Table 2. Summary of the main groups of Regions of Interests of the cal-targets. For each group, the target, the position on the target and the number of selections are listed.
The Extraction of Solar Irradiance through Linear Fits
Following the formal approach of section 2.1, the solar irradiance \(F\)was computed as the \({\text{CT}_{\text{RAD}}/\text{CT}}_{\text{IOF}}\)ratio of equation (1 ), which in practice translated into a linear fit.
For every image of the cal-targets in some filter, we extracted the values of radiance of the eight clean spots as the averages over the pixels of their ROI selections. Simultaneously, the corresponding values of reflectance of the clean spots under the same illumination geometry as the observation were computed. These reflectances were known from laboratory measurements of the eight color and grayscale samples at different geometries across the visible and near infrared spectrum (400-2500 nm), (Kinch et al. , 2020; Buz et al. , 2019).
The values observed for the clean spots were plotted as radiance-versus-reflectance data points, and were fitted with a straight line passing through the origin, in the form \(y=a\bullet x\) (we refer to this model as “one-term fit”, because it only has one multiplicative term). The slope of the fit is equal to the irradiance\(F\), which was then applied to all the pixels of the radiance-calibrated images in that filter to generate the reflectance-calibrated products. This calibration procedure had been employed on the MER and MSL missions, and was tested successfully on Perseverance before launch at NASA ATLO (Assembly, Test and Launch Operations) facility (for reference, see section 5.4.3 from Kinchet al. , 2020).
After the landing of Perseverance on Mars, the fits were efficient indicators of the state of the clean spots in time and under different illumination geometries and atmospheric conditions. Figure 5 shows the fits relative to four different filters (L6, L3, R2 and R5) and three different sols of the mission (12, 178 and 346). One noticeable feature of the plots was the unexpected behavior of the white patch, which displayed a lower radiance than the fit, especially at shorter wavelengths. Consequently, the white clean spot was never employed for the making of the fits. The behavior of this white spot is discussed in detail in section 4.5.
In general, the relative uncertainty on the slopes of the fits was included between 2.32% in R5 (978 nm) and 4.33% in L4 (605 nm), with a mean value of 3.34% over all filters. The data points consistently hint that the fitted line which is constrained to pass through the origin is not the very best line fit to the data, rather a line with a small positive constant additive term (referred to as offset) would produce a better fit (a “two-term fit” model in the form\(y=a\bullet x+b\), with \(b\neq 0\)). This is unlike the similar tests carried out before launch at ATLO (figures 21-22 from Kinchet al. , 2020). For the radiometric calibration of Mastcam-Z we never employed an offset in our linear fit model, but we investigated the time evolution of such an offset to better understand its origin (see section 4.4). As a reference, the one-term fits used for calibration had an average reduced chi-squared \(\chi_{\text{red}}^{2}\)of 22.4, with values ranging from a minimum of 10.7 in R5 (978 nm) to a maximum of 34.4 in L2 (754 nm).
The spectral aspect of the primary clean spots obtained after the extraction of the fit slope is shown in Figure 6 for sols 12 and 339 with their reference laboratory spectra. The radiometric decline of the white patch, more impactful at shorter wavelengths, is evident, while the other clean spots were apparently not affected by the same effect. The data display a good agreement with their laboratory spectra, whereas small deviations might be due to the presence of the offset mentioned above (likely caused by non-magnetic dust and slight residuals in the radiance calibration).