Understanding rough surface scattering is crucial for interpreting radar echoes from the Moon. The high-resolution topographic data from China’s Chang’E (CE) landing missions provide an unprecedented opportunity to measure lunar surface roughness at centimeter scales and investigate lunar rough surface scattering for the lunar radar systems. In this study, we utilize the high-resolution topographic data at the CE-3 and CE-4 landing regions to measure lunar surface roughness at centimeter scales. The derived root-mean-square (RMS) height s, correlation length l, and the fitted correlation function are then used as inputs in the improved integral equation model (IIEM) to compare the modeled and observed backscattering coefficients of the P-band Arecibo and S-band Lunar Reconnaissance Orbiter (LRO) Miniature Radio Frequency (Mini-RF) radar. The roughness results show that the surfaces of the CE-3 and CE-4 landing regions are not radar smooth under the Fraunhofer roughness criterion. Among the exponential, Gaussian, and modulated correlation functions, the modulated exponential correlation function closely matches the measured correlation functions, which can effectively characterize the multiscale properties of lunar surface roughness. The comparison between radar observations and IIEM predictions reveals the significant contribution of volume and dihedral scattering caused by surface and buried rocks in the two landing regions. The surface roughness quantified in this study can provide new insights into understanding radar scattering mechanisms of the Moon and facilitate further interpretation of lunar radar data.

The Martian polar layered deposits (PLD) are extensive, stratified sheets composed primarily of water ice with a small fraction of dust, which is believed to have formed due to climatic variations in the late Amazonian period. The thickness and dust content of layers in the PLD are crucial for understanding the paleoclimate they potentially record. The SHAllow RADar (SHARAD) onboard Mars Reconnaissance Orbiter (MRO) is currently the highest resolution radar sounding instrument for acquiring internal information of PLD. However, previous studies based on high-resolution optical and topographic data show that the thicknesses of the layers are usually smaller than the vertical resolution of SHARAD (~8.5 m in water ice, ε′ice= 3.15). In this case, a bright radar echo is caused by a thin dusty ice layer and its reflectivity is determined by multiple reflections between the upper and lower boundaries of the layer. This leads to the non-unique solution for layer thickness and dust content from the observed reflectivity. In previously published studies, the dust content of a layer was determined by assuming an equal probability distribution of layer thickness, which is usually not realistic. To resolve this problem, we propose a novel algorithm for layer parameter inversion based on the hidden Markov model (HMM) that utilizes the spatial correlation of layer parameters. In this algorithm, the layer parameters and SHARAD measured reflection strength of a dusty layer correspond to the state and observation sequences, respectively. The spatial continuity and correlation of the layer parameter (i.e., layer thickness and dust content) is utilized to construct probability distributions of HMM and the layer parameter with the highest probability is obtained as the inversion result. Compared to the previous method, our algorithm does not rely on prior knowledge of the layer thickness distribution. The algorithm is validated using both simulated reflectivity and SHARAD data. In the experiment with simulated reflectivity, the average inversion errors of the dust content and thickness obtained are 0.048 and 1.66 m, respectively. The error of the inverted dust content is reduced by 23.8% compared to the previous method. The layer thickness inverted from SHARAD data is comparable to that obtained by the high-resolution topographic data in the nearby outcrop region. In the future, our algorithm can be utilized to analyze radargrams collected by the orbital sounding radar onboard China’s Tianwen-1 mission, providing a more detailed view of the internal structure of PLD.

