## 3 Results
### Effect of the Time Sampling Interval on the Angular Combination  
As described in Section 3.2, we found that the angular distributions show differences for different observed points, which will be significantly affected by the selection of time sampling interval. This raises the question of the difference in the angular coverage ratio between different observed points and how much an increased time sampling interval will affect the diversity of angular combinations. To answer these questions, we propose the ACNI and its ratio to characterize and quantify the performance of angular combina  
Figure 6: Angular combination distribution of different points at different time sampling intervals. (**a1–a5**) Point D; (**b1–b5**) Point C; (**c1–c5**) Point E; (**d1–d5**) Point B; (**e1–e5**) Point F; (**f1–f5**) Point A; (**g1–g5**) Point G; (**a1–g1**) 10 min; (**a2–g2**) 30 min; (**a3–g3**) 1 h; (**a4–g4**) 2 h; (**a5–g5**) 4 h. (The polar axis represents the relative azimuth angle, polar diameter represents the viewing zenith angle, and color represents the solar zenith angle). tion. One critical step is to discretize the combination of angles according to the bin size. When the ratio of index is a maximum of 1, the sensor can cover all angular combination bins. In contrast, when the ratio is smaller, the sensor's angular samplings are insufficient. Its minimum is 0, indicating that the observed points cannot be observed. The experiments were conducted assuming the sensor was at (0\({}^{\circ}\), 0\({}^{\circ}\)) on the lunar surface, and the observation period was set as 18.6 years to remove the effect of the observation period. Considering the angular resolution of the angular distribution model for the top-of-atmosphere radiative flux calculation, the angular resolution was selected to be 5\({}^{\circ}\)[6]. Accordingly, there are 18 bins for the viewing and solar zenith angles and 36 bins for the relative azimuth angle. That means, in Equation (29), the values of \(p\), \(q\), and \(m\) are 18, 18, and 36, respectively. Thus, the total number of angular combinations for the three observational angles is 11,664. Figure 7 shows the 18.6-yearly variations over time sampling intervals of 10 min, 30 min, 1 h, 2 h, and 4 h. The values in the Figures 7 and 8 represent the numbers of angular combinations and have no physical unit. As expected, the results in Figure 6a appear to be symmetrical around the Earth's equator and are consistent at the same latitude. This further supports that the angular combination is significantly affected by the latitude of the observed point, whereas the longitude has no significant influence. The angular combination is relatively abundant in the region between 30\({}^{\circ}\) N and 30\({}^{\circ}\) S, and the values of ACNI vary from approximately 9000 to 10,800, as shown in Figure 7a. Thus, more than 78% of the angular combination can be covered by a Moon-based sensor. The index of observed points in the high latitude zone, however, ranges roughly from 2000 to 8000. The observed points in the polar regions have the smallest index value (approximately 2000), regardless of the time sampling interval, although they have the longest continuous observation duration. Therefore, the values of the index clearly vary with the latitudes of observed points, as shown in Figure 7f. The \(x\)-axis represents the latitude of the observed points, and the \(y\)-axis represents the value of this index. The two yellow lines correspond to these two latitude lines with the most abundant angular combination sampling, and the red line represents the latitude of the equator index. The angular coverage ratio of the observed point at the equator is 15% lower than the case of these two latitudes lines. Another important issue is the effect of the time sampling interval.