# Influence of Surface Tilt Angle on a Chromatic Confocal Probe with a Femtosecond Laser
## 4 Experimental Investigation Results for the Tracking Local Minimum Method
### Alignment Method of the Optical System
Figure 10c shows that the measurement light spectrum \(I_{\text{Mea}}\) and the reference light spectrum \(I_{\text{Ref}}\) are affected by the light source spectral shape, making it difficult to confirm the peak wavelength, while the normalized intensity ratio \(I_{\text{TLM}}\) is not affected by the light source spectral shape, and the peak wavelength can be confirmed. Figure 10d shows the cross-sections at the center wavelength \(\lambda=1.56~{}\upmu\)m in Figure 10a,b, respectively. The \(I_{\text{Mea}}\) and \(I_{\text{Ref}}\) in Figure 10d were shown normalized to the maximum intensity. Note that the \(I_{\text{Mea}}\) and \(I_{\text{Ref}}\) in Figure 10d were equivalent to the measurement light confocal response curve \(I_{\text{M}}\) and the reference light confocal response curve \(I_{\text{R}}\). It can be confirmed that Figure 10d differs from Figure 4d in that there is no sidelobe in the negative direction at the \(z\)-position. This was due to the effect of aberrations \(\Phi\) that were not considered in the numerical calculations [31, 35, 36, 37]. Figure 11 shows the results of the experiment conducted to determine the effect of the object tilt angle \(\theta_{X}\) on the TL method. Figure 11a shows the reference light spectrum \(I_{\text{Ref}}\) at different object tilt angles \(\theta_{X}\), and its contour plot is shown in Figure 11b, corresponding to the numerical calculation results shown in Figure 5. Figure 11a,b show that the peak  
Figure 10: Experimental results regarding obtained spectrum by the fiber-detector and the axial response curve based on our developed dual-fiber-detector chromatic confocal probe; (**a**) the measurement light spectrum \(I_{\text{Mea}}\) and the reference light spectrum \(I_{\text{Ref}}\), (**b**) the normalized intensity ratio \(I_{\text{TLM}}\), (**c**) The relationship between \(I_{\text{Mea}}\), \(I_{\text{Ref}}\) and \(I_{\text{TLM}}\) in wavelength, (**d**) the relationship between \(I_{\text{M}}\), \(I_{\text{R}}\) and \(I_{\text{TLM}}\) in \(z\)-position. intensity of the reference light spectrum \(I_{\text{Ref}}\) decreased and the hem of the sidelobe widened as the object tilt angle \(|\theta_{X}|\) increased. However, unlike Figure 5a,b, the peak position shifted toward the positive \(z\)-position as the object tilt angle \(|\theta_{X}|\) increased. Note that this can be considered due to the factors expected from Figures 8b and 9. Figure 11c shows a contour plot of the normalized intensity ratio \(I_{\text{TLM}}\). As can be seen in Figure 11c, it can be realized that the peak of the normalized intensity ratio \(I_{\text{TLM}}\) also shifted to the positive direction at the \(z\)-position in accordance with the shift of the minimum point of the reference light spectrum \(I_{\text{Ref}}\) to the positive direction at the \(z\)-position due to the tilt angle \(\theta_{X}\) of the measurement object. This phenomenon was confirmed over the entire source wavelength band. Figure 11d shows the results of calculating the peak wavelength of the normalized intensity ratio \(I_{\text{TLM}}\) at each object tilt angle \(\theta_{X}\) in the entire light source wavelength band. It was confirmed that the \(z\)-position intercept of the z-\(\lambda\) sensitivity line shifted parallel to the z-position positive direction with the object tilt angle \(\theta_{X}\). This means the effect of the object tilt angle \(\theta_{X}\) cannot be ignored in the TL method since the wavelength in focus on the object surface for detecting the \(z\)-position has changed.