The shape, size, and abundance of rocks on the Moon’s surface are essential for understanding impact cratering and weathering processes, interpreting remote sensing observations, and ensuring landing safety and rover trafficability. In most previous studies, rock information was extracted from optical images using visual identification or automatic detection methods. However, optical images cannot provide 3D information of rocks and cannot be used in lunar permanently shadowed regions (PSRs), where rock information is critical for deciphering anomalously high radar echoes in water ice deposits detection. In this study, we proposed an automatic method for extracting 3D information of rocks from topography data based on the geometry and clustering tendency of lunar surface rocks. A geometric shape model for lunar surface rocks is first developed by analyzing 3196 rocks in elevation data. In the proposed approach, rocks are detected from topography data using multi-scale 2D continuous wavelet transform (2D CWT) and Hopkins statistic, and then a 3D shape parameter extraction method is introduced to obtain the shape information directly from the detected irregular rock boundary by a region growing-based algorithm. To demonstrate the accuracy of the method, we applied the proposed method to both the simulated and real topography data with various spatial resolutions and vertical uncertainties. The results show that, compared to the ground truth and manual detection results, the detection rate of rocks >4 pixels in size varies from 50% to 90%, depending mainly on the vertical uncertainty of elevation data. In addition, for the first time, we provide 3D information of surface rocks (>10 m) in lunar PSRs from topography data. Our analyses suggest that, for future missions to the lunar PSRs (e.g., China’s Chang’E-7), the vertical uncertainty of elevation data needs to be better than 0.2 m in order to accurately gather 3D information of rocks larger than 2 m. Our method can be utilized for extracting 3D information of rocks from topography data, selecting landing sites, and guiding instrument design for future altimeters.

Spaceborne radar sounding is a powerful technique in planetary subsurface exploration due to its large penetration ability into loose desiccated materials. Three radar sounders, Mars Advanced Radar for Subsurface and Ionosphere Sounding (MARSIS), shallow radar (SHARAD), and Mars Orbiter Subsurface Investigation Radar (MOSIR), are orbiting Mars and have obtained a large quantity of radargrams. These direct observations provide valuable information for deciphering subsurface structure and composition of Mars, which are critical for understanding internal stratigraphy, climate change, and orbital variation in the planet. For this reason, automatic, effective, and precise extraction of subsurface reflectors in radargrams is a prerequisite and remains as a challenge though recent studies have made great progresses. In this study, we propose a fully automatic method for reflector detection in radargrams using transform domain techniques and graph theory. In the preprocessing step, the spatial spectrum information is used to automatically extract region with reflectors in a radargram, which can significantly reduce the computational cost. Then, continuous wavelet transform (CWT) with double threshold is used to detect peaks in each frame, and minimum spanning tree (MST) is further used to connect the peaks based on global information. Our proposed method can quickly reconstruct the reflectors in radargrams with a relatively low tracking error rate, which is better than previous methods based on local information. To testify the effectiveness of the algorithm, we applied our algorithm to SHARAD radargrams in the two polar regions. The results show that more than 90% (80%) of the reflectors can be well-detected in the strong (weak) echo regions, and their subsurface information can be extracted efficiently. Compared with previous methods, our method has a higher degree of automation and a wider applicability. The proposed algorithm can be applied to analyze radargrams over large regions of Mars and other bodies.

One of Chinese meteorological satellites, Feng Yun-4M (FY-4M), as one the of new generation of geosynchronous series satellites, is planning to upload multichannel millimeter-wave radiometers, e.g., from 50 to 430 GHz. Due to long-period stability and no atmospheric interference, brightness temperature (TB) of the lunar surface can be seen as a good candidate for thermal calibration of FY-4M radiometers. In this paper, the physical temperature profile of lunar regolith media is first derived by resolving 1-D heat transfer equation with validation of the measurements of the Diviner lunar radiometer experiment onboard the lunar reconnaissance orbiter. Then, the loss tangent is fit and validated using the TiO2 abundances, which is derived from Clementine five-band multispectral data and Chinese Chang'e-2 37-GHz TB data. Multichannel TB of a lunar surface region along the moon equator at certain lunar time (noon and midnight) is numerically derived for all FY-4M channels. TB of lunar equator center area (0°N, 0°E) is presented with variation of the lunar local time. These results can be well applied to calibration of FY-4M, with a sustainable error in the range of 1.8 (425 GHz) to 3.8 K (89 GHz).

