# Preparing Rashid-2 Lunar Mission: calibration of the optical cameras

Nicolas Théret, Maxence Guénin, Thomas Bonassi, Quentin Douaglin, Cédric

Virmontois, Valérian Lalucaa, Sebastian Els

► To cite this version:

Nicolas Théret, Maxence Guénin, Thomas Bonassi, Quentin Douaglin, Cédric Virmontois, et al. Preparing Rashid-2 Lunar Mission: calibration of the optical cameras. EPSC, Sep 2025, Helsinki, Finland. 10.5194/epsc-dps2025-27. hal-05238491

HAL Id: hal-05238491

https://hal.science/hal-05238491v1

Submitted on 3 Sep 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Preparing Rashid-2 Lunar Mission: calibration of the optical cameras

Nicolas Théret<fnref n="1" />, Maxence Guénin<fnref n="2" />, Thomas Bonassi<fnref n="2" />, Quentin Douaglin<fnref n="3" />, Cédric Virmontois<fnref n="1" />,
Valérian Lalucaa<fnref n="1" />, and Sebastian Els<fnref n="4" />

## INTRODUCTION

After the failure of the landing of Rashid-1 on the Moon, in April 2023, the MBRSC (Mohammed Bin Rashid Space Centre) decided to set up a new mission with the same rover design. It is expected that Rashid-2 will land in the mid-latitudes of the Moon in 2026. This paper focuses on the calibration of its optical cameras.

## OPTICAL CAMERAS DESCRIPTION

The Rashid-2 rover carries 3 multispectral visible (RGB) cameras, as shown Figure 1. Their design is identical to that of Rashid-1, see [1]-[2]-[3] for more details. Basically, CAM-1 and CAM-2 are wide-angle navigation cameras, with a full diagonal angle of 115°, and CAM-M is a microscopic camera, with a spatial resolution better than 30µm.

<figure><img src="image_2.png" /><figcaption>Figure 1: Identification and localization of the 3 optical cameras carried by Rashid-2 rover</figcaption></figure>

<footnote n="1">¹Centre National d'Etudes Spatiales (CNES), Toulouse, France (nicolas.theret@cnes.fr)</footnote>

<footnote n="2">²ASTEK Group, Toulouse/Colomiers, France</footnote>

<footnote n="3">³THALES Services Numériques, Toulouse/Labège, France</footnote>

<footnote n="4">⁴Mohammed Bin Rashid Space Centre (MBRSC), Dubai</footnote>
## DETECTOR CHARACTERIZATION

We first characterized the radiometric response of the CMOS detectors, in terms of gain, offset, dark current and readout noise, by measuring the average levels and the spatial non-uniformity maps. The dynamics of the detectors are encoded in 10 bits and the measured gains are:

* CAM-1: 0.346 DN/e⁻

* CAM-2: 0.173 DN/e⁻

* CAM-M: 0.147 DN/e⁻

The average levels are given with respect to the temperature in Figure 2 and the standard deviation of the non-uniformity maps are always between 4% and 5% at ambient temperature (except for CAM-M offset: 7%). The dark current is approximated by an Arrhenius law adapted for the high levels: dark=$exp(62.5-1.5/kT)$. Actually, it is only properly measured for CAM-M because the camera was not yet integrated, so the temperature could be measured directly on the detector. However, we can relate an internal uncalibrated temperature register from the detector to the measured dark current. This relation will be used during the mission.

<figure><img src="image_3.png" /><figcaption>Figure 2: Average offset, readout noise and dark current for the three cameras
The dark current expressed with respect to a calibrated temperature is given only for CAM-M, but supposed identical for CAM-1 and CAM-2</figcaption></figure>

## INTEGRATED CAMERAS CHARACTERIZATION

This section only describes CAM-1 and CAM-2, as they are integrated at CNES. CAM-M is integrated by Kampf Telescope Optics in Munich[3]. These characterizations include the effects of the optical components.

### Radiometry

Radiometric calibration consists of three distinct measurements:

* The spatial non-uniformity of the response, both at low and high frequencies,

* The spectral shape of the response (colorimetric response),

* The absolute radiometric response to a typical scene.
The non-uniformity is evaluated by illuminating the camera with a uniform illuminant generated by an integrating sphere. The integration time is chosen in order to obtain the higher dynamics in the images without saturation. A burst of images is acquired to reduce the noise effects and derive the flat field (Figure 3-left).

A median filter is then applied to extract only the low frequency component, i.e. the vignetting effect. By dividing it to the measured flat, we can also estimate the Pixel Response Non Uniformities (Figure 3-right) and detect defective and "noisy" pixels that are far from the standard response. This vignetting/PRNU separation will be done on the fly during the mission by the CASPIP[4] operational library.

<figure><img src="image_4.png" /><figcaption>Figure 3: CAM-2 full flat field (left) on Pixel Response Non Uniformity (right) with defective (red) and noisy (yellow) pixels</figcaption></figure>

Knowledge of the instrument's colorimetry is necessary for proper interpretation of the spectral distribution of the observed scene, which is required for geological analysis[1]. It is calibrated using color patches of known reflectance, in a dedicated chamber that reproduces a spectrum similar to the sunlight reflected from the lunar surface, in order to mimic the lunar illuminant. The result is a 3x3 matrix that is used to convert camera's readings into human-perceivable colors.

