## 5 Conclusions  
In this paper, efforts have been made to improve the thermal stability of the chromatic confocal probe with a mode-locked femtosecond laser source. At first, the thermal characteristics of the previous first prototype femtosecond laser chromatic confocal measurement setup have been verified through experiments, and the thermal stability has been evaluated to be 5.20 \(\upmu\)m/\({}^{\circ}\)C. Theoretical investigations on the possible reasons for the thermal instability of the probe, such as the thermal instability of the refractive index of the confocal lens and the thermal expansion of mechanical jigs of the probe, have then been carried out. Through the quantitative analysis of the contribution of each possible reason, the mechanical jig, on which the lens holder is mounted, and the mounting plate have been found to be major contributors in the instability of the measurement setup. Regarding the results of theoretical investigations, the second prototype measurement setup has newly been designed and developed. In the second prototype measurement setup, attentions have been paid to minimize the optical path length of the laser beam in the setup, while Super Invar has been employed as the material for the mechanical jig for the improvement of the thermal stability of the chromatic confocal probe. The results of theoretical calculations and experiments have demonstrated that the femtosecond laser chromatic confocal probe in the second prototype measurement setup has achieved thermal stability of 0.01 \(\upmu\)m/\({}^{\circ}\)C, which is far better than that in the previous first prototype measurement setup (4.86 \(\upmu\)m/\({}^{\circ}\)C).  
It should be noted that attention has been paid in this paper to improving the thermal stability of the chromatic confocal probe with a mode-locked femtosecond laser source. Application of the developed optical setup for surface profile measurement is the next step of the research, and will be carried out in future work.  
Figure 12: The thermal stability of focused wavelength \(\lambda_{\text{focused}}\) of the overall second prototype measurement setup shown in Figure 11b.  
Figure 13: A schematic of the chromatic confocal lens and the target sample in the second prototype chromatic confocal measurement setup shown in Figure 11b.  
**Author Contributions:** Conceptualization, W.G. and Y.S.; methodology, R.S. and H.M.; software, R.S.; validation, R.S. and H.M.; formal Analysis, R.S., C.C. and Y.S.; investigation, R.S. and C.C.; resources, R.S.; data curation, R.S. and H.M.; Writing-Original Draft Preparation, R.S. and Y.S.; Writing-Review & Editing, W.G. and Y.S.; Visualization, W.G. and Y.S.; Supervision, W.G.; Project Administration, W.G.; Funding Acquisition, W.G., Y.S. and H.M.  
**Funding:** This work is supported by the Japan Society for the Promotion of Science (JSPS).  
**Acknowledgments:** The authors would like to thank [PERSON] for his help in the preparation of the experimental setup.  
**Conflicts of Interest:** The authors declare no conflicts 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.