Searching for water–ice in the lunar media has been a key issue in the moon explorations. Missions of mini-SAR and mini-RF SAR made compact-pol (polarization) measurements on lunar polar permanent shadowed region (PSR). High circular polarization ratio (CPR) data and a two-layer model were applied to studying if water ice in PSR could be retrieved. However, it has been studied that high CPR is not simply due to the presence of water ice, and the Campbell model is a degenerated half-space model, which confused final inversion. In this letter, using the mini-RF data on the PSR of Hermite-A crater on the north pole, a two-layer model with the Kirchhoff and small perturbation approximations is presented. It takes account of the surface-layering topography, which makes changes of local incidence and polarimetric base rotation. Our results do not support Calla’s conclusions based on the half-space model, suggesting that the inversion of mini-RF is not so straightforward in proving water–ice existence in the PSR media. It points out that the double- and high-order scattering of random volumetric scatters on the lunar surface might play a role, and high-resolution measurements and more elaborate modeling are needed for further studies.

The mystery of the asteroid (4179) Toutatis was revealed by Chang'e-2 spacecraft during a close flyby on December 13, 2012. Optical imaging and navigation of the probe during the flyby were performed entirely under ground-based radio tracking and default sequence built on ground. This paper establishes a set of estimation algorithms of the relative trajectory between Chang'e-2 and Toutatis based on dynamics, optical, and radio constraints that are determined by the unique flyby mode. This study is the first time to precisely reproduce the core process of Chang'e-2's encounter with Toutatis based on several optical images. In addition to constructing a strict photogrammetric model, the shadowing effects caused by the illumination and the deviation of the center-of-mass (COM) from the center-of-figure (COF) in optical images are also considered. The spacecraft trajectory with regard to the COF of the body is estimated using images taken from 120 km or less. The formal one sigma uncertainty is (67, 20, and 11 m) in the principal axes frame of the position error ellipse, and the closest approaching distance between Chang'e-2 and Toutatis's COF is calculated as 1557 ± 11 m, which is more precise than previous results with an uncertainty of hundreds of meters. The spacecraft trajectory with regard to the COM of the body is estimated with an uncertainty of (211, 34, and 17 m), and the corresponding closest distance is estimated as 1451 ± 18 m based on the previously developed shape model of Toutatis. The algorithms and results in this study are important for evaluating the performance of this flyby mission and are also valuable for any similar optical navigation during a close approach. In addition, our results can help in precisely determining the axis of Toutatis and sizes of impact craters, which are critical for understanding the formation and evolution of Toutatis.

In China's first lunar exploration project, Chang-E 1 (CE-1), a multi-channel (3.0, 7.8, 19.35 and 37GHz) microwave radiometer in passive microwave remote sensing, was first aboard the satellite, with the purpose of measuring microwave brightness temperature (Tb) from lunar surface and surveying the global distribution of lunar regolith layer thickness. In this paper, some works on this mission, including the microwave emission modeling and Tb simulation of lunar surface media, CE-1 data validation and retrieval of lunar regolith layer thickness from multi-channel CE-1 Tb data, and evaluation of global inventory of Helium-3 in lunar regolith, are reported.

In China's first lunar exploration project, Chang-E 1, the multichannel (3.0, 7.8, 19.35, 37 GHz) microwave radiometers were aboard the satellite, with the purpose of measuring microwave brightness temperature from the lunar surface and surveying the global distribution of lunar regolith layer thickness, and global evaluation of3He content. To analyze the modeling of microwave radiative transfer from three-layered media of the lunar surface, some factors, such as the cratered lunar surface roughness and scattering of regolith particulate medium with temperature profile, are discussed. The three-layer model makes the predominance of the parameters, such as the regolith layer thickness and stratified structures, to be studied.

Based on the statistics of the lunar cratered terrain, e.g. population, dimension and shape of craters, the terrain feature of cratered lunar surface is numerically generated. According to inhomogeneous distribution of the lunar surface slope, the triangulated irregular network is employed to make the digital elevation of lunar surface model. The Kirchhoff approximation of rough surface scattering is then applied to simulation of lunar surface scattering. The synthetic aperture radar (SAR) image for comprehensive cratered lunar surfaces is numerically generated. Making use of the digital elevation and Clementine UVVIS data at Apollo 15 landing site as the ground truth, an SAR image at Apollo 15 landing site is simulated.