Photometric Characteristics of Lunar Soils: Results from Spectral Analysis of Chang’E-5 In Situ Data Using Legendre Phase Function

Abstract

China’s Chang’E-5 (CE-5) mission has successfully landed in the Northern Oceanus Procellarum of the Moon. Lunar mineralogical spectrometer (LMS), as one of the important payloads onboard CE-5 Lander–Ascender Combination, aims to study the physical and compositional properties of the landing area. This paper applies the Legendre phase function to correct the photometric effects on the LMS in situ spectra and reveal the photometric characteristic of the CE-5 landing area. LMS obtained the reflectance spectra in various geometric configurations by performing full-view scanning of the CE-5 landing area. By fitting these LMS spectral data, the parameters $b=-0.29$ and $c=0.44$ of the Legendre phase function were obtained. This indicates the strong forward scattering characteristic of the CE-5 landing area, which is similar to that of the Chang’E-4 (CE-4) landing area, and the side scattering is weaker than that of CE-4. In addition, we derived the FeO content of the landing area using the photometric-corrected LMS spectral data. Our results demonstrate that the estimated FeO content of the landing area is close to the laboratory measured data of the returned samples. The LMS in situ reflectance data will contribute to a better understanding of the physical and mineralogical properties of the CE-5 landing area.

1. Introduction

The Moon contains valuable resources, such as various minerals [1,2] and potential water ice deposits [3,4]. Precise measurements of the surface reflectance are vital for identifying these resources, which directly impact the planning and success of missions focused on exploration and building habitats. Projects like Chang’E-5/6, NASA’s VIPER [5], and ESA’s PROSPECT [6,7] payload are specifically designed to explore these resources through observations and measurements conducted directly on the lunar surface by instruments deployed on-site, referred to as “in situ” analysis techniques. Analyzing the photometric properties of the lunar surface is essential for both scientific research and practical space exploration. Accurate characterization of the Moon’s surface reflectance provides crucial data for future lunar missions, especially those focused on resource exploration and habitat construction. For instance, missions like China’s Chang’E-5 (CE-5) aim to enhance our understanding of the lunar composition and improve the success of future landings. Hapke’s radiative transfer model [8] has been widely used for estimating the mineral abundance of the lunar surface from visible (VIS) to near-infrared (NIR) reflectance spectra of the Moon (e.g., [9,10]). It calculates lunar surface reflectance based on the lunar soils’ single-scattering albedo (SSA), opposition effect, single particle scattering phase function ($P\left(g\right)$), multiple scattering, roughness, and the viewing geometry of the spectral measurement (e.g., [8,11]).

$P\left(g\right)$ is the function of the phase angle (g) and is used to characterize the angular distribution of the scattered radiance by a single particle. The measured lunar surface reflectance depends on the $P\left(g\right)$ of lunar soils. A two-term Legendre (LG) polynomial (Legendre phase function) is commonly used in the Hapke model, chosen for its consistent use in compositional interpretation and spectral unmixing with outcomes comparable to other phase functions like Henyey–Greenstein (HG) [12]. And the two-term LG phase function is illustrated as follows:

$$P\left(g\right)=1+b·cos\left(g\right)+c·(1.5{cos}^2\left(g\right)-0.5)$$

(1)

