## 2 Background
### Lidar Systems for Control Applications  
A variety of nacelle lidar systems have been developed for wind turbine control applications, both commercially and for research purposes. The first field demonstration of a nacelle-mounted lidar that is reported in the literature was made in 2003 by [PERSON] et al. [2], where the authors tested a single-beam continuous wave (CW) lidar mounted atop a utility-scale wind turbine, measuring 200 m upstream of the turbine. CW lidars measure the wind velocity by focusing a laser beam at a specific range and detecting the Doppler shift of the light backscattered from aerosols at the focus point [3]. Note that, although CW lidars can only measure at a single distance at one time, the focus distance of the lidar can often be adjusted. The technology behind this initial CW lidar [2] eventually led to the creation of the ZephIR DM nacelle-mounted circularly-scanning CW lidar by ZephIR Lidar (Hollybush, Ledbury, UK). With a configurable focus distance between 10 m and 300 m, the ZephIR DM lidar completes a circular scan containing 50 measurement points once per second [4]. A similar ZephIR lidar system was placed in the hub, or spinner, of a MW-scale wind turbine, as discussed by [PERSON] et al. [5], allowing continuous measurement of the wind inflow without periodic obstruction from blade passage. A more complex spinner-mounted lidar system developed by [PERSON] et al. (2016), also based on a ZephIR, uses two rotating beam-redirecting prisms to scan 400 points per second, roughly evenly distributed over a 100 m-diameter disk, at a preview distance of 100 m, allowing two-dimensional turbulence structures to be examined. In contrast to research-oriented lidar systems relying on complex scan patterns, a nacelle-mounted CW lidar developed by Windar Photonics (Taastrup, Denmark) uses four fixed beam directions to measure the wind 80 m upstream of the turbine ([PERSON], 2011). This simple design is meant to reduce the cost of nacelle lidars for control purposes.  
Whereas CW lidars are limited to measuring one point at a time, but are capable of high sampling rates, pulsed lidar systems can measure the wind speed at multiple ranges along the beam simultaneously, but typically require longer sampling periods. Instead of tightly focusing the laser beam at a specific distance, pulsed lidars attribute the backscattered light to different measurement ranges (range gates) according to the elapsed time since the light was emitted by the lidar. [PERSON] et al. (2011) used a custom scanning pulsed lidar system based on the Leosphere Windcube V1 lidar to provide preview measurements for lidar-assisted pitch control field tests. The authors configured the lidar to scan a circular trajectory containing six evenly-spaced beam directions with five range gates from 42.7 m (1 rotor diameter (\(D\))) to 85.3 m (2 \(D\)) upstream of the test turbine with a scan period of 1.33 s. Additionally, a five-beam pulsed nacelle lidar has been developed by Avent Lidar Technology (Orsay, France) for control applications. This lidar was used for LAC field field tests performed by [PERSON] et al. (2011). The five-beam Avent lidar provides measurements at up to 10 range gates per beam with a maximum range of 300 m and a scan period of approximately 1.25 s ([PERSON] et al., 2011). Note that, while CW lidars can typically measure the wind at a greater number of beam directions per scan than pulsed systems, pulsed lidars have the advantage of being able to measure the wind at multiple ranges per beam direction. Because each range gate corresponds to a different radial distance from the center of the rotor, pulsed lidars are capable of measuring a large portion of the rotor disk area with a small number of beam directions.