Figure
12. Top panel: time evolution of the direct fraction \(F_{d}\) of
sunlight on the grayscale rings, as computed using equation (3), for the
filters L6, L4, R2 and R6. Bottom panel: time evolution of the
atmospheric optical depth \(\tau_{I}\) measured at 800nm through
Mastcam-Z observations of the Sun.
The Two-Term Linear
Fits
Since the landing of Perseverance, the linear fits employed for
Mastcam-Z calibration have regularly been performed involving only one
multiplicative term, in the form \(y=a\bullet x\). This is a
consequence of the fact that the radiance and the IOF reflectance of the
clean spots of the cal-targets are expected to be directly proportional
and lie on a line passing through the origin, and the conversion factor
is the solar irradiance. However, our data suggested that a second term,
an additive offset, might provide a better consistency between the
measured data and the fits. Therefore, we tested a “two-term” linear
fit model (in the form \(y=a\bullet x+b\), with \(b\neq 0\)) to
all the radiance-reflectance sets from the RC-files in order to study
how these fits changed within the first 350 sols and for comparison with
the one-term fits. The two-term model was only tested for investigation
reasons, and was never used for Mastcam-Z calibration. Figure 13 is a
collection of radiance-versus-reflectance plots of the clean spots from
sols 51, 210 and 302 and filters L6, R1 and R5, showing both fit models
(one- and two-term) and reporting the corresponding numerical fit
parameters. The white clean spot was excluded from the computation of
the fits, due to its misbehavior (see sect. 4.5). The fits with the
offset appeared to be systematically less steep than the one-term
counterparts and represented better the data points. The average reduced
chi-squared \(\chi_{\text{red}}^{2}\) for the two-term fits among all
narrow-band filters was 2.52, with a roughly decreasing tendency from
the shorter wavelengths to the near infrared filters, ranging between
1.43 in R5 (978 nm) and 4.71 in L4 (605 nm).