In Equation (1), the coefficient b, restricted to the range of [−1, 1] [11], describes the degree of forward or backward scattering. Negative b values indicate more forward scattering (scattering in the direction of the incident light), whereas positive values indicate more backward scattering (scattering in the direction opposite to the incident light). The coefficient c characterizes the degree of side scattering [13]. The general shape of the $P\left(g\right)$ thus depends on these two parameters [12]. In general, minerals with higher albedo (lunar surface silicate minerals, such as olivine, pyroxene, and plagioclase) exhibit forward scattering characteristics, while darker minerals (e.g., ilmenite) exhibit backward scattering characteristics [12]. Accurate b and c values for lunar soils are crucial for spectral unmixing via Hapke’s model to quantitatively retrieve the mineral abundance of the lunar surface [12]. In previous unmixing analysis of lunar spectral data, $b=-0.4$ and $c=0.25$ were widely used based on laboratory spectrophotometric measurements of typical lunar minerals [14]. Using these values, ref. [15] derived the SSA for a number of in situ spectra collected from the same spot of CE-4 landing zone, but under different observation geometries. They found that the derived SSA varied with the viewing geometry, which was in contrast with the fact that SSA should be independent of the viewing geometry of the mesurement. This suggests that the b and c values proposed by [14] may be not suitable for the CE-4 landing zone. Based on the in situ photometric spectral data acquired by Yutu-2-VNIS (Visible and Near-IR Imaging Spectrometer), ref. [15] derived b and c as −0.17 and 0.70, respectively. It can be inferred from [15] that the parameters b and c of the LG phase function could not be the same for different locations of the Moon (Table S1), and it is necessary to derive the suitable b and c values for the detected location. Improper b and c values will affect the derivation of SSA, which will in turn affect the spectral unmixing of the mineral abundance of the detected area. Meanwhile, the accurate b and c can be also used for photometric correction of the spectral data to reduce bias in the evaluation of the optical maturity and FeO content of lunar soils introduced by different viewing geometries.

For the first time, CE-5 collected and returned samples with an age of about 2.0 Ga [16,17] from the lunar surface. During the return process, the porosity and roughness of the collected lunar soils may be changed by external factors such as extrusion and accumulation, changing the original photometric properties of the lunar soil to some extent. Research by Shepard (2002) [18], Foote et al. (2020) [19], Nagori et al. (2023) [20], and Shepard (2011) [21] indicates that the compaction and flattening of samples can lead to a transition in the phase function. Specifically, these studies suggest that changes in the physical state of the samples can significantly impact their scattering characteristics, including shifts in the phase function from isotropic to forward scattering. The Lunar Mineralogical Spectrometer (LMS) onboard the CE-5 Lander–Ascender Combination (LAC) conducted an in situ exploration of the sampling area on the lunar surface and obtained the lunar surface spectra spectroscopic data at a constant incidence angle and varying phase angle in their most original state [22]. The analysis results from th remote sensing data show that the CE-5 landing area is covered by mare basalts with minor difference in their composition [23,24]. Under this assumption, variations in the spectral reflectance are due to the different observation geometry, and can be linked to the physical properties of the lunar regolith. In this study, parameters of LG phase function (b and c) were derived for the lunar soils near the CE-5 sampling area based on the LMS in situ spectral data. The accurate values of b and c will help to achieve more accurate SSA inversion of the sampling area and more reliable mineral abundance. The subsequent spectral interpretation is influenced by albedo, which is affected by illumination conditions. Using the fitted parameters to correct for the effects of illumination geometry can enhance the accuracy of the spectral data inversion [25]. Additionally, the analysis of the LMS in situ spectral data is also beneficial for laboratory sample analysis and for th subsequent calibration of lunar remote sensing data.

This paper first introduces the LMS instrument, the in flight spectral data, and the methods to obtain the photometric properties of the CE-5 landing area. Then, we present the fitting results of the LG function, and discuss the lunar soils’ characteristics that can be inferred by the two parameters. Finally, based on terrain and photometric correction, we derive FeO contant for the CE-5 landing area and compare it with measurements on the returned samples.

2. Instruments, Data, and Methods

2.1. LMS Instrument and Data

The LMS consists of a complementary metal-oxide semiconductor (CMOS) imager ($256\times 256$ pixels, 480–950 nm) and three single-pixel infrared detectors covering 900–3200 nm [22]. The main spectral resolution of the LMS is 2.4–24.9 nm, and the field of view (FOV) is $4.17\times 4.17$(°). The main characteristics of the LMS are provided in the Supporting Materials (Table S2). The LMS is fixed on the southwest part of the LAC, and looks down at the lunar sampling regions at a height of 1.4 m. It mainly has two in-flight detection modes: (1) full-band target observation (hyperspectral mode) and (2) full-view scanning and multispectral observation (20 bands, multispectral mode). The multispectral mode covers the lunar sampling region with a total of 180 scanned FOVs (Figure 1d). The spatial resolution of the CMOS data is 0.4–1 mm/pixel. Before the sampling operation, the LMS detected the sampling area in a multispectral mode. Due to the engineering process, there was a time gap between the observations of 480–1450 nm and 1400–2200 nm. Thus, we only focused on the analysis of the first 12 bands, covering 480–1450 nm of the multispectral data in this study.

