Generalized Virtual-Wave Theory for Photothermal Coherence Tomography under Arbitrary Excitation Toward Non-Contact Industrial Inspection of Composite Materials

Photothermal imaging is a powerful noncontact and nondestructive technique for subsurface inspection of composite materials, yet its performance is fundamentally limited by the diffusive and irreversible nature of heat transport, leading to severe image blurring and ambiguous depth interpretation. The concept of virtual waves provides a route to overcome this limitation by linking diffusion fields to propagating wave fields, but existing approaches are largely restricted to idealized impulsive excitation. Here, we propose a generalized virtual-wave photothermal tomography framework that extends the diffusion-to-wave transformation to arbitrary boundary excitations, including pulsed, harmonic, and chirped waveforms. Starting from the heat equation with a general source term, we derive a Fredholm integral mapping between the measured diffusion field and a virtual wave field governed by a wave equation, explicitly enforcing causality and thermodynamic irreversibility. The resulting ill-posed inverse problem is solved using ADMM or truncated SVD, depending on the excitation characteristics. Numerical and experimental results demonstrate that the proposed method converts blurred thermal responses into wave-like fields with clear wavefronts and reflections, enabling improved depth localization and tomographic reconstruction. Experiments on carbon fiber reinforced polymer samples with embedded defects show enhanced contrast, sharper boundaries, and more reliable depth interpretation compared with conventional thermographic techniques. This work establishes a unified and physically grounded framework for wave-based photothermal tomography under realistic excitation conditions.