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\begin{document}

\title{The Mastcam-Z Radiometric Calibration Targets on NASA's Perseverance
Rover: Derived Irradiance Time-Series, Dust Deposition, and Performance
over the First 350 Sols on Mars.}



\author[1,1]{Marco Merusi}%
\author[1,1]{Kjartan Münster Kinch}%
\author[2,2]{Morten Bo Madsen}%
\author[3,3]{James F. Bell III}%
\author[4,4]{Justin N. Maki}%
\author[5,5]{Alexander G. Hayes}%
\author[5,5]{Jonathan Joseph}%
\author[6,6]{Jeffrey R. Johnson}%
\author[7,7]{Meiissa Rice}%
\author[8,8]{Edward Cloutis}%
\author[9,9]{Daniel Applin}%
\author[10,10]{Mark T Lemmon}%
\author[11,11]{Alicia Fallacaro Vaughan}%
\author[6,6]{Jorge I. Núñez}%
\author[12,12]{Elsa Jensen}%
\author[13,13]{Jessica Z. Kristensen}%
\author[3,3]{Kristen Paris}%
\author[3,3]{Ernest Cisneros}%
\author[14,14]{Megan R Kennedy}%
\author[15,15]{Olivier Gasnault}%
\affil[1]{University of Copenhagen}%
\affil[2]{Niels Bohr Institute, University of Copenhagen, Denmark}%
\affil[3]{Arizona State University}%
\affil[4]{Jet Propulsion Laboratory, California Institute of Technology}%
\affil[5]{Cornell University}%
\affil[6]{Johns Hopkins University Applied Physics Laboratory}%
\affil[7]{Western Washington University}%
\affil[8]{University of Winnepeg}%
\affil[9]{UW}%
\affil[10]{Space Science Institute}%
\affil[11]{Apogee Engineering, LLC}%
\affil[12]{Malin Space Science Systems, Inc.}%
\affil[13]{Niels Bohr Institute, University of Copenhagen}%
\affil[14]{Malin Space Science Systems}%
\affil[15]{Institut de Recherche en Astrophysique et Planétologie (IRAP)}%


\vspace{-1em}



  
  \date{May 25, 2024}


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\selectlanguage{english}
\begin{abstract}
The Mastcam-Z radiometric calibration targets mounted on the NASA's
Perseverance rover proved to be effective in the calibration of
Mastcam-Z images to reflectance (I/F) over the first 350 sols on Mars.
Mastcam-Z imaged the calibration targets regularly to perform
reflectance calibration on multispectral image sets of targets on the
Martian surface. For each calibration target image, mean radiance values
were extracted for 41 distinct regions of the targets, including patches
of color and grayscale materials. Eight strong permanent magnets, placed
under the primary target, attracted magnetic dust and repelled it from
central surfaces, allowing the extraction of radiance values from eight
regions relatively clean from dust. These radiances were combined with
reflectances obtained from laboratory measurements, a one-term linear
fit model was applied, and the slopes of the fits were retrieved as
estimates of the solar irradiance and used to convert Mastcam-Z images
from radiance to reflectance. Derived irradiance time series are
smoothly varying in line with expectations based on the changing
Mars-Sun distance, being only perturbed by a few significant dust
events. The deposition of dust on the calibration targets was largely
concentrated on the magnets, ensuring a minimal influence of dust on the
calibration process. The fraction of sunlight directly hitting the
calibration targets was negatively correlated with the atmospheric
optical depth, as expected. Further investigation will aim at explaining
the origin of a small offset observed in the fit model employed for
calibration, and the causes of a yellowing effect affecting one of the
calibration targets materials.%
\end{abstract}%



\sloppy


\textbf{The Mastcam-Z Radiometric Calibration Targets on NASA's
Perseverance Rover: Derived Irradiance Time-Series, Dust Deposition, and
Performance over the First 350 Sols on Mars.}

M. Merusi\textsuperscript{1}, K. B. Kinch\textsuperscript{1}, M. B.
Madsen\textsuperscript{1}, J. F. Bell III\textsuperscript{2}, J. N.
Maki\textsuperscript{3}, A. G. Hayes\textsuperscript{4}, J.
Joseph\textsuperscript{4}, J. R. Johnson\textsuperscript{5}, M.
Rice\textsuperscript{6}, E. A. Cloutis\textsuperscript{7}, D.
Applin\textsuperscript{7}, M. T. Lemmon\textsuperscript{8}, A. F.
Vaughan\textsuperscript{9}, J. I. N\selectlanguage{ngerman}úñez\textsuperscript{5}, E.
Jensen\textsuperscript{10}, J. Z. Kristensen\textsuperscript{1}, K.
Paris\textsuperscript{2}, E. Cisneros\textsuperscript{2}, M. R.
Kennedy\textsuperscript{10}, O. Gasnault\textsuperscript{11}.

\textsuperscript{1}Niels Bohr Institute, University of Copenhagen,
Copenhagen, Denmark

\textsuperscript{2}School of Earth and Space Exploration, Arizona State
University, Tempe, AZ, USA

\textsuperscript{3}Jet Propulsion Laboratory, California Institute of
Technology, Pasadena, CA, USA.

\textsuperscript{4}Department of Astronomy, Cornell University, Ithaca,
NY, USA

\textsuperscript{5}Johns Hopkins University Applied Physics Laboratory,
Laurel, MD, USA

\textsuperscript{6}Geology Department, Western Washington University,
Bellingham, WA, USA

\textsuperscript{7}Department of Geography, University of Winnipeg,
Winnipeg, Manitoba, Canada

\textsuperscript{8}Space Science Institute, Boulder, CO, USA

\textsuperscript{9}USGS Astrogeology Science Center, Flagstaff, AZ

\textsuperscript{10}Malin Space Science Systems, San Diego, CA, USA

\textsuperscript{11}Institut de Recherche en Astrophysique et
Planétologie (IRAP), Université de Toulouse, CNRS, CNES, Toulouse --
France

Corresponding author: Marco Merusi (marco.merusi@nbi.ku.dk)

\textbf{Key Points}

\begin{itemize}
\tightlist
\item
  The Mastcam-Z Calibration Targets ensured quality and stability in the
  reflectance calibration of images over the first 350 sols on Mars.
\item
  Dust deposited frequently on the deck of the rover and on the
  calibration target surfaces, especially on its permanent magnets.
\item
  A small offset in the fits used for calibration and a yellowing effect
  of one material were observed and will be further investigated.
\end{itemize}

\textbf{Abstract}

The Mastcam-Z radiometric calibration targets mounted on the NASA's
Perseverance rover proved to be effective in the calibration of
Mastcam-Z images to reflectance (I/F) over the first 350 sols on Mars.
Mastcam-Z imaged the calibration targets regularly to perform
reflectance calibration on multispectral image sets of targets on the
Martian surface. For each calibration target image, mean radiance values
were extracted for 41 distinct regions of the targets, including patches
of color and grayscale materials. Eight strong permanent magnets, placed
under the primary target, attracted magnetic dust and repelled it from
central surfaces, allowing the extraction of radiance values from eight
regions relatively clean from dust. These radiances were combined with
reflectances obtained from laboratory measurements, a one-term linear
fit model was applied, and the slopes of the fits were retrieved as
estimates of the solar irradiance and used to convert Mastcam-Z images
from radiance to reflectance. Derived irradiance time series are
smoothly varying in line with expectations based on the changing
Mars-Sun distance, being only perturbed by a few significant dust
events. The deposition of dust on the calibration targets was largely
concentrated on the magnets, ensuring a minimal influence of dust on the
calibration process. The fraction of sunlight directly hitting the
calibration targets was negatively correlated with the atmospheric
optical depth, as expected. Further investigation will aim at explaining
the origin of a small offset observed in the fit model employed for
calibration, and the causes of a yellowing effect affecting one of the
calibration targets materials.

\textbf{Plain Language Summary}

The calibration targets of Mastcam-Z camera, mounted on the NASA's
Perseverance rover, are used to calibrate Mastcam-Z images from units of
radiance to reflectance. Reflectance expresses how the sunlight is
reflected by geologic targets under different geometries and wavelengths
to give insights on their nature. The radiances measured within
calibration targets were combined with known reflectances to obtain
estimates of the local sunlight. These estimates were used to calibrate
Mastcam-Z images. Our analysis shows that the calibration targets
ensured a high quality of calibration over the first 350 sols (martian
days) on Mars. The sunlight derived from the measurements can be
monitored in time and shows a smooth trend with variations due to the
changing distance between Mars and the Sun, and larger disturbances due
to significant amounts of dust raised in the atmosphere by the wind.
This dust settled on the top surface of the rover, but it minimally
affected the calibration process. We also noticed that when the
atmosphere is rich in dust, less sunlight can make it to the surface,
and vice-versa. More investigation will aim at explaining small
variations in our calibration model and a weird effect affecting one of
the materials of the calibration targets.

