# Optical Angle Sensor Technology Based on the Optical Frequency Comb Laser
## 5 Conclusions  
A mode-locked femtosecond laser has been employed in a variety of applications in dimensional metrology for production engineering. In recent years, mode-locked femtosecond lasers have expanded application to precision angle measurement, which is also an important activity in production engineering. In this article, some angle measurement techniques employing a mode-locked femtosecond laser have been reviewed. With the employment of the dispersive characteristic of diffraction grating, equally-spaced modes of the mode-locked femtosecond laser in frequency domain can be converted into the \"angle scale comb\", which is a series of scale graduations for angle measurement. With the enhancement of the highly-stabilized optical modes of a mode-locked femtosecond laser over a wide spectral range, highly stable optical angle measurement can be achieved over a wide measuring range. In addition, by combining the angle scale comb with the laser autocollimation, a mode-locked femtosecond laser autocollimator with a high resolution over a wide angular range can be realized. The mode-locked femtosecond laser autocollimator has the possibility of realizing a direct link of angle measurement to the national standard of time/frequency by observing the reading output in the frequency domain. A mode-lock femtosecond laser can also be employed for angle measurement by utilizing physical phenomena such as the second harmonic generation of a nonlinear crystal or lateral chromatic aberration of a single lens. In addition, novel optical setups for the absolute distance measurement with a mode-locked femtosecond laser source can also achieve the measurement of angular displacement/absolute angular position of an object. Table 2 summarizes the features of the angle measurement techniques reviewed in this paper, including the achieved resolutions and measuring ranges.  
Figure 19: Variation of the light intensity of generated second harmonic light observed in experiments [59]: (**a**) Angle dependency of the second harmonic generation; (**b**) Variation of the light intensity of second harmonic light due to the angular displacement of the BBO crystal in a step of 0.4 arc-seconds.  
One of the disadvantages of the above-mentioned techniques is the high cost of the mode-locked femtosecond laser source. With the decrease of the cost of the femtosecond laser source, the angle measurement techniques explained in this review article are expected to be employed in many industrial applications in the near future where the traceability of measurement becomes a more important issue to be addressed.  
Conceptualization, W.G. and Y.S.; methodology, W.G. and Y.S.; software, W.G. and Y.S.; validation, W.G. and Y.S.; formal analysis, W.G. and Y.S.; investigation, Y.S. and H.M.; resources, W.G. and Y.S.; data curation, W.G., H.M. and Y.S.; writing--original draft preparation, Y.S.; writing--review and editing, W.G. and Y.S.; visualization, Y.S. and W.G.; supervision, W.G.; project administration, W.G.; funding acquisition, W.G., Y.S. and H.M. All authors have read and agreed to the published version of the manuscript.  
A part of this research is supported by the Japan Society for the Promotion of Science (JSPS) 15H05759 and 18H01345.  
The authors would like to thank all our laboratory members who joined the related projects at Tohoku University for their contributions to the achievements described in this paper.  
The authors declare no conflict of interest. The founding sponsors 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.