where \(\text{RAD}_{\text{illum}}\) and \(\text{RAD}_{\text{shad}}\) are the measured radiances of illuminated regions and shadowed regions, respectively. On the cal-targets, the illuminated regions used for this calculation are the four grayscale rings exposed to the sunlight, while the shadowed regions are the four small portions of the grayscale rings under the shadow of the central gnomon. For each ring for which the shadow was selected and the radiance measured, a value of \(F_{d}\) was computed using equation (3) and then the average was retrieved over the rings. Changes in \(F_{d}\) in time usually indicate an increase or decrease of the light diffusion in the atmosphere and hence, in turn, a change in the amount of airborne dust. The trends of \(F_{d}\) are often correlated with the detections of the atmospheric optical depth\(\tau\), which describes the attenuation of the solar radiation penetrating the atmosphere. Visible optical depth was measured via direct solar images taken by Mastcam-Z using solar filters (Bellet al., 2021, 2022). Solar images were taken with an RGB filter and with an 880 nm filter, the latter of which was used here. Optical depth varies by <5% across the Mastcam-Z wavelength range (Lemmon et al. , 2019). Solar images were reduced to optical depths following the procedure of Lemmon et al. (2015), simplified due to the lack of need for a temperature correction and the lack of observed dust on the optics so far.
Figure 12 represents the comparison between the time trends of \(F_{d}\)in four different filters (L6, L4, R2 and R6) and \(\tau_{I}\), the latter being observed at 880 nm. The direct fraction \(F_{d}\) and the optical depth are expected to vary in an inverse fashion, with increases in \(F_{d}\) corresponding to drops in the optical depth and vice-versa. The time range from landing to the solar conjunction (sol 217) was characterized by a fairly stable, low optical depth. This is shown in Figure 12 by a slight depression around the martian aphelion counterbalanced by the local peak of \(F_{d}\), which reaches 0.81 at 605 nm. After conjunction (from sol 236) a first decrease in\(\tau_{I}\) was followed by a series of spikes between sol 285 and 305. Subsequently, the aforementioned major dust event occurred on sols 314-316, with a corresponding drop in \(F_{d}\) to 0.41 at 605 nm. In the aftermath of the dust event and up to sol 350, \(F_{d}\) remained stable and low in all filters, suggesting that the dust raised and transported by the wind persisted in the atmosphere. The values of\(F_{d}\) represented by triangles in the \(F_{d}\) plot of Figure 12 that appear considerably lower than the general trend (sols 64, 82, 83 and 236) are cal-target observations made with \(i>60\).