\textbf{Introduction}

NASA's Mars 2020 Perseverance Rover mission (Farley \emph{et al.} ,
2020) was launched from Cape Canaveral (FL) on July
30\textsuperscript{th}, 2020 and landed successfully within Jezero
crater on February 18\textsuperscript{th}, 2021. During its first 350
sols on Mars, Perseverance achieved a number of significant milestones
in planetary exploration, including the completion of a campaign of
scientific investigation of the floor of Jezero crater (Mangold \emph{et
al.} , 2021), the successful helicopter Ingenuity technology
demonstration (Balaram \emph{et al.} , 2021), the extraction of six rock
core samples, and driving almost 4 km. Among its seven scientific
instruments, the Mastcam-Z cameras (Bell \emph{et al.} , 2021) captured
thousands of images. Mastcam-Z is a multispectral, stereoscopic pair of
cameras capable of multiple focal lengths mounted on the rover's mast.
It consists of two CCD sensors with Bayer pattern that can acquire
broad-band Red/Green/Blue color images when imaging through a broad
IR-cutoff filter. In addition, 12 narrow-band filters (six for each
sensor, or `eye') span visible and near-infrared wavelengths from 440 to
1022 nm. In order to correctly calibrate Mastcam-Z images to units of
reflectance, the camera relies on a set of calibration targets
(Kinch\emph{et al.} , 2020), or cal-targets, fixed on the deck of the
rover. During the first 350 sols on Mars, the cal-targets were the most
imaged objects by Mastcam-Z.

In this manuscript we show the methods that were employed to extract
radiometric data from the images of the cal-targets and the main
results, including their performance based on calibration models, the
time evolution of the derived solar irradiance, a basic assessment of
the deposition of dust on the cal-target surfaces and its nature, the
observed fraction of direct sunlight versus diffuse illumination, and
its dependence on the optical depth of the martian atmosphere. We also
discuss an observed offset in the linear relation between radiance and
reflectance, and a ``yellowing effect'' on the white patch of the
cal-targets.

In section 2 we present the cal-targets and the basic concept of the
reflectance calibration. Section 3 is a summary of the methods used to
obtain our results, including the selection of regions of interest of
the cal-targets, the computation of the solar irradiance through linear
fits and the storage of the cal-target radiometric data. In section 4 we
report all the results concerning the calibration and performance of the
cal-targets in the first 350 sols, the dust deposition on the
cal-targets and its spectral characteristics, and the relation between
direct and diffuse solar light in time with a reference to the
atmospheric optical depth. Furthermore, we discuss the observed offset
in the linear radiance-reflectance relation. In section 5 we evaluate
the general performance of the cal-targets and the overall performance
of the current calibration procedure, based on variations in the dust
and the environment. All the figures portraying the Mastcam-Z
calibration targets are listed in a CSV file available in the supporting
material (table S1). The list includes information such as the image-ID,
sol, sequence number and the graphic values (gamma and thresholds)
employed for the display within this work.

\textbf{The Mastcam-Z Radiometric Calibration Targets}

The Mastcam-Z Calibration Targets (Kinch \emph{et al.} , 2020), or
cal-targets, are a pair of physical devices mounted on the Perseverance
rover deck (Figure 1) and primarily used to assist in the conversion of
Mastcam-Z images from units of radiance to reflectance (I/F). They were
designed and assembled at the Niels Bohr Institute of the University of
Copenhagen.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

Figure 1. Context image of the Mastcam-Z primary and secondary
calibration targets, taken by the left eye of Mastcam-Z (L0) on sol 23
at 26 mm focal length (Image-ID:
ZL0\_0023\_0668982043\_910IOF\_N0030770ZCAM03003\_0260LMA01, sequence
ZCAM03003). In the upper center, the SuperCam calibration target is also
visible.

The principal device, known as ``primary target'', is bolted to the top
of the Rover Pyro Firing Assembly (RPFA) and consists of eight round
color and grayscale ceramic patches, four concentric grayscale rings and
a central shadow post fixed on a gold-plated aluminum frame. The
circular patches, mounted in the periphery of the primary target, are
four in colors (here referred to as green, yellow, blue, red) and four
in grayscales (black, dark gray, light gray, white). Eight
hollow-cylindrical magnets are mounted underneath the round patches.
These Sm\textsubscript{2}Co\textsubscript{17} magnets are strongly
magnetized along the axis of symmetry. They attract even weakly magnetic
(in the sense of having significant magnetic susceptibility) martian
dust grains on the external annular portion of the patches, while
actively repelling such grains from the central circular part, leaving
it relatively clean from dust. The grayscale rings placed in the center
of the target are the same colors and materials as the peripheral
grayscale patches. From the innermost to the outermost, the colors of
the rings are light gray, black, white, and dark gray. The shadow post
(or gnomon) is placed at the center of the rings and painted with an
IR-black paint. The base of the primary target is made from aluminum
with silver and gold anodization and fits inside a square with a side of
98 mm. The ``secondary target'' is fixed on the vertical side of the
RPFA just below the primary target, in direct sight of Mastcam-Z, and
contains two rows of seven square tiles each mounted on an aluminum
frame. One row is situated parallel to the plane of the rover deck,
while the other row is situated perpendicularly. Both rows have the same
color tiles, with the colors being the same as the round patches of the
primary target except for the yellow. From left to right, as seen from
Mastcam-Z, they are black, dark gray, light gray, white, red, green, and
blue. The horizontal length of the secondary target is 80 mm. For a
complete technical description of the calibration targets and their
heritage from previous Mars rovers, see Kinch \emph{et al.} (2020).

In this work we adopt a simple nomenclature scheme for the different
patches and rings according to their positions, which is illustrated in
Figure 2. In the primary target, the inner circular portions of the
eight round patches are named ``central spots'' or ``clean spots'',
while the external annular portions, which lie over the magnets, are
called ``magnet rings'', not to be confused with the four concentric
grayscale rings at the center of the primary target. The name ``clean
spots'' is a consequence of the action of the magnet rings, which
capture the magnetic fraction of the airborne dust. For the secondary
target, the square patches are named ``secondary horizontal tiles'' or
``secondary vertical tiles'', depending on their orientation.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

Figure 2. The Mastcam-Z Calibration Targets imaged by the left eye (L0)
of Mastcam-Z on sol 180 at 48 mm zoom (Image ID:
ZL0\_0180\_0682919878\_394IOF\_N0062666ZCAM03014\_048085A02, sequence
ZCAM03014). The main regions of the primary and secondary targets are
indicated with the names used in this work.

From landing to sol 350, Mastcam-Z acquired 2578 images of the
cal-targets. Among those images, and all the filters of Mastcam-Z, the
L0/R0 Red/Green/Blue (RGB) Bayer broad-band filters installed within the
sensors of the two eyes of the camera were the most used, not only for
calibration as part of multispectral sequences but also to obtain color
images for testing and verification of the camera and the calibration
targets, photometric analysis, and public outreach. The amounts of
images taken among the filters of Mastcam-Z are listed in Table 1. The
RGB images in the two eyes are considered as ``single shot'' images, but
they can be split into three frames corresponding to their three Bayer
components (named L0R, L0G, L0B for the left eye and R0R, R0G, R0B for
the right eye), each one covering a different spectral range. Of the
2578 images mentioned above, 344 were transmitted losslessly, without
any lossy compression. The remaining 2234 were transmitted using an 85\%
quality level compression.\selectlanguage{english}
\begin{longtable}[]{@{}llllll@{}}
\toprule
Filter name & Range {[}nm{]} & Total images & Filter name & Range
{[}nm{]} & Total images\tabularnewline
\midrule
\endhead
L0B & 480 \(\pm\) 46 & 197 & R0B & 480 \(\pm\) 46
& 197\tabularnewline
L0G & 544 \(\pm\) 41 & & R0G & 544 \(\pm\) 42
&\tabularnewline
L0R & 630 \(\pm\) 43 & & R0R & 631 \(\pm\) 43
&\tabularnewline
L1 & 800 \(\pm\) 9 & 185 & R1 & 800 \(\pm\) 9 &
185\tabularnewline
L2 & 754 \(\pm\) 10 & 179 & R2 & 866 \(\pm\) 10 &
185\tabularnewline
L3 & 677 \(\pm\) 11 & 179 & R3 & 910 \(\pm\) 12
& 179\tabularnewline
L4 & 605 \(\pm\) 9 & 179 & R4 & 939 \(\pm\) 12 &
179\tabularnewline
L5 & 528 \(\pm\) 11 & 185 & R5 & 978 \(\pm\) 10
& 179\tabularnewline
L6 & 442 \(\pm\) 12 & 185 & R6 & 1022 \(\pm\) 19
& 185\tabularnewline
\bottomrule
\end{longtable}

Table 1. Summary of the total number of images of the Calibration
Targets taken by Mastcam-Z in each filter within the first 350 sols on
Mars. For each filter, the corresponding spectral range is reported.

