# Optical Angle Sensor Technology Based on the Optical Frequency Comb Laser
## 1 Introduction
Furthermore, a three-axis laser autocollimator and six-degree-of-freedom (6-DOF) surface encoder capable of measuring the three-axis angular displacement of a grating reflector with a single measurement laser beam [29, 30, 31, 32, 33], as well as a three-axis inclinometer [34] based on the principle of the three-axis laser autocollimator, have been developed. In the field of dimensional metrology, many types of optical sensors employing a mode-locked femtosecond laser, in which the optical frequency of each mode can be directly linked to a national standard of frequency/time, have been developed in the past two decades since the establishment of the laser source [35, 36, 37, 38, 39]. For example, methods for measurement of the absolute distance of an object [40, 41, 42, 43, 44, 45, 46] and the absolute thickness of an optical glass [47, 48, 49] have been developed with the enhancement of a well-controlled pulse repetition rate of the mode-locked femtosecond laser. The establishment of a fiber-based mode-locked femtosecond laser [50, 51, 52, 53] designed in a compact size and capable of being operated stably even in a limited environmental condition has contributed to the growth of these techniques in dimensional metrology. In recent years, the trend of employing a mode-locked femtosecond laser source can also be seen in angle measurement technologies. A new concept of generating an absolute angle scale with the enhancement of the dispersive characteristic of a diffraction grating has been proposed [54], and a femtosecond laser autocollimator based on the concept as well as laser autocollimation, has been established [55, 56]. Furthermore, the method has been extended to the measurement of the absolute position of an object [57]. The above-mentioned femtosecond laser autocollimators are based on the well-controlled, equally spaced frequency comb in the spectrum of the mode-locked femtosecond laser. Angle measurement with a mode-locked femtosecond laser source has also been achieved by the phenomenon of chromatic aberration [58], as well as second harmonic generation (SHG) which is a well-known phenomenon in nonlinear optics [59]. Table 1 summarizes the optical methods for angle measurement employing a mode-locked femtosecond laser source. The new angle measurement techniques with a mode-locked femtosecond laser are expected to achieve the performances that cannot be achieved by conventional optical angle sensors with a single-mode laser source or a white light source. In this review article, optical angle sensors employing a mode-locked femtosecond laser source are investigated. It should be noted that an optical fiber gyro based on the Sagnac effect [64; 65] is another method for angle measurement. Many types of optical fiber gyros such as an interferometric Fiber optic gyroscope (I-FOG) [66], a resonator Fiber optic gyroscope (R-FOG) [67] and Brillouin scattering [68] have been developed so far, and some trials have been performed using optical fiber gyros to employ a mode-locked femtosecond laser [60; 61]. The measurement principles of these optical fiber gyros are the same as the conventional ones employing a pulsed laser [69]. In addition, optical fiber gyros are not appropriate for applications in production engineering, such as the evaluation of the angular error motion of a precision linear slide or the measurement of the freeform or the aspheric form of an optical component, due to their drift characteristics associated with their principle based on the detection of angular velocity. The optical fiber gyros with a mode-locked femtosecond laser are thus not included in this review article. Angle Measurement Methods Based on the Discrete Modes of a Mode-Locked Femtosecond Laser in Frequency Domain