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).