# Optical Angle Sensor Technology Based on the Optical Frequency Comb Laser
## 1 Introduction
### A Method Employing the Dispersive Characteristics of a Diffraction Grating
#### 2.1.2 Light Intensity Detecting-Type Mode-Locked Femtosecond Laser Autocollimator
Denoting the number of first-order diffracted beams in the angle scale comb as \(N\), a theoretical measurement range of the femtosecond laser autocollimator becomes \(N\) times that of the conventional laser autocollimator employing a single-mode laser source and with a single focused spot on the PD active cell. It should be noted that the detection of the displacement of a focused beam in the femtosecond laser autocollimator shown in Figure 3b is based on the photocurrent output from the PD, the amount of which is associated with the intensity of the light rays captured by the active cell on the PD. Therefore, the femtosecond autocollimator with a PD is referred to as the light intensity detecting-type femtosecond laser autocollimator. Figure 4a,b show a schematic and a photograph of the optical setup for the light intensity detecting-type femtosecond laser autocollimator, respectively. In the setup, a Fabry-Perot etalon with a free spectral range (FSR) of 770 GHz was employed as an optical bandpass filter to enlarge the distance between the neighboring modes in the spectrum of the optical frequency comb. Figure 5 shows the obtained photocurrent from the PD converted into the voltage output by a trans-impedance amplifier. As can be seen in the figure, the cycle of the obtained voltage output agreed well with the FSR of the etalon. These results demonstrated that the light intensity detecting-type femtosecond laser autocollimator has a measurement range greater than 11,000 arc-seconds (3.06), which is much larger than that of the conventional laser autocollimator with a single-mode laser source [4; 27]. Figure 3: A comparison between the conventional laser autocollimator and the femtosecond laser autocollimator [55]: (**a**) A laser autocollimator with a single-mode laser source; (**b**) A femtosecond laser autocollimator with a mode-locked femtosecond laser source. 1.3 An Optical Frequency Domain Angle Measurement Method Associated with a Mode-Locked Femtosecond Laser Autocollimator  
Most of the commercial fiber-based mode-locked femtosecond lasers have a pulse repetition rate on the order of 100 MHz. When such a laser source is employed in the light intensity detecting-type femtosecond laser autocollimator, the distance between the neighboring spots in the focal plane of the collimator objective reaches the order of several nanometers, and the spots cannot be distinguished separately. The pulse repetition rate is thus required to be extended by a Fabry-Perot etalon in the femtosecond laser autocollimator described in Section 2.1.2. Due to the diffraction limit, it is unavoidable for the neighboring spots in the focal plane of the collimator objective to overlap with each other in most of the cases. This results in the degradation of the signal quality (visibility) of the reading output of the light intensity detecting-type femtosecond laser autocollimator. As can be seen in the result shown in Figure 5, maximum visibility that can be achieved by the femtosecond laser is approximately 0.5; this prevents the light intensity detecting-type femtosecond laser autocollimator to achieve further higher sensitivity. To address the issue, an optical frequency-domain femtosecond laser autocollimator has been established [56]. Figure 6 shows a schematic of the detection of the angle scale comb in optical frequency domain. A detector unit composed of a collimator objective, a single-mode fiber, and a spectrometer is newly employed. By observing the spectrum of the first-order diffracted beams captured by the single-mode fiber, the angle scale comb can be detected with a visibility of 100%. Furthermore, this technique realizes the direct conversion of the optical frequency comb to the angle scale comb, which contributes to achieving further precision angle measurement. Figure 7 shows the developed optical frequency-domain femtosecond laser autocollimator.