## 3 Results
### Effect of the Time Sampling Interval on the Angular Combination
Based on a comparison of the four subfigures shown in Figure 6, an increase in the time sampling interval will lead to the loss of consistency at the same latitude, and the pattern in the mid-low latitude zone gradually presents as a scattered petal shape. Because of the apparent \"gaps,\" the results no longer appear horizontally striped. Interestingly, the number of gaps and time sampling interval are negatively linearly correlated. When the time sampling interval was 1, 2, and 4 h, 48, 24, and 12 gaps were presented, respectively. This is because a larger time sampling interval means more sparse observations. As the Moon orbits the Earth, when the time sampling interval increases, the samples are decreased along the longitude uniformly. Consequently, gaps are presented with increased time sampling intervals, and a larger time sampling interval leads to a larger gap. To evaluate the difference between different time sampling intervals, we calculated a difference map during an 18.6-year period, as shown in Figure 8. The results over a time sampling interval of 10 min were used as the reference map. The results show that the difference of angular coverage presents regular variations and time sampling interval has a larger effect on the angular combination of the observed points in the mid-low latitude zones and latitude ranges from around 30\({}^{\circ}\) N to 30\({}^{\circ}\) S. To express the trend more clearly, Figure 9 shows the maximum and minimum variations of the ACNI ratio difference with increasing time sampling interval differences. The \(x\)-axis represents the difference between the time sampling interval and 10 min. The blue line represents the maximum difference of the index, and the orange line is the minimum difference. When the time sampling interval increases from 10 min to 2 h, the maximum loss reaches 50% in the mid-low latitude zone, whereas the minimum loss in the high latitude zone is less than 0.02%. When the time sampling interval increases to 4 h, the maximum loss rate reaches 70%, and the minimum loss rate is about 0.06%. Figure 8: Difference maps between global ACNI maps at time sampling intervals of (**a**) 30 min, (**b**) 1 h, (**c**) 2 h, (**d**) 4 h, and 10 min. Figure 7: Global angular combination number index (ACNI) maps at time sampling intervals of (**a**) 10 min, (**b**) 30 min, (**c**) 1 h, (**d**) 2 h, (**e**) 4 h, and (**f**) variation in the ACNI with the latitude in (**a**). As mentioned in the Section 1, the angular combination characteristics of the Moon-based platform differ from the traditional satellites. Figure 10 shows the angular sampling of LEO, GEO, L1 satellites, and Moon-based platform over an orbital period. The time sampling interval is 1 min, and the Earth location is assumed at (\(0^{\circ},0^{\circ}\)). The results show that the LEO satellite samples sparsely due to the limitation of orbital altitude and field of view. The solar zenith angles of the GEO/L1 satellites can almost cover from \(0^{\circ}\) to \(90^{\circ}\). They mainly lack the corresponding view zenith angle (GEO satellite) or relative azimuth angle (L1 satellite) sampling. To quantify this difference, we further simulated the angular sampling of hemispheric-scale observation platforms from global observed points over 18.6 years based on ACNI. To eliminate the effect of time sampling interval, it is set to 1 h in all cases. We compared all observed points and calculated the largest and smallest ACNI values and their ratios. The comparison results are tabulated in Table 2. For the GEO satellite, limited by the fixed viewing direction, its maximum ACNI value is only 372, and the maximum ratio is 3.19%. Because it always \"stares\" at the same side of the Earth in a fixed direction, some observed points cannot be observed, and thus the minimum ACNI is zero. For the special L1 satellite, because of its extremely high orbital altitude, it can achieve global coverage.