## 3 Experiments and Discussion  
### Standard Film Samples Measurement  
Figure 4 shows two standard film samples of different thicknesses and varieties used in this study. The wavelength and linearity of the system were calibrated using a mercury/argon lamp, eliminating the effect of high-order dispersion of the probe. The standard film samples were then measured 20 times at the test point to verify the effectiveness and accuracy of the proposed method. Figure 3: Optical configuration (**a**) and photo (**b**) of the proposed measurement system. Figure 5 shows the measurement results of the SiO\({}_{2}\) standard film sample. The certified thickness of the SiO\({}_{2}\) standard film sample is 689.13 \(\pm\) 3 nm, and the refractive index is 1.462. The spectral curve was calibrated to an interference curve with a fixed period in the wavenumber domain, as shown in Figure 5f. Figure 5g shows the power spectral density estimate of the spectral interference signal. The film thickness can be extracted by quadratic linear fitting of the peak value corresponding to the frequency. The extremum method, the Fourier frequency transform method, and the proposed method were respectively used to calculate the film thickness, as shown in Figure 5h. Due to the dark noise of the system, several measurement results of the SiO\({}_{2}\) standard film sample were different. Limited by the sampling rate of the spectrometer, the minimum frequency interval conversion leads to relatively large deviations in the results of the Fourier frequency transform method. However, the proposed method improves the calculation accuracy of film thickness by quadratic linear fitting of 50% of the peak value of the power spectral density. Figure 4: Photo of two standard film samples. Left: SiO\({}_{2}\) on Si thickness standard (Filmetics, TS-SiO\({}_{2}\)-4-7200, San Diego, CA, USA). Right: parylene on Si thickness standard (Filmetics, TS-Parylene-8 um, San Diego, CA, USA). Figure 5: Measurement results of the SiO\({}_{2}\) standard film sample. (**a**) Dark noise curve of the system. (**b**) Reflectance curve of the standard mirror. (**c**) Raw and corrected optical response of the system. (**d**) The original and (**e**) the corrected spectral interference curve in the wavelength domain. (**f**) The corrected spectral interference curve in the wavenumber domain. (**g**) The power spectral density estimate of the spectral interference signal. (**h**) Calculation results of the film by three methods. The detailed calculation results of the SiO\({}_{2}\) standard film sample by the extremum method, the Fourier frequency transform method, and the proposed method are shown in Table 1. The measurement results indicated the mean thickness deviations of these three methods were \(-20.48\) nm, \(-81.22\) nm, and \(-2.61\) nm, respectively. The measurement standard deviations of these three methods were \(1.65\) nm, \(0.26\) nm, and \(0.27\) nm, respectively. Compared with the extremum method and the Fourier frequency transform method, the proposed method was distinguished by a smaller deviation for film thickness. The computing time of the proposed method for a single spectrum was about \(1.17\) ms, which was longer than that of the other two methods. However, the total measurement and computing time of the proposed method was approximately \(3\) ms, which can meet the needs of online inspection in industrial production. The detailed measurement results for the two standard film samples are detailed in Table 2. The certified thickness of the parylene standard film sample is \(7166\) nm, and the refractive index is \(1.661\). The maximum deviations of the multichannel measurement results of the two films were \(-2.61\) nm and \(-15.1\) nm, while the maximum standard deviations were \(0.30\) nm and \(1.1\) nm, respectively. The results demonstrate that the relative deviation of the system is less than \(0.38\%\), and the relative standard deviation is less than \(0.044\%\).