## 4 Conclusions  
A new method for expanding the Z-directional measurement range of a fiber-based dual-detector chromatic confocal probe with a mode-locked femtosecond laser source has been proposed. The dual-detector chromatic confocal probe has been designed to detect the axial position of a measurement target by using the normalized intensity ratio calculated from light intensities obtained by the two identical fiber detectors. In the proposed method, for the expansion of the measurement range of the dual-detector chromatic confocal probe, invert normalized intensity ratio, which is the inverse of the normalized intensity ratio, has also been employed to realize seamless measurement with the main-lobes and the side-lobes of the axial responses obtained from both the normalized intensity ratio and the invert normalized intensity ratio. Theoretical calculations and experiments have been carried out to verify the feasibility of the proposed method, and the results have demonstrated that the measurement range can be expanded to 250 \(\upmu\)m, which is four times wider than that of the conventional dual-detector chromatic confocal probe developed in the previous work by the authors.  
It should be noted that this paper is mainly focused on the proposal of the method for expansion of the Z-directional measurement, and subsequent experimental work will be carried out in 3D microstructure imaging in our future research. It should also be pointed out that in order to make good use of the side-lobes to extend the Z-directional measurement range, we set a defocus \(d\) to be 110 \(\upmu\)m, which achieves a bigger full width at half maximum (FWHM) value compared with the FWHM value when the defocus \(d\) is set to be 150 \(\upmu\)m in our previous work [3]. That means there will be a reduction in axial resolution. However, when the defocus \(d\) is fixed, the axial resolution will not be affected during the measurement range expansion processing because our expansion method is performed without modifying the optical setup of the dual-detector chromatic confocal probe, and therefore will not change the point spread function of our confocal imaging system theoretically. Furthermore, future research will also focus on the depth measurement provided by the optical phase and optical complex amplitude of the dual-detector chromatic confocal probe, compared with the depth measurement given by the optical intensity in this paper. Measurement uncertainty analysis together with the identification of the absolute optical wavelengths based on the optical frequency comb will also be carried out in the next stage of research.  
Conceptualization, W.G.; methodology, C.C. and T.N.; software, C.C. and T.N.; validation, C.C., H.M., and R.S.; formal analysis, C.C., T.N., and R.S.; investigation, C.C., T.N., and R.S.; resources, C.C. and R.S.; data curation, C.C. and R.S.; writing--original draft preparation, C.C.; writing--review and editing, Y.S., H.M., and C.C.; visualization, W.G. and Y.S.; supervision, W.G.; project administration, W.G.; funding acquisition, W.G. and Y.S.  
This research was funded by Japan Society for the Promotion of Science (JSPS).  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.