CE-5 LMS 2B radiance data were used in this study. These data were taken after dark reduction, scattering-background removal, thermal correction, and radiometric calibration. The radiometric calibration of the LMS included both laboratory and in-flight calibrations. The laboratory radiometric calibration determined the transfer relationship between the input signals and the output digital numbers (DN) before launch. The uncertainty of the radiometric calibration was below 6% in 98% of the bands [22]. In-flight radiometric calibration was used to compare the spectral radiance from the standard diffuser for solar incidence at the optical entrance pupil (measured radiance), with the spectral radiance calculated through ground radiometric calibration (calculated values). The goal was to calculate the differences between the measured and calculated values, and then compensate for the ground radiance correction matrix [26]. The uncertainty of in-flight radiometric calibration was less than 2.7%.

2.2. Methods

The reflectance factor (REFF) [11,27] was obtained from the ratio of CE-5 LMS radiance data to the solar spectral irradiance data [28]. These spectra were obtained at a constant incidence angle (ranging from 39.02° to 39.24°), while the phase angle varied by the LMS adjusting its two-dimensional scanning mechanism. In order to protect the model from the abnormal areas, the shadows and stray-light-affected areas were first removed [29].

To study the photometric properties of the CE-5 landing area, we employed the Hapke model [11] with a two-term LG polynomial phase function, as shown in Equation (1). The parameter setting is presented in Text S1. To simplify the calculation, we averaged the reflectance of pixels within about 2° phase angle assuming that these regions have the same photometric properties [30]. To reduce the influence of the terrain, we used a similar method as [31] for terrain correction in order to obtain the accurate incidence and emission angles (demonstrated in Text S2).

The determination of the initial values of the free parameters had significant effects on the final results. Therefore, we combined a heuristic piecewise approach and a grid-search method [11] to fit the phase curves. To avoid random initial values, we conducted a grid search in the parameter space of the free parameters for each model to determine the parameter values of the first band.

3. Results

3.1. Parameters of Hapke Model

Figure 2 shows the derived SSA, b, and c of the LG phase function using the Hapke model, and the fitted parameters are presented in Table S3. It can be seen from Figure 2a,b that SSA and b are wavelength dependent. Generally, SSA is positively correlated with reflectance. There is an absorption feature around 1 $\mathsf{\mu }$m for SSA, and the SSA of the CE-4 landing site [15] is also included in Figure 2a for comparison. The SSAs are consistent with the reflectance spectra of lunar soils. Parameter b, characterizing the degree of forward scattering, has an average value of −0.29, and parameter c, characterizing the side scattering, has an average value of 0.44. b at the CE-5 landing area is less than 0 at every wavelength, indicating that the lunar soil of this region is more forward scattering [13], consistent with the result of [32]. Compared with the CE-4 landing area, the CE-5 landing area has similar b values, while the values of parameter c are clearly smaller (Figure 2d), indicating that the side scattering of the CE-5 landing area is weaker than that of the CE-4 landing area. This could be caused by the differences in soil compsoition and/or surface roughness. Future laboratory mesurements in a controlled setting will help to quantify the effects of those two factors on the side scattering parameter c. We also find that the values of parameter b for the CE-5 and CE-4 landing sites are close to the parameter distributions of minerals with a higher albedo (e.g., olivine, pyroxene, and plagioclase). Usually, minerals with a higher albedo tend to present forward scattering properties. In contrast, dark minerals (e.g., ilmenite) are more likely to present backward scattering properties.

To verify the accuracy of parameters b and c, we compared the SSA calculated using b and c values derived from this study and from [14]. Theoretically, the SSA is independent of the observation geometry. Therefore, the SSA derived for the 180 FOVs should be uniform, with a low standard deviation (STD) for each wavelength. For better comparison, b and c fitted in this paper were averaged by wavelength to represent the typical parameter values for the CE-5 landing area. The derived SSA values are illustrated in Figure 3 and Table S4. The results show that the mean STD of SSA at different wavelengths is 0.0297 using the b and c values from this study. Meanwhile, the mean STD of SSA at different wavelengths is 0.036 using the b and c values from [14]. The calculated SSA, using the b and c values from this study, tends to be more uniform than that calculated using the parameters from [14].

