Quantitative Depth Estimation in Lock-In Thermography: Modeling and Correction of Lateral Heat Conduction Effects

Lock-in thermography is a widely used nondestructive testing technique for detecting subsurface defects in solid materials. In this study, one-dimensional analytical modeling and three-dimensional finite element simulations were combined to elucidate how lateral heat conduction influences quantitative depth estimation in titanium alloy material using two inversion strategies: the blind frequency method and the phase difference method. Parametric analyses were conducted for defect radius-to-depth ratios ranging from 0.5 to 8 under various excitation frequencies. Results show that the blind frequency method can significantly underestimate defect depth with errors of up to 20.7% when the radius-to-depth ratio is as small as 0.5. To mitigate this bias, an exponential correction model was developed to compensate for lateral conduction effects, reducing the error to within ±5%. The accuracy of the phase difference method is found to depend jointly on defect depth, excitation frequency, and the ratio of defect radius to thermal diffusion length; estimation errors become negligible when this ratio exceeds 3. The novelty of this work lies in identifying lateral conduction as a key bias source and establishing a quantitative correction framework for the depth inversion based on the blind frequency method. The proposed approach is expected to enhance the accuracy of quantitative thermography for engineering applications.