Simulation of laser travel-time on Mercury for BELA

Abstract

Recent laser altimeters are able to not only measure the ranging distance between the spacecraft and the surface but also the full time-of-flight of the photons or pulse shape. This new capabilities allows to measure the intra-footprint properties: surface slope distribution and surface microtexture. Here we simulate and discuss for the first time the effect of surface microtexture, especially for ice covered surface with longer penetration depth. Using the WARPE simulation software, two kind of microtextures are simulated: compact slab and granular. Laser pulse shape for an ideal instrument is simulated using physical properties such as the grain size, material composition, thickness, compacity (filling factor, porosity) rather than radiative properties. The effects of these parameters on the pulse shape are discussed as well in the range that could be possibly be observed with actual BELA measurement. Finally, examples of WARPE's simulated pulse shapes are used as input in the precise simulation chain of the BELA measurement output, to further assess the capability to detect variation in surface microtexture.

Figures (12)

• Figure 1: Determination of the numerical field of view. (a) WARPE's simulation for a water ice slab of 1 mm with 1% of CO$_2$ impurities with 25 $\mathrm{\mu m}$ grain size. Blue domain selects the background scattering ; Red domain selects the back and forth diffuse wave Barron_2025. Domains are determined using the characteristics return time for back and forth to properly discriminate its influence on background scattering. Here the specular reflection and back and forth (BF) direct are ignored since these features are geometrically (in perfectly 0° of emergence) and timely condensed. Thus, these graphs only consider rays with at least 1 scattering event. (b) Mean reflectance along azimuth for the background scattering. The reflectance is flat (locally lambertian) from 0° to 12° with a RMS of 0.0006. We set the numerical FOV value at 12°. (c) Mean reflectance along azimuth for back and forth diffuse wave. The reflectance is flat (locally lambertian) from 0° to 3° with an RMS of 0.0023. We set the numerical FOV value at 3°.
• Figure 2: Effect of physical thickness on the waveform in pure water ice compact slab. The absence of features for $h=1000$$\mathrm{mm}$ is explained by the medium being optically thick ($\tau=15$) with a significant extinction coefficient $k$ of $1.272\times10^{-6}$. The analytical solution gives a reflectance of $1.47\times10^{-15}$$\mathrm{sr}^{-1}$. The transparent color-filled domain corresponds to the limits of non-constrained waveform due to the limitation of the Monte-Carlo approach of WARPE (see Barron_2025 for more details). Each color plot has its own domain. When there is a superposition of the domains, the resulting color depends on each individual the color plots and is thus non informative by itself.
• Figure 3: Effect of physical thickness on the waveform in pure CO$_2$ ice compact slab. This time the feature is visible for $h=1000$$\mathrm{mm}$. The medium is less optically thick ($\tau=0.01$) with an extinction coefficient $k$ of $8.47\times10^{-10}$. The analytical solution gives this time a reflectance value of $0.026$$\mathrm{sr}^{-1}$. On the logarithmic scale, the return time of the first BF almost reach BELA sampling resolution but in this case the required physical thickness is 1335 $\mathrm{mm}$.
• Figure 4: Effect of physical thickness on the waveform in water ice compact slab with $1-\gamma_{c}=$10% of CO$_2$ impurities of 100 $\mathrm{\mu m}$. The impurities, even less absorbing, have a significant effect on the scattering inside the medium and will therefore smooth the waveform. Comparing to figure \ref{['fig:Slab_h2o_h']}, only at $h=1$$\mathrm{mm}$, an attenuated BF is visible.
• Figure 5: Effect of grain size $d$ of CO$_2$ impurities on the waveform in water ice compact slab with $1-\gamma_{c}=$10% volumetric impurities and a thickness $h=1000$ mm. As $d$ increases, the absorption becomes more dominant (low value of $\omega$) and the waveform tends to the case without impurities (see Fig. \ref{['fig:Slab_h2o_h']}, case $h=1000$ mm). When $d$ is small, more scattering occurs then more rays leave the medium and the waveform tends to be shorter. This situation can be considered as optically thick because no rays reach the bottom interface.