Development on the reconstruction of photothermal imaging method for subsurface structure

Abstract

The photothermal imaging technique is a nondestructive inspection technique that visualizes the inside of a metal by utilizing the photothermal effect. Although the concept of photothermal imaging techniques has been proposed, systematic research on the characteristics thereof has not been conducted. This study attempts to enhance the measurement and reconstruction process for a photothermal imaging method. To detect the edge of a subsurface pattern more accurate, low-pass FFT (fast Fourier transform) filter for noise reduction of measured data, and derivative detectors are adopted for the reconstruction of photothermal imaging. The adopted methods are applied to and visualize 20 mm × 25 mm × 1.5 mm copper block including radius 5 mm, height 1 mm cylindrical resin as a subsurface pattern. The results show that the developed method can detect the edge of the resin subsurface 50% more accurately than the previous reconstruction method for photothermal imaging.

Graphical abstract

Appendix

In this appendix, we describe in detail the process of obtaining the smoothed result using the low-pass FFT filter from the experimental data in Fig. 4.

To explain the smoothing process, it is necessary to clarify the Fourier transform. Equations (1, 2) are a general expression for Fourier transform. As is already well known, the function of the spatial domain $f(x)$ can be represented by the integration of sinusoidal functions ($e^{{i\omega_{s} x}}$, Euler’s formula) such as sine/cosine, and the amplitude and phase information of the sinusoidal function is included in $F(\omega_{s} )$. Therefore, complex numbers (sinusoidal function), amplitude and phase can be obtained by performing FFT. Figure 8 shows the graphs for the real part of the complex numbers (sinusoidal functions) and amplitude of the FFT result on the experimental data.

Fig. 8

Complex number (real only, a) and amplitude (b) of FFT result

In this study, a low-pass FFT filter is designed based on amplitude to remove noise for small amplitude. To remove the noise, the following transformation process was performed. First, as shown in Fig. 9a, the cutoff spatial frequency is determined as the bottom 5% of amplitude for the maximum one the FFT result. According to the cutoff spatial frequency, only the lower spatial frequency signals than the 5% cutoff one are left from the experimental result, as shown in Fig. 9a. Then, the filtered FFT result using the low-pass filter (which depends on the filter criteria) is restored to a smoothed signal through the IFFT. The same transformation process applies to all other filter criteria (1%, 0.5%, 0.05%).

Fig. 9

Cutoff region for complex number (real only, a) and amplitude (b) of FFT result