## 3 Experiments and Discussions
### Experiments  
Experiments were carried out to investigate the feasibility of the proposed measurement range expansion method. The plane mirror was made to move along the \(Z\)-direction in a step of 2 \(\upmu\)m to obtain the axial responses. It should be noted that the displacement of the plane mirror was measured by a capacitive displacement sensor simultaneously for comparison. Peak wavelengths were calculated from the centroid positions of the corresponding normalized intensity ratio, as well as the invert normalized intensity ratio at each \(Z\)-position of the mirror. Figure 8a shows the normalized intensity ratio obtained at each \(Z\)-position over a \(Z\)-directional scanning range of 250 \(\upmu\)m. As can be seen in Figure 8a, not only the main-lobe but also the side-lobes were clearly observed. Although the peak widths of the sub-lobes were found to become wider as the increase of the \(Z\)-displacement of the plane mirror, the sharpness of the sub-lobes was enough to be used in the wavelength-to-displacement encoding. Figure 8b shows the peak wavelength obtained from the normalized intensity ratio in Figure 8a at each \(Z\)-directional position of the plane mirror. As can be seen in the figure, a linear relationship between the peak wavelength and the axial \(Z\)-directional displacement of the plane mirror was found for the main-lobe and each of the side-lobes. Meanwhile, as predicted in the results of the above theoretical calculations, a gap between each of the neighboring lobes was found. Figure 8c shows the invert normalized intensity ratio obtained at each \(Z\)-position, which was calculated from the same intensities employed to calculate the corresponding normalized intensity ratio shown in Figure 8a. As can be seen in Figure 8c, the main-lobe and the side-lobes were clearly observed in the obtained invert normalized intensity ratio. In the same manner, as the case of normalized intensity ratio \(I_{\text{a}}\), the relationship between the peak wavelength and the axial \(Z\)-directional displacement of the flat mirror was investigated by extracting the peak wavelengths in the invert normalized intensity ratio \(I_{\text{n}}\) shown in Figure 8c. The result is summarized in Figure 8d. As predicted in the results of the above theoretical calculations, the peak frequency in the invert normalized intensity ratio at a specific \(Z\)-directional position of the plane mirror was found to shift along the axial direction with respect to that of the normalized intensity ratio shown in Figure 8b. Figure 7: A schematic of the setup for the dual-detector chromatic confocal probe with a mode-locked femtosecond laser source. Figure 9 summarizes the wavelength-to-displacement encoding curves obtained from the axial responses of the normalized intensity ratio \(I_{\mathrm{a}}\) and that of the invert normalized intensity ratio \(I_{\mathrm{n}}\). As can be seen in the figure, a gap between each neighboring lobe in the axial response of the normalized intensity ratio was successfully covered by the axial response from the invert normalized intensity ratio. These experimental results demonstrated that measurement range of the fiber-based dual-detector chromatic confocal probe was successfully expanded from 40 \(\upmu\)m to 250 \(\upmu\)m by the proposed method without any modification on the optical setup of the developed confocal probe. Figure 8: The main-lobes and the side-lobes extracted from the normalized intensity ratio and the invert normalized intensity ratio obtained at each Z-directional position of the plane mirror, with target positions ranging from 0 to 250 \(\upmu\)m and a defocus \(d\) of 110 \(\upmu\)m. (**a**) Normalized intensity ratio obtained at each Z-position over scanning range of 250 \(\upmu\)m. (**b**) The lobes extracted from the normalized intensity ratio. (**c**) Invert normalized intensity ratio obtained at each Z-position over scanning range of 250 \(\upmu\)m. (**d**) The lobes extracted from the invert normalized intensity ratio.