These images were captured by Mastcam-Z at several illumination
geometries relative to the cal-targets. The illumination geometry of an
observation is described by three angles. We define these three angles
as \emph{incidence} , \emph{emission} and \emph{azimuth} . The incidence
angle (\(0\leq i\leq 90\)) is measured between the zenith of the target
and the Sun-target direction, the emission angle (\(0\leq e\leq 90\)) is
measured between the zenith of the target and the detector-target
direction, while the azimuth angle (\(0\leq\text{Az}\leq 180\) for hemispheric
symmetry) is measured on the plane of the target and is the angle
between the planes of incidence and emission. The angles
\(i\) and \(e\) are measured from the zenith.
The emission angle is fixed by the geometry of the rover with the
primary and secondary targets seen by Mastcam-Z under emission angles of
approximately 58 and 54, respectively. The overall distributions of the
incidence and azimuth angles of the cal-target images are reported in
Figure 3. A total of 197 cal-target sequences (which include images in
only L0/R0 or all filters) were acquired by Mastcam-Z over the first 350
sols, each of which can be identified by its incidence and azimuth
angles. The left plot in Figure 3 shows the combinations of incidence
and azimuth angles of those 197 sequences. Summing the data points along
the two axes of the plot yields the two histograms of azimuth and
incidence in Figure 3 on the right. Given the changing orientations of
Perseverance, the azimuth angles are evenly distributed, though with a
larger frequency in the 5-10 interval, which corresponds to the Sun
being approximately behind Mastcam-Z during the observation (Sun in
front of the rover), and a much lower frequency of observations at
opposite azimuth. In addition, most observations were made with the Sun
relatively high above the horizon, with 88\% of images taken at
incidence angles lower than 30 and a peak around 10-15.

As studied by Buz \emph{et al.} (2019) and by Kinch \emph{et al.} (2020)
in the pre-flight tests, at the typical emission angle of 58 all the
color and grayscale materials of the cal-targets (though to a lesser
extent for the white patches) show a strong forward scattering peak with
incidence angles \(>45\). The smaller number of observations
on Mars with the Sun opposite to the camera (high azimuth) reduced the
impact of the forward scattering, which in some cases
(\(i\geq 50\)) was quite significant. In addition, at higher
incidence angles the diffuse light acquired importance within the dusty
atmosphere, reducing the contrast between the sunlit and shadowed
regions. Early martian morning or late afternoon observations proved
challenging for estimating the solar irradiance as part of the
reflectance calibration, and this will serve as a starting point for
improvements in our data processing in the future. The best estimates of
the irradiance were obtained when the Sun was high in the sky, with a
smaller atmospheric path length and negligible forward or backward
scattering. Mastcam-Z acquired most cal-target images at incidence
angles lower than 30. However, since the diffuse light had a major
impact at low Sun, this geometry was particularly useful to monitor the
dust suspended in the atmosphere. This was done by comparing the
radiance from the regions in the gnomon shadow on the grayscale rings to
those in the direct sunlight (see sect. 4.3.2).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

Figure 3. Distributions of incidence and azimuth angles of all the 197
cal-target image sequences. The plot on the left shows the
incidence-azimuth combinations of the sequences, while the histograms on
the right illustrate how those sequences are distributed in terms of
azimuth and incidence. Each data point in the plot on the left,
corresponding to an entry in the two histograms on the right, is a
single cal-target sequence, which includes at least one image for each
eye of Mastcam-Z in the same observation (in most cases it is either in
all filters or only in L0/R0).

\textbf{The Radiance-to-Reflectance Calibration}

The primary objective of the cal-targets is the generation of
reflectance-calibrated images. As a last step of the radiometric
calibration, all Mastcam-Z images in units of radiance
(i.e.,\(W/(m^{2}\bullet\ \text{nm}\bullet\text{sr})\)), (Hayes \emph{et al.} , 2021), are calibrated
to radiance factor I/F (or IOF), where \(I\)is the radiance
from the scene and \(F\) is the instantaneous solar
irradiance. IOF is defined as the reflectance relative to that of a
perfect Lambertian scatterer illuminated from the zenith. While the
radiance can be measured, the local irradiance \(F\) is
challenging to model at the martian surface due to its dependency on
illumination geometries and atmospheric conditions that change over
short timescales. To address this directly, frequent imaging of the
cal-targets in all filters is performed (in general cal-target images
accompanied any multispectral observation of surface targets).

The following equation is used to convert radiance images into IOF
(Kinch \emph{et al} ., 2020):\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(\text{Image}_{\text{IOF}}=\text{Image}_{\text{RAD}}\frac{\text{CT}_{\text{IOF}}}{\text{CT}_{\text{RAD}}}\ ,\) & (1)\tabularnewline
\bottomrule
\end{longtable}

where \(\text{Image}_{\text{RAD}}\) and \(\text{CT}_{\text{RAD}}\) are the pixel-by-pixel
measured radiances of the image to calibrate and the cal-targets,
respectively, and \(\text{CT}_{\text{IOF}}\) is the reflectance of the
cal-target materials, which is known from laboratory spectra. The ratio
between \(\text{CT}_{\text{IOF}}\) and\(\text{CT}_{\text{RAD}}\) in equation (\emph{1} )
is equal to the inverse of the irradiance \(F\). The IOF
calibration allows the extraction of reflectance spectra of interesting
terrain units and specific geologic targets that can be consistently
compared and for which the nature can be assessed in detail (e.g., from
this issue: Garczynski \emph{et al.} , Horgan \emph{et al.} , N\selectlanguage{ngerman}úñez
\emph{et al.} , Rice \emph{et al.} , Vaughan \emph{et al.} for Mastcam-Z
reflectance data, and Royer \emph{et al.} , Mandon \emph{et al.} , for
SuperCam data). In addition, frequent estimates of the solar irradiance
\(F\) constrain atmospheric conditions and dust
displacement over time.

IOF values can be converted to units of reflectance factor R* through
the equation:\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(R^{*}=\frac{\text{IOF}}{cos(i)}\ ,\) & (2)\tabularnewline
\bottomrule
\end{longtable}

where \(i\) is the incidence angle of the observation.
This, of course, requires knowledge of \(i\) or
alternatively a simplifying assumption (e.g., modeling the martian
surface as a flat plane). R* is defined as the reflectance relative to
that of a perfect Lambertian scatterer illuminated in the same geometry
as the observation.

\textbf{Methods}

\textbf{Selection of the Regions of Interest on the Calibration Targets}

In the practical implementation of the IOF calibration, the radiance
values of the eight primary clean spots (expected to be the least dusty
surfaces) were extracted. The process of selection of these regions was
part of a more general context, which aimed at collecting the average
radiance values of all the main areas, named Regions of Interest (ROIs),
of the cal-targets. This process was similar to that implemented for MER
(Bell \emph{et al.} , 2003, 2007) and MSL (Bell \emph{et al.} , 2017)
calibration targets. The selection of ROIs was made automatically by an
algorithm that, by recognizing the pattern of the cal-targets, overlaid
two model templates (one for each eye) on the cal-target images. Each
template consisted in a graphic mask (over transparent background)
containing all the ROI selections in different colors (Figure 4). This
operation required regular human intervention, usually in order to
manually edit the regions when the algorithm did not recognize shadows.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

Figure 4. Example of ROI selections over an image of the cal-targets
taken by the left eye of Mastcam-Z in the L1 filter (800 nm) on sol 69
at 48 mm focal length (Image-ID:
ZL1\_0069\_0673052731\_973IOF\_N0032208ZCAM03014\_048085A03, seq.
ZCAM03014). All 41 regions of interest are visible in colors, including
those under the gnomon's shadow on the grayscale rings. The two ROI's
partially selected in the secondary target were edited to exclude the
shadows due to the bolts of the support.

The maximum number of ROIs was 41, though not all of them were always
selectable due to the position of the gnomon shadow on the grayscale
rings, which depended on the incidence and azimuth angles. For these
reasons, the number of ROIs on the grayscale rings within the gnomon
shadow ranged from 0 to 4. On sols 3, 206, 290 and 305 some clean spots
appeared shadowed by the gnomon owing to low Sun angles. More commonly,
shadowing of one or both rows of the secondary target occurred due to
its location on the side of the RPFA.

Once all the ROIs were selected suitably, their locations were
documented along with the average and standard deviation of measured
radiances over their pixels. The list of ROI groups is reported in Table
2.\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
Target & Regions & Number of selections\tabularnewline
\midrule
\endhead
Primary & Clean spots & 8\tabularnewline
Primary & Magnet rings & 8\tabularnewline
Primary & Sunlit grayscale rings & 4\tabularnewline
Primary & Grayscale rings in the gnomon shadow & Up to 4, depending on
gnomon shadow size and observation geometry\tabularnewline
Secondary & Horizontal tiles & 7\tabularnewline
Secondary & Vertical tiles & 7\tabularnewline
All scene & Primary target and rover deck & 3 (portion of deck, portion
of the golden base and top of the gnomon)\tabularnewline
\bottomrule
\end{longtable}

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.