The absolute response is measured in the same chamber with a spectralon. The Digital Numbers are averaged around the center of the image, where the effect of vignetting is negligible. Knowing the mean offset and the mean dark current from the detector characterization, we can calculate the absolute radiometric coefficient that relates the measurement (in DN) to the flux (in W/m²/sr/µm), see Figure 4 for the resulting values.

<table><caption>Figure 4: Absolute calibration coefficients, in W/sr/m²/µm/DN.s - Radiance = K x DN / integ_time</caption><thead><tr><td>Spectral band</td><td>CAM-1</td><td>CAM-2</td></tr></thead><tbody><tr><td>Red</td><td>1.05 x 10<sup>-4</sup></td><td>1.68 x 10<sup>-4</sup></td></tr><tr><td>Green</td><td>0.93 x 10<sup>-4</sup></td><td>1.60 x 10<sup>-4</sup></td></tr><tr><td>Blue</td><td>1.56 x 10<sup>-4</sup></td><td>2.61 x 10<sup>-4</sup></td></tr></tbody></table>

## Resolution
The cameras resolution is measured using the slanted-edge method[5], which is extended over the field of view with a checkerboard pattern (Figure 5-a). The slanted-edge method directly calculates the MTF curves in the vertical and horizontal directions for each transition, but it is affected by noise at high frequencies. Moreover, it is necessary to demosaic the Bayer pattern before computing the MTF, so as not to be limited to half the sampling frequency, and thus the MTF is also affected by the mosaicing/demosaicing operations[6]. However, it results in a representative MTF as obtained on the final product. It is approximated and extrapolated by an exponential law (Figure 5-b).

<figure><img src="image_5.png" /><figcaption>Figure 5: MTF measurement setup (left) and typical results (CAM-1, vertical direction)</figcaption></figure>

Geometry

These wide-angle cameras introduce a large distortion to the images. It is approximated by a specially tuned polynomial model[1]. The parameters of the model are calculated by fitting it to images of the checkerboard pattern captured at different positions and orientations (Figure 6-up). The transitions on the checkerboard are detected using a Canny filter and the MTF response to account for the smoothing of the edges. The resulting polynomial is given in Figure 6-bottom.
<figure><img src="image_6.png" /></figure>

$$x' = x + (x - x_c) \frac{(R1 \cdot r^2 + R2 \cdot r^4 + R3 \cdot r^6)}{1 + R4 \cdot r^2} + (P1 \cdot (r^2 + 2 \cdot (x - x_c)^2) + 2 \cdot P2 \cdot (x - x_c) \cdot (y - y_c))$$

$$y' = y + (y - y_c) \frac{(R1 \cdot r^2 + R2 \cdot r^4 + R3 \cdot r^6)}{1 + R4 \cdot r^2} + (P2 \cdot (r^2 + 2 \cdot (y - y_c)^2) + 2 \cdot P1 \cdot (x - x_c) \cdot (y - y_c))$$

Variables are normalized

<table><caption>Figure 6: Distortion measurement setup (up) and results (bottom)</caption><thead><tr><th>Parameter</th><th>CAM-1</th><th>CAM-2</th></tr></thead><tbody><tr><td>R1</td><td>-150.48</td><td>-146.79</td></tr><tr><td>R2</td><td>13.699</td><td>12.848</td></tr><tr><td>R3</td><td>-0.1566</td><td>-0.2940</td></tr><tr><td>R4</td><td>0.05251</td><td>0.0535</td></tr><tr><td>P1</td><td>-0.1082</td><td>0.1691</td></tr><tr><td>P2</td><td>0.2684</td><td>-0.1276</td></tr></tbody></table>

## CONCLUSION

The Rashid-2 cameras have been calibrated on-ground and are now integrated on the rover. Launch and landing operations, as well as thermal variations on the Moon, may affect some parameters, so additional calibrations will be performed onboard during the mission, with more constraints on their realization.

## REFERENCES

[1] N. Théret, E. Cucchetti, E. Robert et al., Enhanced Image Processing for the CASPEX Cameras Onboard the Rashid-1 Rover. Space Sci Rev 220, 60 (2024). https://doi.org/10.1007/s11214-024-01091-0

[2] Z. Ioannou, S. Amilineni, S.G. Els et al., Onboard and Ground Processing of the Wide-Field Cameras of the Rashid-1 Rover of the Emirates Lunar Mission. Space Sci Rev 221, 8 (2025). https://doi.org/10.1007/s11214-024-01127-5

[3] S.G. Els, N. Ageorges, M. Bogosavljevic et al., The Microscope Camera CAM-M on-Board the Rashid-1 Lunar Rover. Space Sci Rev 220, 81 (2024). https://doi.org/10.1007/s11214-024-01117-7

[4] N. Théret, Q. Douaglin et al., CASPEX Image Processing: a tool for space exploration, https://doi.org/10.5194/epsc2024-15

[5] M. Estribeau et P. Magnan, Fast MTF measurement of CMOS imagers using ISO 12233 slanted-edge methodology, SPIE Optical System Design 2003

[6] N. Théret, A. Courtois, Q. Douaglin et S. Lucas, Mesure de FTM optique sur caméras intégrées avec motifs Bayer, in preparation