Performance of frequency and/or phase modulated excitation waveforms for optical infrared thermography of CFRPs through thermal wave radar: A simulation study

Following the developments in pulse compression techniques for increased range resolution and higher signal to noise ratio of radio wave radar systems, the concept of thermal wave radar (TWR) was introduced for enhanced depth resolvability in optical infrared thermography. However, considering the highly dispersive and overly damped behavior of heat wave, it is essential to systematically address both the opportunities and the limitations of the approach. In this regard, this paper is dedicated to a detailed analysis of the performance of TWR in inspection of carbon fiber reinforced polymers (CFRPs) through frequency and/or phase modulation of the excitation waveform. In addition to analogue frequency modulated (sweep) and discrete phase modulated (Barker binary coded) waveforms, a new discrete frequency-phase modulated (FPM) excitation waveform is introduced. All waveforms are formulated based on a central frequency so that their performance can be fairly compared to each other and to lock-in thermography at the same frequency. Depth resolvability of the waveforms, in terms of phase and lag of TWR, is firstly analyzed by an analytical solution to the 1D heat wave problem, and further by 3D finite element analysis which takes into account the anisotropic heat diffusivity of CFRPs, the non-uniform heating induced by the optical source and the measurement noise. The spectrum of the defect-induced phase contrast is calculated and, in view of that, the critical influence of the chosen central frequency and the laminate's thickness on the performance of TWR is discussed. Various central frequencies are examined and the outstanding performance of TWR at relatively high excitation frequencies is highlighted, particularly when approaching the so-called blind frequency of a defect.