\textbf{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 (\emph{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 \emph{et al.} , 2020; Buz \emph{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
Kinch\emph{et 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 Kinch\emph{et 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).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

Figure 5. Examples of one-term linear fits (in the form
\(y=a\bullet x\)) over the data points of measured radiance and model
reflectance factor for three sols (sol 12, 178, 346, along the columns)
in four filters (L6, L3, R2, R5, along the rows). The straight black
lines are the fits. All the eight clean spots are plotted, but the white
was not used to compute the fits.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image6/image6}

\end{center}
\end{figure}

Figure 6. Calibration Target spectra from sol 12 and 339. The circles
are the observed calibrated R* reflectances of the clean spots, while
the solid lines represent the corresponding laboratory spectra.

\textbf{The Radiometric Coefficients Files}

A major portion of the cal-target sequence processing included the
generation and storage of information on the images and their ROI
selections. We refer to these as Radiometric Coefficients files, or
simply RC-files, which were created simultaneously with the linear fits
described in section 3.2. The first part of a typical RC-file included
metadata (e.g., name of the corresponding cal-target image, local
martian time of the original image). The body of the file included a
list of arrays, each of which was formed by 41 fields (one for each ROI
selection). The algorithm that selected the ROIs for each region
included the complete name of the region, its average radiance over the
pixels and uncertainty of this radiance, number of pixels selected,
illumination geometry angles and model reflectance related to the color
material and to the geometry of the region. The inverse of the slope of
the linear fit described in section 3.2 was also included in the
RC-files, along with three Boolean arrays of flags (expressed in terms
of 0 and 1) that specified which regions had been selected, which ones
were ``bad'' and should not be used (usually due to unwanted shadows),
and which should be used to make the linear fits for calibration. We
used a graphic interface to mark the regions appropriately. Whenever a
region had not been selected, its place in the data arrays of the
RC-files did not show any numerical value. An example of an RC-file is
given in appendix 1.

\textbf{Results}

All quantitative results that we present here have been obtained from
the values stored in the entire set of RC-files covering the time range
from landing to sol 350. In each color image in L0 and R0, one RC-file
was extracted individually from each of the three broad-band channels
(L0B, L0G, L0R, and R0B, R0G, R0R). Hence, the total number of RC-files
in our set was 3366. The regions of the cal-targets that were not
selected or were marked as bad were not included in the following
analysis.

\textbf{Imaging of the Calibration Targets on Mars}

The considerable number of color images of the cal-targets acquired by
Mastcam-Z allowed a regular visual check of their conditions over time,
including the accumulation and displacement of airfall dust and
monitoring the color and grayscale materials.

Figure 7 is a comparison of four selected Bayer RGB images of the
cal-targets taken by the left eye of Mastcam-Z. The most evident details
that can be visually evaluated in time are the progressing change of hue
of the primary white patch (that effect is reflected in the fits shown
in section 3.2) and the accumulation of dust and sand on the surfaces.
The former is commonly referred to as ``yellowing'' effect that degraded
the reflectivity at shorter wavelengths of the visible layer of the
white material (AluWhite98) since landing. The term ``yellowing'' merely
comes from the fact that the white patch was noted to fade towards a
yellowish tone in the color images. A more detailed treatment of the
problem is reported in section 4.5.

Figure 7 also illustrates the progressive increase in the amount of
magnetic dust with time on the primary magnet rings, manifested as an
overall dark reddish color. This outcome, which was also observed on the
MER (Madsen \emph{et al.} , 2009) and MSL (Bell \emph{et al.} , 2017)
rovers, was expected from the cal-target design. The underlying colors,
that were already attenuated but still visible after the first sols
(Figure 7a), were not as discernible at the end of the period under
analysis in this work (Figure 7d). On other surfaces, such as the other
parts of the cal-targets or the deck surroundings, the deposition seemed
to be ruled by either original deposition of small grains during the
landing event, wind activity capable of transporting larger grains on
top of the deck, and/or airfall dust. In general, airfall dust and
larger grains were displaced frequently, allowing the cal-targets to
remain rather clean. In addition, the deposition of dust on the
secondary target was affected by its position on a vertical surface,
which would limit the fraction of dust falling on the horizontal tiles.
During the first 350 sols of the mission Perseverance experienced
several significant episodes of high wind and local dust lifting. The
strongest event occurred between sols 314 and 316 (Lemmon \emph{et al.}
, 2022), with consequences visible for several sols (Figure 7d).
Appreciable layers of brownish airfall dust and sand were conspicuous on
the grayscale rings, on the deck next to the primary target (including
the vertical side of the golden base), and on the secondary horizontal
target following this event.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image7/image7}

\end{center}
\end{figure}

Figure 7. Appearance of the calibration targets in 4 Mastcam-Z color
images taken by the left eye on (a) sol 23, (b) sol 130, (c) sol 237 and
(d) sol 346. Image (a) was acquired at 63 mm zoom and had sequence
number ZCAM03003, while (b), (c) and (d) at 48 mm and had sequence
number ZCAM03014. Image-IDs: (a)
ZL0\_0023\_0668982767\_910IOF\_N0030770ZCAM03003\_0630LMA01, (b)
ZL0\_0130\_0678477333\_428IOF\_N0042222ZCAM03014\_048085A03, (c)
ZL0\_0237\_0687977979\_443IOF\_N0072050ZCAM03014\_048085A02, (d)
ZL0\_0346\_0697653263\_269IOF\_N0092982ZCAM03014\_048085A02. The four
images have the same color thresholds (Red: {[}0.014054-0.990546{]},
Green: {[}0.013349-0.928501{]}, Blue: {[}0.014054-0.959881{]}) and the
gamma set to 1.5.

Since the ROIs that were normally used for IOF calibration were the
eight clean spots, it is interesting to show some statistics of the
number of pixels for the corresponding eight regions at three zoom
settings: the two extremes (26 mm and 110 mm) and the most employed zoom
setting (48 mm). The 26 mm zoom was used to image the cal-targets only
at the beginning of the mission, between sols 9 and 26, in a total of 54
frames. The average number of pixels over the eight regions and the 54
frames was approximately 15. For the 110 mm zoom, the average on the
values obtained on Mars (42 frames) was 396 pixels. Kinch \emph{et
al.}(2020) considered the shapes of the clean spots as ellipses when
seen from Mastcam-Z, retrieving their major and minor axes respectively
of 10 by 5 pixels for the 26 mm zoom and 40 by 20 pixels for the 110 mm
zoom. These numbers give areas of 40 and 630 pixels, respectively. The
values that we obtained were lower than these estimates, likely because
their prediction was computed over the entire surface of the clean
spots. The algorithm that selected those regions always picked a smaller
central portion of the clean spots, leaving a reasonable margin from the
boundary of the magnet rings in order not to select dusty pixels that
could systematically affect our measurements. However, 93\% of the total
number of cal-target images in the first 350 sols of the mission were
captured with a 48 mm focal length. For this setting, the average number
of pixels was 67.

\textbf{Solar Irradiance Time Series}

The slopes of the one-term linear fits used for IOF calibration are
indicators of the instantaneous solar irradiance. Because this could be
affected by multiple factors, such as Sun-Mars distance, atmospheric
conditions, dust and light diffusion, monitoring the slope values is an
efficient way to evaluate indirectly the martian environment and its
variations in time. In addition, the illumination geometry could
influence the slope extracted from the fit, especially when the Sun is
low on the horizon. Therefore, we distinguished between observations
with incidence angle smaller and greater than 30. The plot in Figure 8a
shows the temporal evolution of the slopes for the 12 narrow-band
filters. All filters followed a smooth curve with a higher dispersion at
shorter wavelengths, forming a shallow depression with the minimum on
the martian aphelion, which was expected due to the larger distance from
the Sun. The maximum will occur at the perihelion (sol 475). Notably,
around sol 315 a major wind event left new particles on the cal-targets
and raised a significant amount of dust in the atmosphere, causing a
sudden drop in the irradiance. Since then, the irradiance kept
increasing at levels lower than those before the event.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image8/image8}

\end{center}
\end{figure}

Figure 8. (a) Time evolution of the solar irradiance from landing to sol
350, in terms of slopes of the one-term linear fits between radiance and
reflectance of the cal-targets. The colors represent the different
narrow-band filters of Mastcam-Z. The blue dashed line is the martian
aphelion. (b) Solar irradiance spectrum around the martian aphelion. The
black points are the sample spectrum of solar irradiance obtained as the
average of the slopes in each filter between sols 100 and 180 (the two
black solid lines in plot (a)). The blue solid curve is a model black
body curve for the Sun (T=5775 K) as seen from Mars.

The subsequent step of the analysis was the extraction of the spectral
irradiance of the Sun. For each narrow-band filter, we computed the
average of the slopes over the time range which showed the most flatness
of the curves. This was centered on the aphelion (sol 140) with a margin
of 40 sols in each time direction (i.e., from sol 100 to 180). The
resulting spectrum, sampled in the 11 wavelengths, is reported in the
Figure 8b together with a model black body spectrum of the Sun (T = 5775
K) as reference. Considering the atmospheric extinction, which affects
the data but is not included in the model, the data points and the model
spectrum are in good agreement at longer wavelengths but the data points
fall below at shorter wavelengths as expected due to absorption by dust
in the Martian atmosphere.

