Quadrature Frequency Modulated Thermal Wave Imaging with Compressive Sensing Technology

Establishing a multi-layered model is a quite common engineering process in the industrial fields such as geophysics exploration and additive manufacturing technology. The excitation of different types of sources in such a model can generate diversified wave modes under the guidance of wave propagation mechanisms. A deep discussion on the characteristics of these wave modes can help us optimize the scale and shape of the model to make it better fit for the industrial production. We extend the Real Axis Integration (RAI) method and improve the Staggered Grid Scheme of the Finite Difference Time Domain (FDTD) method to investigate the wave modes excited by the ring-source and the azimuthally-orthogonal-point-sources with low and high center frequencies in a special multi-layered cylindrical model. We simulate the two types of source excitation methods using both of the RAI method and the FDTD method accurately and efficiently. Mutual comparison on the two modeling methods ensures the validity and reliability of our theoretical analysis and modeling results. The modeling results indicate that the ring-source can only excite wave modes of certain orders. The azimuthally-orthogonal-point-sources can excite pure monopole or multipole wave modes only at the lower frequencies, but at higher frequencies, they might further excite wave modes of higher orders with significant amplitude. These modeling results may guide the design of measurement tools or manufacturing molds, and provide an essential basis for the further analysis on the engineering problems with anisotropic materials and/or eccentric cylindrical conditions.