## 2 Background
### Lidar System Optimization for Control Applications
#### Practical Lidar Considerations  
Although the frequency domain measurement coherence models discussed in the previous section provide an efficient way to assess the accuracy of different scan patterns, they do not incorporate many practical lidar considerations. Several studies have focused on more practical aspects of lidar optimization, however.  
In addition to their assessment of feedforward controller performance for different scan pattern parameters mentioned in Section 2.4.1, [PERSON] and [PERSON] [31] discuss the need for high availability and reliability for LAC applications. For a collective pitch feedforward control system relying on measurements from a multiple-beam pulsed lidar system, the authors conclude that the load reduction and rotor speed regulation performance begins to suffer significantly when the availability drops below 50%. Here, availability is defined as the fraction of measurements that are considered acceptable during a given time series, with the majority of the unavailability arising from blockage by passing blades. Given that controller performance is acceptable with 50% availability, the authors suggest that nacelle mounting is a sufficient approach. Note that more specific definitions of availability for control applications, where even a few seconds of measurement unavailability can compromise control performance, are discussed by [PERSON] et al. [47]. Using a 5-beam pulsed lidar with 10 range gates, the authors identify the number of valid measurements out of all beam directions and range gates during the previous 3 s as a good indicator of usefulness, concluding that at least 40 valid measurements (out of a maximum of about 130) are needed for reliable control.  
[PERSON] et al. [48] explore the impact of the scan parameters of a nacelle-mounted Avent pulsed lidar on availability, as well as the relationship between atmospheric conditions and availability. With respect to rotor blockage, the authors explain that one of the most important parameters that determines availability is the fraction of time that a lidar beam direction is unobstructed by a passing blade. This parameter is a function of the diameter of the blade root and the position where the beam intersects the rotor disk. The fraction of time when the lidar beam is unobstructed by the blades increases as the lidar cone angle increases, the height of the lidar above the rotor axis becomes larger, or the position of the lidar behind the rotor plane increases.  
[PERSON] et al. [48] show that an additional parameter that impacts availability is the ratio between the averaging time used to measure a single LOS velocity and the time it takes for a blade to pass across the lidar beam direction. If this parameter is greater than 1, then the lidar beam will be unobstructed by the blade for part of the signal integration time. As long as the carrier-to-noise ratio (CNR) of the measurement remains above the necessary threshold, a reliable measurement can still be formed. The authors show that lidar availability can be described as a linear combination of the aforementioned geometrical blockage ratio and averaging time ratio parameters, improving as either parameter increases until the averaging time parameter reaches 1. Therefore, availability can be improved not only by adjustments to scan geometry and lidar position, but also by the measurement integration time.