\textbf{Dust Assessment and Properties}

Some insights on the martian dust within the rover site can be retrieved
from Mastcam-Z images of the cal-targets. These include the deposition
of dust and other materials on the cal-target surfaces, the magnetic
properties of the dust on the magnet rings, as well as the evolving
atmospheric dust content.

\textbf{Deposition of Material on the Calibration Targets}

During the first 350 sols of Perseverance on Mars, we observed
variability in the dust patterns on the cal-target surfaces and on the
deck in the immediate vicinity of the primary target. Sol after sol,
layers of airfall dust and larger sand grains were transported by the
wind, deposited on those flat areas and were displaced or even cleaned
out by wind events and the motion of the rover. In order to monitor the
dust settlement and displacement more efficiently, we realized a movie
sequence of all the radiance-calibrated RGB images of the cal-targets
acquired by the left eye of Mastcam-Z from landing to sol 350, suitably
aligned by an algorithm to minimize shifts and distortions between the
frames. The movie is available in the supporting material (movie S2).
From the movie, the deposition of dust and sand was very modest up to
sol 86, when several small grains were transported on the deck. Between
sols 124 and 138 there was a more intense wind activity, which
continuously displaced larger sand grains and swept away the finer dust.
Around sols 166 and 169 fine grains deposited on the deck, the grayscale
rings and the secondary horizontal target. From sol 280 to 299 more fine
grains deposited on the grayscale rings, while the larger sand grains
were translated several times by a few millimeters. On sol 314 a major
dust event struck, bringing a large amount of dust and fine sand grains
on all the surfaces of the deck and the cal-targets, that was more
perceivable from sol 316. A considerable fraction of this dust was swept
off of all these surfaces first between sols 327 and 333, and then on
sols 349 and 350, when the deck and the grayscale rings appear quite
clean and on the secondary target the dust is concentrated along the
side between the horizontal and the vertical rows.

Figure 9 displays the distribution of a significant dust layer on sol
318, which formed during the major dust event that struck from sol 314.
This fine dust, recognizable from the darker brown tone in the color
image on the left, is more discernible in the corresponding
decorrelation stretch (DCS) in the L2, L5 and L6 filters on the right, a
technique that enhances color differences in an image (Gillespie\emph{et
al.} , 1986). Within the DCS image, the dust appeared as a purple
coating on the deck around the primary target, on the grayscale rings
and on the secondary horizontal tiles.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image9/image9}

\end{center}
\end{figure}

\emph{Figure 9. Highlight of the airfall dust on the cal-targets and the
rover deck on sol 318, as result of the dust event that started on sol
314. The left image is an RGB shot by the left eye of Mastcam-Z on sol
318 at 48 mm zoom (seq. ZCAM03014), while the image on the right is the
outcome of a decorrelation stretch (DCS) performed on the left image.
The DCS was obtained using the L2 (754 nm), L5 (528 nm) and L6 (442 nm)
filters for the Red, Green and Blue channels, respectively. Image-ID:
ZL0\_0318\_0695174407\_428IOF\_N0090000ZCAM03014\_048085A02.}

Large sand grains appeared frequently in the cal-target frames, with a
characteristic dark color. These grains were able to persist for several
sols on the deck around the cal-targets, since a strong drag force of
the wind or vibrations due to the rover's drive are required to move
such massive and large grains. Figure 10 shows four examples of such
grains on the deck around the primary target imaged by Mastcam-Z on sols
23 and 302, with a zoom-in on one of those grains (Figure 10c).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image10/image10}

\end{center}
\end{figure}

Figure 10. Primary target imaged by the left eye of Mastcam-Z (a) on sol
23 at 100 mm focal length (seq. ZCAM03014) and (b) on sol 302 at 48 mm
focal length (seq. ZCAM03014) with the presence of large sand grains
indicated by arrows. (c) One of the grains in the sol 23 image is
magnified for better display. Image-IDs: (a)
ZL0\_0023\_0668983099\_910IOF\_N0030770ZCAM03003\_1000LMA01, (b)
ZL0\_0302\_0693748246\_223IOF\_N0090000ZCAM03014\_048085A02.

However, the regions which experienced the greatest accumulation of dust
were the magnet rings of the primary target. As anticipated in section
2, the aim of the underlying magnets was to attract magnetic dust on the
external rings of the round patches. The visible condition of these
rings was shown in Figure 7, where a small quantity of dust already
deposited during the first 23 sols and the thickness of the dust layer
was quite considerable at the end of the period under examination, in
which the color of the patches was almost completely invisible under the
dark red/brown coating (Figure 7d). We extracted the reflectance factor
values of the magnet rings from several sols, where the ROIs of the
magnet rings were selected with the template of Figure 4. Four spectra
of the magnet rings are shown in Figure 11 for sols 12, 129, 265 and 346
for the eight color and grayscale materials. Generally, the dust layers
decreased the reflectance of the brighter patches and raised that of the
darker patches, bringing their appearance to a convergence with a
reduction of the contrast and reddening. At the end of the time range
under examination (Figure 11d), the magnet rings were almost coincident
at shorter wavelengths, but showed a slight separation in the near
infrared, suggesting that in that range the dust was less optically
thick with respect to the color patches underneath.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image11/image11}

\end{center}
\end{figure}

Figure 11. Reflectance spectra of the magnet rings of the primary
calibration target in four different moments of the mission: (a) sol 12,
(b) 129, (c) 265, (d) 346. Each color corresponds to a different color
or grayscale material. The scales of reflectance factor have been
adapted to the plot size for better display.

\textbf{Direct and Diffuse Sunlight on the Grayscale Rings}

Suspended dust is one of the main sources of diffuse sunlight within the
thin martian atmosphere. This phenomenon affects the measured radiance
of the observed targets because the surfaces directly illuminated by the
Sun will receive the sum of direct sunlight and diffuse light, while the
shaded regions will receive only light from the diffuse component. The
diffuse light and the presence of dust in the atmosphere can be
evaluated using the direct fraction of sunlight \(F_{d}\)
(Kinch\emph{et al.} , 2007), defined as follows:\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(F_{d}=\frac{\text{RAD}_{\text{illum}}-\text{RAD}_{\text{shad}}}{\text{RAD}_{\text{illum}}}\ ,\) & (3)\tabularnewline
\bottomrule
\end{longtable}

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 (Bell\emph{et 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 \textless{}5\% across the
Mastcam-Z wavelength range (Lemmon \emph{et al.} , 2019). Solar images
were reduced to optical depths following the procedure of Lemmon
\emph{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 \(i>60\).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image12/image12}

\end{center}
\end{figure}

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.

\textbf{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).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image13/image13}

\end{center}
\end{figure}

Figure 13. Plots of measured radiance versus model reflectance factor
for 3 sols (51, 210 and 302) and 3 filters (L6, R1 and R5), showing the
related one-term fit model (solid line) and the two-term fit model
(dashed line). The values of the slopes and offset are reported for both
models in the lower right corner of each box. The white clean spot was
not used for the computation of the fits.

The slightly greater flatness of the two-term fits that came out of the
slope computation also resulted from the relative difference between the
slopes in the two models. We quantify this relative
difference\([(\text{slope}_{\text{two}\_\text{term}}-\text{slope}_{\text{one}\_\text{term}})/\text{slope}_{\text{one}\_\text{term}}]\)in Figure 14a for four filters (L6, L3, R2,
R6). The data points at very low values on sol 9 and 23 were due to a
low resolution (26 mm and 34 mm, respectively). If we exclude these two
observations and those after sol 314, that were strongly perturbed by
the dust event, the differences were negative and slightly increasing in
absolute value with time. The difference in filter L6 (442 nm, purple
circles) had a net decrease from -0.09 to -0.12 (-35\%), while R6 (1022
nm, black circles) went from -0.17 to -0.20 (-13\%). All the other
filters followed a similar trend, with rates between -15\% and -28\%. In
addition, the relative differences in slopes did not follow any linear
dependency on wavelength. The plot of Figure 14b shows the averages of
the relative differences for each filter over the sol range 100-180
(across the martian aphelion, highlighted by the two vertical solid
lines in Figure 14a). All the points are included between -0.2 and
-0.07, with L6 being the highest and R6 the lowest. The spectrum of the
relative difference is characterized by a decrease from -0.09 in L6 to
-0.15 in L4 (442 nm to 605 nm), followed by a rough slight increase up
to -0.14 in R5 (978 nm) and a drop to -0.19 in R6.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image14/image14}

\end{center}
\end{figure}

Figure 14. (a) Time evolution of the relative difference between the
slopes of the two- and one-term fits for four narrow-band filters. Each
color corresponds to a different filter. The relative difference is
computed as\([(\text{slope}_{two\_term}-\text{slope}_{one\_term})/\text{slope}_{one\_term}]\). The circles are observations with
\(i\leq 30\), the triangles are\(i>30\). The vertical
dashed line is the martian aphelion. (b) Average of the relative
difference of slopes for all 12 narrow-band filters, over the range from
sol 100 to 180 (corresponding to the two vertical solid lines in panel
(a)).

