# A Second Harmonic Wave Angle Sensor with a Collimated Beam of Femtosecond Laser  
[PERSON]  
1 Precision Nanometrology Laboratory, Department of Finemehancians, Tohoku University, Sendai 980-8579, Japan; [EMAIL_ADDRESS] (W.D.A. ); [EMAIL_ADDRESS] (K.L. ); [EMAIL_ADDRESS] (R.S. ); [EMAIL_ADDRESS] (H.M.); [EMAIL_ADDRESS] (W.G.) [PERSON]  
1 Precision Nanometrology Laboratory, Department of Finemehancians, Tohoku University, Sendai 980-8579, Japan; [EMAIL_ADDRESS] (W.D.A. ); [EMAIL_ADDRESS] (K.L. ); [EMAIL_ADDRESS] (R.S. ); [EMAIL_ADDRESS] (H.M.); [EMAIL_ADDRESS] (W.G.) [PERSON]  
1 Precision Nanometrology Laboratory, Department of Finemehancians, Tohoku University, Sendai 980-8579, Japan; [EMAIL_ADDRESS] (W.D.A. ); [EMAIL_ADDRESS] (K.L. ); [EMAIL_ADDRESS] (R.S. ); [EMAIL_ADDRESS] (H.M.); [EMAIL_ADDRESS] (W.G.) [PERSON]  
1 Precision Nanometrology Laboratory, Department of Finemehancians, Tohoku University, Sendai 980-8579, Japan; [EMAIL_ADDRESS] (W.D.A. ); [EMAIL_ADDRESS] (K.L. ); [EMAIL_ADDRESS] (R.S. ); [EMAIL_ADDRESS] (H.M.); [EMAIL_ADDRESS] (W.G.) [PERSON]  
3 Laboratory of Precision Metrology and Robotics, Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, Japan; [EMAIL_ADDRESS] (W.D.A. ); [EMAIL_ADDRESS] (W.D.A. ); [EMAIL_ADDRESS] (W.D.A. ); [EMAIL_ADDRESS] (W.D.A. ); [EMAIL_ADDRESS] (W.G.) [PERSON]  
1 Precision Nanometrology Laboratory, Department of Finemehancians, Tohoku University, Sendai 980-8579, Japan; [EMAIL_ADDRESS] (W.D.A. ); [EMAIL_ADDRESS] (W.D.A. ); ik.kuangyi. that are sensitive to contamination. These reasons encourage more intensive research on new angle measurement methods, especially non-contact angle sensors, as the solution to bridge these problems. A second harmonic wave angle sensor, a non-contact optical-based angle sensor, offers a well-suited measurement configuration system to satisfy the aforementioned requirements [15; 16]. The second harmonic generation (SHG) is a phenomenon, in which the optical wave source passes through a nonlinear optical material and generates a frequency-doubled harmonic wave where the power of the second harmonic wave is highly dependent on the wavelength and the incident angle of the source toward the nonlinear material [17]. SHG has attracted attention as advantages can be found in many fields of study, especially in the biological and medical sciences for bioimaging spectroscopy [18; 19; 20], nonlinear microendoscope [21; 22], and surface chemistry sensing [23; 24]. However, the application of SHG in angle displacement measurement is relatively new, and related research is still limited. In the previous study by the authors' group, a new angle measurement based on the SHG by focusing a Femtosecond laser (Fs) laser beam with lenses [15] and a parabolic mirror [16] into a nonlinear optical (NLO) crystal serving as a measurement target has been proposed. The focused beam method is one practical way to obtain highly intense fundamental waves of Fs laser for generating harmonic waves. A good performance has been achieved when the NLO crystal is placed at the focal point or within the Rayleigh length region of the parabolic mirror, where the beam can be treated to have a plan wave nature. This measurement method holds promise in the angle shift detection of fixed-positioned measurement targets, but could encounter problems when the target has misalignment along the laser propagation direction. To accommodate the possibility of positional changes over the axis, a new SHG angle sensor configuration is needed. This study proposes an angle sensor using the SHG generated not by a focused Fs laser beam, but by a collimated Fs laser beam. A collimated beam is expected to have no significant change in physical properties during propagation. The Fs laser beam is highly collimated, but a more intense laser beam is required to generate the second harmonic wave. Therefore, a Keplerian lens configuration is needed to intensify the laser beam while keeping the beam collimated.