# Optical Angle Sensor Technology Based on the Optical Frequency Comb Laser
## 1 Introduction  
The angle and length are among the most fundamental parameters that determine the form of an object [1, 2]. As can be seen in measurements of the angle between two surfaces of parts or assemblies by a protractor or fixed angle gauges, angle measurement has been carried out since ancient times [3]. In the current production engineering, angle sensors play important roles in many types of machine tools, arm robots, and measuring instruments [4]. For measurement of the angular displacement or angular position of an object with a fixed axis of rotation, rotary encoders are often employed. In a rotary encoder, a relative angular displacement between a rotating scale disk coupled coaxially with that of the rotating object and a reading head kept stationary with respect to the axis of rotation can be detected by reading circular graduations on the scale disk in an optical or electromagnetic manner [5, 6, 7, 8]. Rotary encoders are capable of carrying out high-precision angle measurement over an angular range of \(360^{\circ}\) and can be employed as a feedback sensor for the control of the axial position of an object. In the state-of-the-art rotary encoder, a self-calibration method has been established [9, 10]. Furthermore, the improvements in the resolution and measurement speed of absolute rotary encoders contribute toachieving further higher positioning accuracy and fabrication throughput in machine tools and robot systems [11]. On the other hand, precision positioning is one of the key technologies for the precise fabrication of a component with a complex surface form such as an aspheric form or a freeform, as well as the fabrication of a device with three-dimensional micrometric or nanometric structures [11]. One-axis precision positioning can be achieved by employing a linear slide equipped with precision displacement sensors such as laser interferometers or linear encoders [12]. In multi-axis machine tools and measuring instruments, multi-dimensional precision positioning is carried out by employing positioning systems composed of such precision linear slides. For further higher precision positioning, it is necessary to evaluate the angular error motions of such linear slides with a high measurement throughput in a non-contact manner [4, 13]. The rotary encoders cannot be employed in such applications, since the distance between a reading head and a scale disk cannot be changed during the measurement. For such a purpose, optical autocollimators are often employed [14, 15]. By employing a two-dimensional image sensor such as an area sensor or a multi-cell photodiode as the photodetector, two-axis angular displacement can be measured simultaneously [4, 16]. Nowadays, optical autocollimators have expanded applications to the surface form measurement of precision optical components [17, 18, 19, 20, 21]. In recent years, most of the commercial autocollimators employed a charge-coupled device (CCD) or a complementary metal-oxide semiconductor (CMOS) as their photodetectors for the achievement of a large angle measurement range as well as a high resolution [22, 23, 24]. One of the disadvantages of employing a CCD image sensor is its low measurement throughput; this can be overcome by employing a CMOS or a PSD (position-sensitive detector) [24]. The relatively large size of the optical setup is another issue for the conventional optical autocollimator, since its large footprint could prevent the optical autocollimator from being employed in machine tools where the space for such a sensor is limited. For the achievement of high measurement throughput and high resolution in a compact manner, a laser autocollimator based on laser autocollimation [25] has been developed. With the employment of a laser diode and a photodiode as a compact light source and a photodetector, respectively, highly sensitive high-speed angular displacement measurement has been achieved [26, 27]. A laser autocollimator can also be applied for surface form measurement of precision components [28].