The offsets for all the two-term fits over time from landing to sol 350
are represented in Figure 15 for the primary clean spots, the grayscale
rings, and the secondary horizontal tiles. The white patch was excluded
from the computation of the fits for the primary clean spots and the
secondary horizontal target, but not for the grayscale rings, since it
was not observed there. The offsets are calculated in radiance units,
which we converted to units of IOF for easier comparison by
filter-to-filter and sol-to-sol. The offset values are roughly
wavelength dependent, increasing with increasing wavelength. Most
filters fall fairly close in a tight band between 0.05 and 0.1 while the
shortest and longest wavelengths fall outside this range. The clean
spots (Figure 15a) and secondary horizontal target (Figure 15d) are
quite similar, while the grayscale rings (Figure 15c) are characterized
by a more dramatic divergence in the near infrared filters (R4-R6, from
900 nm to 1000 nm), though also in this case the L6 is consistently well
below the other filters. The average increase of the offsets for the
grayscale rings was 14\% and for the secondary horizontal target 25\%,
on average. In particular, for the secondary horizontal target the
increase rate became flatter towards the longer wavelengths (from 56\%
in L6 to 7.7\% in R6). The grayscale rings present a more random
distribution, with the filters R4-R6 (from 900 nm to 1000 nm) following
a slight decrease (-8\% in R6). The offsets are quite stable in time
showing a limited increase over the 350 sols. Figure 15b shows the
offsets of the clean spots as function of the wavelengths of the 12
narrow-band filters, where the offsets in each filter have been averaged
over the first 100 sols (blue circles) and the last 100 sols (red
circles) considered in our analysis (sols 0 to 350). The spectral shape
of the offsets showed a smooth trend with first increase between L6 and
L2 (442 nm and 754 nm, respectively), followed by a slight decrease and
a final increment from R2 (866 nm) to R6 (1022 nm). In addition, the
mean offsets in the 250-350 sol interval were 14\% higher than those in
the first 100 sols of the mission, with a minimum increase in the near
infrared (6.3\% in R6) and larger increase at shorter wavelengths
(20.7\% in L6).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image15/image15}

\end{center}
\end{figure}

Figure 15. Time evolutions of the two-term linear fit offsets within the
first 350 sols on Mars for (a) primary clean spots, (c) grayscale rings
and (d) secondary horizontal patches. Each color corresponds to a
different narrow-band filter. The dashed vertical line is the martian
aphelion. (b) Offsets for the clean spots averaged over the first 100
sols of the mission (blue circles) and on the last 100 sols considered
in this work (sols 250-350, red circles), represented as function of the
wavelength of the corresponding narrow-band filters.

\textbf{The Yellowing of the AluWhite98}

One of the prominent discoveries related to the cal-targets was the
``yellowing'' effect of the AluWhite98 material. The evolution of this
problem with time was documented since landing through the progressive
visible yellowing of the white patches in the color images, and the
advancing decrease of the corresponding measured short-wavelength
radiance, which is reflected in the linear fits (Figure 5) and hence,
the cal-target spectra (Figure 6). Therefore, the primary white patch
was always excluded from the IOF calibration procedure, which relied on
the other seven clean spots. Figure 16 presents a close-up on the
primary white and light gray patches in four different sols. The gradual
deterioration of the white color is evident as time passed, especially
if compared to the light gray and to the white grayscale ring, which did
not show any change. Both secondary AluWhite98 tiles were also affected.
In addition, the issue was more pronounced at shorter wavelengths (L6,
L5 and L4) and the effect was gradually fainter and imperceptible
towards the near infrared. Curiously, the white ring, which is
manufactured from the same material, was unaffected or only affected to
a very limited degree.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image16/image16}

\end{center}
\end{figure}

Figure 16. Visual juxtaposition of 4 close-ups of the primary white and
light gray patches of the cal-targets imaged by the left eye of
Mastcam-Z on sol 9, 128, 208 and 349 to highlight the progressive visual
yellowing of the AluWhite98. In each image, the white patch is on the
left, the light gray on the right. Image-IDs: (a)
ZL0\_0009\_0667741621\_113IOF\_N0020000ZCAM03000\_1100LMA01, (b)
ZL0\_0128\_0678304502\_223IOF\_N0041860ZCAM03014\_048085A03, (c)
ZL0\_0208\_0685400431\_053IOF\_N0071836ZCAM03014\_048085A02, (d)
ZL0\_0349\_0697919843\_098IOF\_N0092982ZCAM03014\_048085A02.

To have a better overview on the spectral dependency of the yellowing,
the time evolution of the ratio between the measured and the expected
IOF reflectance is reported in Figure 17 for the primary white patch,
the primary light gray patch, the white grayscale ring, and the white
secondary horizontal tile.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image17/image17}

\end{center}
\end{figure}

Figure 17. Ratio between the measured IOF and the model IOF values of
(a) the primary white clean spot, (b) the light gray clean spot, (c) the
white grayscale ring and (d) the secondary horizontal white patch. The
colors of the points are the same for the four plots and represent the
narrow-band filters. The vertical dashed line is the martian aphelion.

For the primary white patch (Figure 17a), the points were systematically
just below 1 for all filters spanning the range between 677 nm and 1022
nm, while filters L4 (605 nm), L5 (528 nm) and L6 (442 nm) displayed
progressively lower values. These three filters followed a similar
trend: a first interval, from landing to sol 100, characterized by a
linear and faster decrease, followed by a flatter decline which lasted
at least until the solar conjunction of sols 217-235. After conjunction,
they tended to be overall more stable (L6 seemed to increase slightly)
up to the period of the major dust event of sol 315. There was not a
clear relationship with the solar aphelion. For reference, Figure 17b
shows unchanging ratios for the light gray primary patch. This material
did not exhibit any significant deviation from the unit ratio before the
dust event. Although manufactured from the same material as the other
white patches, the white primary ring was not or only very slightly
influenced by the yellowing effect (Figure 17c).

\textbf{Discussion}

In this section we discuss the performance of the Mastcam-Z radiometric
calibration targets in light of the methods presented in section 3 and
the results presented in section 4. Principally, we want to evaluate the
performance of the cal-targets over the first 350 sols on Mars and the
model used to generate the reflectance-calibrated products. In addition,
we display a basic assessment of the dust on the cal-targets and the
effect on the diffuse light. Eventually, we describe the tests that were
aimed at understanding the visual and spectral deterioration of the
AluWhite98 material.

\textbf{The Cal-Target Performance and the Linear Fit Model for IOF
Calibration}

The performance of the Mastcam-Z calibration targets can be assessed
from the results reported in sections 3.2 and 4.2, and the visual
inspection of the regions involved in the IOF calibration process within
the color images (section 4.1). The plots of Figure 5 show a limited
dispersion of the data from the fit lines (except for the white spot),
where this dispersion was quantified as a relative error on the slopes
of less than 3.5\% on average. This small deviation indicates that the
cal-targets were successful in achieving their main goal, especially
thanks to their design and the inclusion of the permanent magnets. The
number of clean spots, higher than in the previous missions,
considerably reduced the impact of the exclusion of one of those regions
(the AluWhite98) from calibration, thanks to the other seven regions.
The presence of the hollow magnets below the primary patches but not in
the secondary target was a useful way to visually infer the accumulation
of airfall dust on the surfaces. The magnet rings, as expected, were the
first regions to be covered in dust, as shown in and Figure 11. We
should also consider the action of the wind, which contributed to a
frequent and efficient deposition and cleaning from dust on other parts
of the cal-targets (e.g., on sols 327 and 349, as shown in the movie
S2). These effects on the clean spots were critical for the radiometric
calibration, because they ensured minimal dust disturbance of the clean
spots' radiances when the linear fits were made with the corresponding
laboratory reflectances (Figure 5). As a consequence, the data points in
those plots were well described by the one-term fit model, which was
expected by the theory (equation (\emph{2} )). The `cleanliness' of the
clean spots due to the magnets and the wind was adequately maintained in
time, as suggested by the solar irradiance time series (Figure 8a).
Indeed, the irradiance \(F\) followed a quite stable and
smooth trend in all filters up to the dust event of sols 314-316 that
caused a significant unsettlement in images and radiance values, but
that did not compromise the cal-targets or their surfaces. Further proof
of the effectiveness of the clean spot-magnet ring system was the solar
irradiance spectrum at the aphelion (Figure 8b), which is consistent
with a solar black body model allowing for some atmospheric absorption,
particularly at short wavelengths.

