# Evaluation and Improvement of Lidar Performance Based on Temporal and Spatial Variance Calculation
## 3 Data Distribution Characteristics of the Lidar Probing Traces  
In principle, the variance calculation models for evaluating the data distribution characteristics of lidar probing traces can be applied to any atmospheric lidar system. In this paper, the ultraviolet elastic scanning lidar was taken as the research object [23; 24], and a probing profile with a summed result of 20 laser shots or the lidar scanning profiles with a fixed elevation angle was analyzed to calculate the spatial and temporal variance. Based on the variance calculation results, the techniques for evaluating and improving the lidar performance were studied and implemented. In ultraviolet elastic scanning lidar, the PMT of Hamamatsu R9880 (Hamamatsu Photonics K. K., Hamamatsu, Japan) was selected as the photo-electric converter, and the Licel transient recorder TR40-160 (Licel GmbH, Berlin, Germany) was chosen as the data acquisition system, as it can provide the analog detection mode and PC detection mode simultaneously. It has a range resolution of 3.75 m and a maximum detection range of 61.4 km. Figure 2 shows the raw probing traces of analog data and PC data from the ultraviolet elastic scanning lidar, which is a summed result of 20 laser shots. The raw data in PC mode is expressed using photons, while the raw data in analog mode is expressed by the values from the A/D acquisition card (for a 12 bit A/D, the maximum value is 4095, corresponding to 500 mV). Compared with the PC data, the analog data were more easily affected by the electronic noise of the data acquisition card. In the calculation of temporal variance, the successive probing profiles with a fixed elevation angle from the ultraviolet elastic lidar scanning measurements were selected as the study objects, as these probing profiles have the same lidar system constant. Figure 3 shows an example of the  
Figure 2: A typical lidar profile with a summed result of 20 laser shots from the ultraviolet elastic scanning lidar with simultaneous analog detection mode and photon-counting detection mode. calculation results of temporal variance for both analog and PC data, which selected 14 successive probing profiles at the fixed elevation angle of 15\({}^{\circ}\) as the study objects and express the atmospheric variation within 14 s. It can be seen clearly that the data points of the noise signal in analog data are at the tail of the variance-mean scatter plot, and the data points of the PC data that suffered from the pile up effect are at the head of the variance-mean scatter plot. The data points of the cloud signals in both the analog and PC data are distributed in a disordered way in the variance-mean scatter plot. The variance values from the sample distributions of the normal lidar return signals in analog data are distributed parallel to the line of \(\mu=\sigma^{2}\), while the variance values from the sample distributions of the normal lidar return signals in PC data are distributed along the line of \(\mu=\sigma^{2}\). This shows that the PC data have the necessary condition of Poisson distribution, while the analog data do not have Poisson properties and have the potential to be converted to photon-like data using a linear transformation. In the calculation of spatial variance, a single probing profile with a fixed elevation angle from the ultraviolet elastic lidar scanning measurements is selected was the study object. Figure 4 shows an example of the calculation results of spatial variance for both analog and PC data, which set \(N_{\rm sv}\) to be 30 and expressed the atmospheric variation within a range interval of 112.5 m. The scatter plots of the spatial variance distributions from the analog data and PC data are similar, with the scatter plots of the temporal variance distribution, including the noise components in the analog data, the pile-up effect in PC data, and the cloud signals in both analog data and PC data.