Frequency-phase modulated waveform optimization for depth-resolved thermal wave radar imaging of carbon steel defects

Carbon steel components are widely used in petrochemical pipelines, welded structures, and pressure equipment. However, internal defects such as pores, slag inclusions, cracks, and corrosion-induced wall thinning can compromise structural integrity. Thermal wave radar (TWR) combines modulated thermal excitation with matched filtering and can improve defect signal-to-noise ratio and depth-resolved imaging performance in active infrared inspection. To address the weak surface thermal response of deep defects in carbon steel, which is associated with high thermal conductivity and pronounced lateral heat diffusion, this study investigates the applicability of frequency-phase modulated (FPM) excitation for depth-resolved characterization of internal defects in carbon steel. A three-dimensional transient heat-transfer model of a carbon-steel plate containing flat-bottom-hole defects is first established, and the calculation procedures for the modulated heat flux, thermal diffusion length, matched filtering, time-lag features, and phase features are formulated. Finite-element simulations and experimental validation are then conducted for sinusoidal, sweep, Barker-coded, and FPM waveforms under identical center frequency, excitation duration, and sampling conditions.The results show that FPM excitation produces clearer time-lag and phase maps in carbon-steel TWR imaging, particularly for moderately buried and weak-response defects. Finite-element simulations show that the defect/background feature contrast increases with defect diameter and decreases with burial depth under FPM excitation. Experimental results show that FPM excitation increases the feature-map SNR by 45%, 52%, and 125.8% relative to Barker-coded, sinusoidal, and sweep excitation, respectively. These results indicate that, under the investigated conditions, FPM excitation can improve TWR feature contrast and defect visibility in carbon-steel specimens and support further waveform optimization for infrared nondestructive testing.