As mentioned in section 3.2 and fully treated in section 4.4, though the
one-term linear fits characterize well the radiance-reflectance data
points, we noticed a small offset in the distribution of the data points
with respect to the straight line passing through the origin. The
testing of a two-term model for the linear fits gave better statistical
outcomes. Over the whole sets of radiance-reflectance data, the one-term
model yielded a reduced \(\chi^{2}\) between 10.7 and 34.4, the
two-term yielded values between 1.43 and 4.71. The exact nature of this
offset is not yet known. It might be due to some computational source,
such as residuals from the radiance-calibration process when the
corrections (e.g., bias frames, flat fields, shutter frame subtraction)
are applied to the raw images, or slight discrepancies in the
reflectance model that is employed to give an estimate of the expected
reflectance of each clean spot at any illumination geometry. The
presence of dust on the surfaces would also tend -- to first order -- to
result in a straight line with an offset. The slowly increasing trend of
the offset in all the narrow-band filters might indicate a dust-related
origin. This may imply that a small fraction of weakly or even
non-magnetic airfall dust (not attracted or repelled by the magnets)
gradually deposited within the clean spots and adhered
electrostatically, such that it could not be swept by wind interaction.
The appearance of the offset shortly after landing might suggest that
dust and sand were raised by the rockets of the skycrane during landing.
Deeper investigation is required to fully understand the origin and the
nature of this offset.

\textbf{Preliminary dust assessment}

We observed the martian dust both directly (by deposition on the
surfaces from which we measured the radiance and their surroundings) and
indirectly (by analyzing its effect on the light that illuminated the
cal-targets). As shown in the irradiance time series in Figure 8a, which
only refer to the clean spots (expected to be the cleanest regions of
the cal-targets), in absence of larger events dust never had a
significant impact on the cal-targets or their ability to correctly
perform the IOF calibration. On the other hand, as mentioned above, the
frames of the movie S2 express a frequent change in the material that
accumulated on the deck of the rover. We could recognize patterns of
fine dust layers, which were more evident on the deck and on the bright
materials due to the higher light/dark-toned contrast, and single larger
grains of sand or regolith raised from the surface, which in some cases
moved a few mm or even cm across two consecutive sols. Whereas the
peripheral regions of the primary target were likely ruled by the
magnetic field of the permanent magnets (in particular the round patches
and the outermost grayscale rings), which produced an optically thick
buildup of dark reddish dust on the magnet rings, the variations in all
the other regions were probably controlled by wind (e.g., several dust
devils were observed by Mastcam-Z in the rover site; Newman \emph{et
al.} , 2022) and possibly aided by vibrations caused by the motion of
the rover, which traveled almost 4 km in the first 350 sols. This fine
dust not only deposited on horizontal surfaces, but also adhered to
vertical sides, such as the lower part of the golden base of the primary
target where the magnetic field from the permanent magnets is prominent
and on the cylindrical structure of the gnomon (the reddish dust coating
is just perceivable on its boundaries in Figure 7).

The model of the direct fraction of sunlight on the illuminated and
shaded grayscale rings was a powerful method to follow the presence of
dust suspended within the martian atmosphere. The two time series shown
in Figure 12 display a roughly inverse correlation in the sense
that\(F_{d}\) rises when \(\tau_{I}\) falls and
vice-versa. This can be interpreted in a way that a growth in the
density of dust in the atmosphere leads to an increase of the optical
depth measured from Mastcam-Z images and increased diffuse scattering of
sunlight, leading to a decrease in \(F_{d}\). In addition,
\(F_{d}\) and \(\tau_{I}\) show a shallow local maximum
and minimum, respectively, around the martian aphelion. The correlation
can be recognized after the solar conjunction, when stronger
perturbations caused a higher variability in \(F_{d}\)
and\(\tau_{I}\), and upon the major dust event from sol 314.

The spectra of dust accumulated on the magnet rings (Figure 11d) are
consistent with previous observations of martian dust attracted to
permanent magnets (e.g., Madsen \emph{et al.} , 2009). The dust is
brownish-red with very low reflectance factor at ultraviolet and blue
wavelength, a characteristic rise from green to red consistent with the
presence of ferric iron and higher reflectance factors in the red and
infrared. Overall, though, the spectrum is darker than a typical
spectrum of martian bright dust, again consistent with expectations for
magnetically attracted material that can be expected to be richer in
magnetite and with a larger average grain size (Kinch \emph{et al.} ,
2006).

\textbf{The AluWhite98}

We have not yet been able to identify a root cause of the observed
yellowing of the white patches of the cal-targets. The white material is
different (AluWhite98 manufactured by Avian Technologies) from the seven
other materials (glazed ceramic material manufactured by Lucideon)
(Kinch \emph{et al} ., 2020). This explains why this effect was only
observed in the white patches but it remains enigmatic why the white
ring was not or almost not affected. One hypothesis suggested that a
possible cause was the different type of epoxy adhesive employed to fix
on one hand the primary and secondary patches and tiles (Henkel/Loctite
EA-9309NA) and on the other hand the white ring (3M-2216B/A Gray) to
their supports.

Several tests of martian environment simulation were carried out on four
spare AluWhite98 samples. Three of these samples were fixed onto an
Aluminum support using the two types of epoxies mentioned above, whereas
the fourth was put in place without any adhesive. The samples underwent
the same baking process of preparation as those currently within the
cal-targets on Mars, and were treated with UV irradiation at the
University of Winnipeg. However, the tests did not reproduce the
visible, radiometric, and spectral outcomes of the in-flight materials.
This issue therefore remains unsolved.

\textbf{Conclusions and future work}

In this work we assessed the performance of the Mastcam-Z radiometric
Calibration Targets (or cal-targets; Kinch \emph{et al.} , 2020),
regularly employed to convert Mastcam-Z images (Bell \emph{et al.} ,
2021) from units of radiance to reflectance, over the first 350 sols on
Mars.

The cal-targets proved to be efficient not only for calibration, but
also to retrieve information on the environment and the dust dynamics
within Jezero crater. The design of the regions of interest for
calibration, surrounded by strongly magnetized hollow cylindrical
magnets, allowed accurate measurements of the local radiances
(Hayes\emph{et al.} , 2021) involving low disturbance due to dust, which
was mostly attracted or repelled by the magnets, or deposited and
cleaned off by the wind. Linear fits between model reflectances and
observed radiances are of good quality with only limited dispersion of
data points around the fit line. A continuous monitoring of the linear
fits, as well as their slopes (equal to the instantaneous local solar
irradiance), will ensure a correct application of the reflectance
calibration procedure in the future, as significant natural events (such
as e.g., the major dust event of sols 314-316) can directly affect the
atmospheric optical thickness and the cal-target materials, hence
perturbing the stability of the calibration process. This includes the
implementation of a dust model, which was already performed in the MER
mission (Kinch \emph{et al.} , 2007). Due to the satisfying results from
Mastcam-Z cal-targets within the first 350 sols, we do not contemplate
the urgency of a dust model.

We did observe that the linear fits could consistently be improved by
the inclusion of a slight offset term. The origin of this offset is not
yet understood but plausible hypotheses include residuals of the
radiance calibration, imperfections of the reflectance model, or dust,
or some combination of the three.

Finally, the yellowing effect of the AluWhite98 patches of the primary
and secondary cal-targets could not yet be reproduced by experiments and
therefore for now it remains an unexplained phenomenon. Determining the
physical trigger of this effect could help establish the starting point
and provide a useful reference in the design of the new calibration
targets for the cameras of coming planetary missions.

\textbf{Acknowledgements}

M. Merusi is supported by the European Union's~Horizon 2020 research and
innovation programme under the Marie Sk\selectlanguage{polish}ł\selectlanguage{english}odowska-Curie grant agreement
No~801199. Support from the Carlsberg Foundation, grant CF16-0981,
CF17-0979, and CF19-0023 are gratefully acknowledged. This support made
it possible to build the cal-targets and to allow Danish team members to
participate in a number of team meetings. J. R. Johnson is supported by
ASU Contract 151112, 15-707. E. A. Cloutis thanks the Canadian Space
Agency, the Natural Sciences and Engineering Research Council of Canada,
and the University of Winnipeg for their funding support. M. T. Lemmon
is supported by contract 15-712 from Arizona State University and
1607215 from Caltech-JPL. O. Gasnault's work with SuperCam on
Perseverance was supported by CNES.

\textbf{Open Research (availability statement)}

The methods and results described in this manuscript are based on the
radiometric calibrated images from the Mastcam-Z instrument. All image
data presented here instrument are available through the Planetary Data
System Imaging Node
(https://pds-imaging.jpl.nasa.gov/portal/mars2020\_mission.html) and
GeoSciences Node (https://pds-geosciences.wustl.edu/missions/mars2020/),
under the Mars 2020 Mission. The Radiometric Coefficient files are
second-order products and will also be available as part of the
Mastcam-Z Science Calibrated Bundle
(https://pds-imaging.jpl.nasa.gov/data/mars2020/mars2020\_mastcamz\_sci\_calibrated/),
in a calibration collection, in the summer 2023 at the latest. Before
then, the RC-files can be requested directly to the corresponding
author.

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\textbf{Appendix 1 -- The Radiometric Coefficient files}

The Radiometric Coefficient files (or RC-files) are second-order
products obtained from the elaboration of Mastcam-Z radiance-calibrated
cal-target images (see section 3.3). Here we present an example of a
Radiometric Coefficient file. The following RC-file was extracted from a
Mastcam-Z cal-target image in filter L1 (800 nm) on sol 349. In this
example, each line of the RC file, denoted by the initial `\#', is
followed by a brief explanation in brackets.