3.2. Implication for FeO Content of CE-5 Landing Area

As proposed by [33], the FeO content of the lunar surface can be calculated using the following equations:

$$\begin{array}{c}\hfill {\theta }_{Fe}=-arctan[(R_{950}/R_{750}-y_{0Fe})/(R_{750}-x_{0Fe})]\end{array}$$

(2)

$$\begin{array}{c}\hfill FeO=a_1·{\theta }_{FeO}-a_2\end{array}$$

(3)

where $R_{750}$ and $R_{950}$ represent the reflectance at 750 nm and 950 nm, respectively. $x_{0Fe}$ and $y_{0Fe}$ are the spectral angle parameters, the selection of which has a strong correlation with the observation instrument. In this study, the parameters proposed for the Clementine [34], ${\mathrm{M}}^3$ [35], and CE-4 VNIS [36] spectral analysis were calculated separately to derive the FeO contents. The derived results varied obviously, as shown in Table S5. As the detection mechanism of the LMS was closest to CE-4 VNIS, $(x_{0Fe},y_{0Fe})=(1.39,-0.1)$ derived by [37] for CE-4 spectral data were used for the application of this study. $a_1$ and $a_2$ in Equation (3) are the linear coefficients, which were set as 22.928 and 6.075, respecitvely—the same as those used for lunar sample 62231 of Apollo 16 landing site [14].

Based on the corrected 750 nm and 950 nm reflectance of the LMS multispectral mode, we derived the FeO distribution of the whole FOV of the landing area (Figure 4b). The calculation process and results are shown in Figure 4, and the photometric correction method is illustrated in Text S3.

The blank areas circled in Figure 4 are the rocks and areas affected by shadows and stray lights (unwanted light, mostly composed of specular reflections from the thermal control multilayer on the LAC surface due to solar illumination), which have been removed from the calculation [29]. The average FeO contents of the whole FOV is 20.63 wt.%, and the variance is 1.432 wt.%. Thus, the FeO contents can be considered as uniformly distributed.

The average FeO content of the returned CE-5 lunar soil is 22.5 wt.% with uncertainty of 0.33 [38]. To analyze the relationship between in situ detection and returned lunar soils, we also analyzed the FeO content at locations near the sampling site (marked numbers in Figure 4b). As can be seen in Table S6, the FeO contents between the in situ detection and returned samples were quite consistent, with the average of the differences being close to 2 wt.%.

4. Conclusions

In this study, the LG phase function parameters b and c of the CE-5 landing area were derived using CE-5 LMS mutispectral data. The parameters were compared to those of the CE-4 landing area and a number of lunar-type minerals with grain sizes of 45–75 $\mathsf{\mu }$m [13,14]. b was less than zero for the CE-5 landing area, and increased negatively with the reflectance. The lunar soil in this area showed characteristic of forward scattering; while parameter c, representing the side scattering characteristics, was stronger than that of plagioclase, ilmenite, and other minerals, and weaker than that of CE-4 landing area. Compared with using the common b and c values of [14], the single scattering albedo of the CE-5 landing area calculated using the derived b and c in this study showed a small variation among the 180 scanned FOVs of LMS multispectral detection mode. Based on the derived b and c values, the mean FeO content of the lunar soil in the CE-5 landing area (180 scanned FOVs) was 20.63 wt.%. The FeO content between the undisturbed lunar soil at the sampling area and the returned lunar soil samples were relatively close.

In the future, further research should be conducted to better understand the lunar optical characteristics and improve the data comparisons between missions. Future missions should also consider using multi-angle observations to achieve more accurate reflectance data and enhance the applicability of the phase function models. Additionally, comparing the photometric characteristics of the compacted and flattened returned samples with those obtained from in situ measurements will help in better describing the physical properties of the lunar soil, particularly in terms of compaction and surface modifications. Such comparisons are crucial for improving our understanding of how sample handling affects optical properties and for refining phase function models to accurately reflect these changes.