EM) computation part, which integrates the principles of the physical optics method (PO) to compute the EM fields. Our algorithm takes the configuration of the incident wave as input and outputs the corresponding scattered field, and then optimizes the SDF by minimizing the residual between the output and the measured scattered field. Additionally, two optimization strategies are introduced to enhance the performance of the DPO-SDF. Numerical experiments show that the proposed approach is highly effective for 3-D reconstruction tasks. Furthermore, by leveraging physical knowledge, the DPO-SDF achieves high accuracy with low computational cost.