## 4 Application of the Interferometric Spectral Image System Based on LC Delayers  
Based on the calibration of the optical path difference at different times at a single pixel during the relaxation of the LC, hyperspectral imaging was performed using a resolution chart, where the sample was placed between the imaging lens and the second polarizer. The image was relayed to the high-speed camera. The signal generator was turned off so that the driving voltage (V\({}_{\text{b}}\)) controlling the LC cell changed from 5 V to 0 V. A high-speed camera was used to acquire the spatial interferogram changes during the LC relaxation process over a 20-s period. The desired spectrum was obtained by Fourier processing of 400 images with useful two-dimensional spatial information selected from 10,000 images. By recovering the spectrum for each pixel point, a hyperspectral data cube was obtained and is shown in Figure 8, which characterizes the two-dimensional spatial information and one-dimensional spectral information.  
Figure 9a shows the integrated two-dimensional spatial information acquired using the entire spectrum. Figure 9b-d show the two-dimensional spatial information at different wavelengths. Figure 9e-h, corresponding to Figure 9a-d, respectively, show the one-dimensional intensity information for x = 158 and y values from 200 to 280. Figure 9 shows that the spatial resolution is different for different wavelengths. The spatial resolution is 50.8 LP/mm when the wavelength is 650 nm, whereas the spatial resolution is 40.3 LP/mm when the entire spectrum is included. The spatial resolution of 650 nm is clearly higher than the values obtained for other spectral surfaces.  
Considering the size of the damage point, K9 glass was utilized for the damage analysis of the sample. From Figure 10b, the spectra of the damaged and undamaged points can be obtained. Figure 10c,d indicate the one-dimensional intensity information acquired at x = 203 for the whole spectrum and at 580 nm. In Figure 10c, the minimum size of the damage point detected is 16 \(\upmu\)m, while the minimum size of the damage point is 12 \(\upmu\)m in Figure 10d. The information expressed in Figure 9 is further confirmed in Figure 10c,d. When white light was used as the source of illumination, light waves of different intensities and wavelengths were superimposed on each other, causing the defect information to be obscured or ignored. As shown in Figure 10, it  
Figure 8: The hyperspectral data cube of the resolution chart.  
Figure 7: Recovery spectra of (**a**) 1053 nm and (**b**) halogen light.  
method of spectral imaging for defect detection can identify damage points that are not easily observed using a broadband source. So, choosing a suitable wavelength can improve the spatial resolution. It can be used in optical illumination for machine vision methods by effectively selecting the wavelength or combining multiple wavelengths of the light source. The proposed optical component defect inspection method based on interference spectral imaging on the basis of LC relaxation enables rapid non-destructive testing of optical components.  
Figure 9: (**a**) Integration of the two-dimensional spatial information acquired for the whole spectrum. (**b–d**) The two-dimensional spatial information at 540 nm, 580 nm, and 650 nm. (**e–h**) correspond to (**a–d**) for the intensity information at each point for x = 158 and y values from 200 to 280.