## 4 Results and Discussion  
Figure 4a-d show the sample photo and the evaluation procedure of the PVP film thickness, which was determined to be 1480 nm. The measured and calculated results of CPA, at an incidence angle (\(\theta_{\rm air}\)) of 88.5\({}^{\circ}\), are shown in Figure 5a,b, respectively. The measured reflectance is normalized to a maximum value of 1. From the full width at half maximum of the mercury emission line, the wavelength resolution of the experiment is 2.57 nm.  
Figure 3: The wavelength dependence of the refractive index (\(n_{0}\)) of MgF\({}_{2}\) (**a**), and that of the refractive index (\(n\)) and the extinction coefficient (\(\kappa\)) of PVP (**b**) [20,21].  
Figure 2: (**a**) Experimental setup. (**b**) Definition of the incidence angle in the experiment. The incidence angle for each layer in Figure 1 is determined so that \(n_{\rm air}\sin\left(\frac{\pi}{2}-\theta_{\rm air}\right)=n_{0}\sin\left( \frac{\pi}{2}-\theta_{0}\right)\), \(n_{0}\sin\theta_{0}=n_{1}\sin\theta_{1}\), and \(n_{2}=n_{\rm air}\).  
Figure 5a,b show that the experimental results were close to the calculated results, and that dips with a depth of nearly 90% were observed with the white lamp light source. The calculation shows that a dip with a 99.28% depth can be observed with p-polarization at 783 nm if the ideal measurement is realized. In the experiment, the depth of the dips decreased drastically when the angle of incidence was lower than 87.5 degrees (not shown). In Appendix A, the incidence angle (\(\theta_{\text{air}}\)) dependences of \(|r|^{2}\), the real and imaginary parts of \(r_{01\text{S}}\), \(r_{01\text{P}}\), \(r_{12\text{S}}\), and \(r_{12\text{P}}\) at the wavelengths of the reflectance dips, are calculated to show that the deepest dip reaches 99.41% in depth.  
The reasoning of the experimental CPA being a bit far from the 100% expected from the calculations is that the calculations were made assuming a plane wave (i.e., infinitely wide wavefront) and a perfectly flat and uniform thin film, whereas in the experiments, the beam was not perfectly collimated (because we collimated the light from an incoherent white light source with the finite spot size to a beam diameter of 1.3 mm) with an incidence angle distribution. Even without the angle distribution, oblique incidence with the finite beam size also deteriorated the visibility of interference. In addition, the thin film was neither perfectly flat nor uniform, and the spectrometer resolution was finite.  
It is interesting to note that the spectral separation of the dips between s- and p-polarization is systematically larger in the experiment than in the calculation. A possible contribution of birefringence of the PVP film or the MgF\({}_{2}\) substrate was checked by measuring the interference spectra of normal incidence, as in Figure 4c, with vertical and horizontal polarization, but little difference was found. Currently, therefore, the reason for this larger separation is unknown.  
Figure 4: **(a)** The photo of the PVP coated MgF\({}_{2}\) substrate. At nine positions in (**b**), the reflectance relative to aluminum mirror was measured at an incidence angle of 5\({}^{\circ}\) in air using a spectrophotometer (SolidSpec-3700 DUV, Shimadzu, Kyoto, Japan) as shown in (**c**). The position dependent variation of the interference fringe patterns was not significant. The film thickness was determined to be 1480 nm by comparing the experimental results (**c**) with the calculated result (**d**) using Equation (1).