\# responsivity constants file:
rc\_ZL1\_\_0697919834\_0092982ZCAM03014\_1.txt

(full-path filename of this file when it was created)

\# associated selection filename:
Z00349\_0092982ZCAM03014\_048018831\_FO1.sel

(full-path filename of selection file used to generate these
responsivity constants)

\# dust correction: none

(Dust correction model used when generating responsivity constants)

\# outliers excluded from selections: Yes

(are ''outliers'' excluded from selection regions when generating the
responsivity constants\ldots{}

There is currently a very strict algorithm defining outliers to be
excluded. It is designed

to exclude hot pixels and the like that may be included in a selection.
It is NOT meant to

be used to ignore inadvertently selected shadows or otherwise bad
selections. The algorithm

operates as follows: Exclusion is determined on a per-channel basis.
Histogram the pixel values

into 11 bins of equal value range from the minimum value to the maximum
value. Find any outlier

bins (bins that are separated from the main cluster of values by one or
more empty bins). Any

values in these outlier bins are considered to be outlier values. If the
total number of

outlier values is \textless{}= 10, the mean selection value will be
computed excluding these outlier

values. NOTE: If the number of outlier values is \textgreater{} 10, the
values will not be excluded, instead

the user will be warned of this condition (which usually indicates a
faulty selection), and

prompted to correct it before saving the responsivity constants.)

\# force fit to intercept origin: Yes

(fit line is forced to go through the point {[}0,0{]})

\# RC file creation time: 2022-02-12T18:26:52Z

(timestamp of when this file was created)

\# RC file format version: 1.1 2021-12-03

(file format version)

\#

\# cal-target file:
ZL1\_0349\_0697919834\_098RAD\_N0092982ZCAM03014\_048085A01.IMG

(full-path or relative-path filename of the RAD-calibrated cal-target
file used

to generate these responsivity constants)

\# unique sequence identifier: 00349\_zcam03014\_01883\_001

(unique identifier of the cal-target sequence from which these
responsivity

constants were generated)

\# local true solar time: 12:22:03

(LTST of the cal-target image)

\# solar azimuth (rover frame): 16.5834

(solar azimuth in rover frame at time of cal-target acquisition)

\# solar elevation (rover frame): 64.5552

(solar elevation in rover frame at time of cal-target acquisition)

\# fit method: use\_only\_chip\_centers

(method used to fit a line to the selection values. Possibilities are:

use\_only\_chip\_centers

use\_all\_sunlit\_regions: chip centers + sunlit rings

use\_only\_sunlit\_rings

use\_all\_rings: sunlit rings + ring shadows

use\_all\_regions: chip centers + sunlit rings + ring shadows)

\# ROI names: ''Blue Chip Center'' ''Green Chip Center'' ''Yellow Chip
Center'' ''Red Chip Center'' ''Black Chip Center'' ''Dark Gray Chip
Center'' ''Light Gray Chip Center'' ''White Chip Center'' ''Black Ring''
''Dark Gray Ring'' ''Light Gray Ring'' ''White Ring'' ''Black Ring
Shadow'' ''Dark Gray Ring Shadow'' ''Light Gray Ring Shadow'' ''White
Ring Shadow'' ''Black Secondary Horizontal'' ''Dark Gray Secondary
Horizontal'' ''Light Gray Secondary Horizontal'' ''White Secondary
Horizontal'' ''Red Secondary Horizontal'' ''Green Secondary Horizontal''
''Blue Secondary Horizontal'' ''Black Secondary Vertical'' ''Dark Gray
Secondary Vertical'' ''Light Gray Secondary Vertical'' ''White Secondary
Vertical'' ''Red Secondary Vertical'' ''Green Secondary Vertical''
''Blue Secondary Vertical'' ''Blue Chip Outer'' ''Green Chip Outer''
''Yellow Chip Outer'' ''Red Chip Outer'' ''Black Chip Outer'' ''Dark
Gray Chip Outer'' ''Light Gray Chip Outer'' ''White Chip Outer''
''Gnomon'' ''Gold'' ''Deck''

(names of all regions)

\# ROI is selected: 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

(1 if a selection exists for the corresponding named region, else 0)

\# ROI marked bad: 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 1 0 0 0

(1 if a selection for the corresponding named region has been marked bad
and is

not used in the fit, else 0: the selection is allowed to be used in the
fit)

\# ROI used in fit: 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(1 if a selection for the corresponding named region IS used in the fit,

else 0: the selection for this region is not used in the fit. Will be 0

if there is no selection for the corresponding region)

\# ROI radiances: 0.034506816 0.039897159 0.10376279 0.10554330
0.022406472 0.056729008 0.092273153 0.12006555 0.025852364 0.056776047
0.088735089 0.12321232 0.014249836 NaN NaN 0.044461299 0.025365373
0.058788035 0.096467562 0.12703149 0.10993537 0.042618129 0.039442647
0.014147431 0.039987970 0.069789968 0.095307037 0.079999320 0.027067456
0.024401680 0.030651826 0.030116336 0.031713024 0.032213278 0.030008674
0.031119999 0.030178478 0.033819154 0.014333907 0.058045797 0.10957697

(mean of USED values in each selected region - regions with no selection
will have NaN)

\# ROI uncertainty: 0.0011226007 0.0011313090 0.0022528207 0.0015802836
0.0012730183 0.0015016926 0.0018925177 0.0026042091 0.0012016993
0.0013950781 0.0029164302 0.0034273181 0.0010719281 NaN NaN 0.0017609603
0.0010725553 0.0020828459 0.0047955393 0.0069235163 0.0071730291
0.0012393190 0.0010976408 0.00051002479 0.0011881783 0.0020589134
0.0032437530 0.0027616147 0.00083441847 0.00063337773 0.0025638362
0.0025350361 0.0040774076 0.0044082675 0.0027280322 0.0040012537
0.0036807128 0.0043153809 0.0029024197 0.0022435802 0.0033396325

(standard deviation of USED values in each selected region - will be NaN
if no selection)

\# ROI count: 73 65 74 70 64 61 63 66 1517 3239 799 2239 56 0 0 100 906
882 870 872 872 870 859 1270 503 1236 1250 1250 430 1199 463 446 461 434
409 391 399 414 459 522 1732

(number of USED pixels in each selected region)

\# ROI incidence angle: 25.444830 25.444830 25.444830 25.444830
25.444830 25.444830 25.444830 25.444830 25.444830 25.444830 25.444830
25.444830 25.444830 25.444830 25.444830 25.444830 25.444830 25.444830
25.444830 25.444830 25.444830 25.444830 25.444830 65.683873 65.683873
65.683873 65.683873 65.683873 65.683873 65.683873 25.444830 25.444830
25.444830 25.444830 25.444830 25.444830 25.444830 25.444830 25.444830
25.444830 25.444830

(Angle between the vector from the region to the sun and region surface
normal for each region)

\# ROI emission angle: 58.310048 58.310048 58.310048 58.310048 58.310048
58.310048 58.310048 58.310048 58.310048 58.310048 58.310048 58.310048
58.310048 58.310048 58.310048 58.310048 55.257824 55.257824 55.257824
55.257824 55.257824 55.257824 55.257824 37.229207 37.229207 37.229207
37.229207 37.229207 37.229207 37.229207 58.310048 58.310048 58.310048
58.310048 58.310048 58.310048 58.310048 58.310048 58.310048 58.310048
58.310048

(Angle between the vector from the region to the detector and the region
surface normal for each region)

\# ROI azimuth angle: 30.933419 30.933419 30.933419 30.933419 30.933419
30.933419 30.933419 30.933419 30.933419 30.933419 30.933419 30.933419
30.933419 30.933419 30.933419 30.933419 31.807842 31.807842 31.807842
31.807842 31.807842 31.807842 31.807842 28.666222 28.666222 28.666222
28.666222 28.666222 28.666222 28.666222 30.933419 30.933419 30.933419
30.933419 30.933419 30.933419 30.933419 30.933419 30.933419 30.933419
30.933419

(Angle in the plane of the region surface between the vector from the
region to the sun

and the vector from the region to the detector)

\# reflectances: 0.19100898 0.20369039 0.78817137 0.77029269 0.077399921
0.35798268 0.66099199 0.96044053 0.077399921 0.35798268 0.66099199
0.96044053 0.096936364 NaN NaN 0.95641705 0.077704355 0.35960730
0.66544664 0.96462831 0.77566164 0.20423820 0.19140617 0.075323097
0.33880119 0.62680637 0.92161635 0.70466609 0.19663292 0.18165617
0.19100898 0.20369039 0.78817137 0.77029269 0.077399921 0.35798268
0.66099199 0.96044053 NaN NaN NaN

(Calculated reflectance for each region. Nan if there is no selection or
no lab reflectance model for the region)

\# camera id, filter number, rad-to-iof scaling factor, uncertainty

4007 1 6.9130400 0.39587878

(camera id, filter number, calculated rad-to-iof scaling factor,
uncertainty in the scaling factor)

\selectlanguage{english}
\FloatBarrier
\end{document}

