EUSAR 2018
Hybrid Polarimetric Decomposition Modelling of Lunar Surface for Scattering Characterization using Miniature RADAR data Shashwat, Shukla, Indian Institute of Remote Sensing (IIRS, ISRO),
[email protected], India Shashi, Kumar, Indian Institute of Remote Sensing (IIRS, ISRO),
[email protected], India
Abstract Planetary surface and subsurface exploration have made RADAR imaging a prominent tool in spatially characterizing the physical properties of the regolith. The study was carried out for various lunar morphological features, including craters and Apollo 15 landing site, by analyzing their polarization behavior using Chandrayaan-1 MiniSAR and Lunar Reconnaissance Orbiter Mini-RF Circular Transmit Linear Receive (CTLR) dataset. Hybrid decomposition techniques have been used to model dominant scattering patterns from a single resolution cell. Furthermore, the linear received signals captured by Chandrayaan – 1 MiniSAR were found to be ambiguous. Results are expected to showcase the potential of EM wave interaction with the lunar surface.
1 Introduction
cated antenna technology (in case of quadrature polarimetric mode) have led to a lower demand in such interplanetary missions [5], [7]. Therefore, a hybrid polarimetric RADAR system proved to be reliable with less number of polarimetric combinations, large swath and fully polarimetric property. Utilizing the above technology, the S-band radar data of Chandrayaan – 1 MiniSAR mapped more than 95% of the areas of 80 o latitude pole wards at a resolution of 150 meters [8]. In complementary to this, evidences of water ice were found by correlating the scattering contributions of shadowed regions with proposed locations of polar ice based on the prospector neutron data [9]. Similarly, MiniRF system on board LRO demonstrated an integrated approach of synthetic aperture radar (SAR) at two wavelengths (S-band and X-band) and two resolution (150 m and 30 m) in a way to measure the Stokes parameter of the reflected signal [10]. It offered an incremented version with an additional task to perform, i.e. characterizing the pyroclastic volatile deposits [5], [10]. In the present study, both the sources were utilized for extracting the scattering mechanism throughout the lunar surface, thereby deriving the spatial dissemination of the surface composition and a more elaborated sub-surface characteristics in a qualitative way. For a given transmission polarization, the Stokes parameters were derived by capturing all of the information that are a characteristic attribute to backscattered signals. Apart from this, various hybrid decomposition modelling approaches were investigated on the basis of the Stokes child parameters like degree of polarization (m), Poincare ellipticity parameter (χ), relative phase ( ) and polarization angle (α). The present work reveals a significant understanding for the interaction of Electromagnetic wave (EM) with the lunar regolith. It also serves as a priori for the dual frequency SAR imaging in the upcoming Chandrayaan – 2 mission. .
Lunar surface has been a great source of interest for facilitating us, a more reliable insight of the evolution of solar system. Various missions have explored the surface and held back with an informative essence of, what is commonly known as, “Geological Rosetta” of the Earth [1]. Even after understanding different aspects of its geological makeup, there are still many questions unanswered on revealing the reliable model for spatially distributing the scattering patterns across the surface. RADAR imaging has made it possible in characterizing the physical properties of the regolith, thereby, studying the significance of planetary ice, ejecta characteristics and geomorphological features existing on the surface [1], [2]. This technology gained its importance in detecting patchy ice deposits in the permanently shadowed polar regions of the Moon, by deriving pseudo quad information from dual polarized data in case of hybrid polarimetric architecture [1]–[4]. Miniature Radio frequency radars, on board Lunar Reconnaissance Orbiter (LRO) and Chandrayaan–1, orbiting near polar are first of a kind in transmitting circular polarized wave while receiving coherently orthogonal linear polarizations at 2.38 GHz [5]. These polarimetric combinations support the quantification of second order coherency matrices of the backscattered field which further computes the Stokes vectors in such a way that they tend to follow rotational symmetry [6], [7]. Previous studies analyzed the potential of transmission of interleaved polarization for the implementation of fully polarimetric conventional system [5]– [7]. Furthermore, the pulse repetition frequency followed a negative correlation with the swath width, thereby minimizing the area of coverage of the scene. In addition to this, the complexity of the system design, data usage and high power consumption due to compli-
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1.1 Stokes Vector Representation
1.2 Stokes Child Parameters
To characterize the polarization state of an observed EM wave, four Stokes parameters are used. They provide information of ellipticity and polarization ellipse orientation angle [6]. In the case of fully polarized waves, the amplitude and relative phase are determined by their gradually varying nature with time or constant in some instances. The utilization of Stokes parameters to implement partially polarized waves has the form of 2x2 complex Hermitian positive semi – definite wave coherency matrix [J] [6], [7]. This is derived from scattering matrix based Pauli feature vector, also known as Wolf’s coherency matrix for hybrid polarimetric systems and expressed as (1):
The parameters derived with the help of Stokes parameters for understanding various properties of the surface, are called Stokes child parameters [7]. The degree of polarization (m) determines the ratio of polarized power to the total power of the EM wave and characterizes the polarity of the backscatter. Random volumetric scattering has the m value close to 0 while the value approaches to 1 for odd and even bounce scattering. This parameter is fundamentally related to Entropy (E) [5]. The relative phase ( ) parameter signifies the phase reversal indicated in the type of scattering. It is an angular phase difference between two components and hence, a sensitive measure of double bounce scattering [6]. One of the shape parameter for preserving the sense of rotation while describing the relative phase and magnitude of the horizontal and vertical components is Poincare ellipticity parameter (χ) [6], [7], [11]. It is sensitive to even vs odd bounce scattering. The polarization angle (α) is closely related to the ellipticity of the scattered wave [6], [7]. For representing the scattering associated with the planetary ice deposits and fresh crater ejecta, circular polarization ratio (CPR) has been widely used. It could also be attributed to strong even bounce scattering due to rough lunar surface with large blocky rocks producing the CPR values greater than unity at times [7], [11], [12]. Fa et al.[2] also concluded on the significance of CPR towards low subsurface roughness indicating anisotropic buried ice inclusions. Along with this, the linear polarization ratio (LPR) closely relates with the degree of polarization describing the coherency of the surface. All the above parameters reconstructed from Stokes vector are formulated as in (5).
[ ]=
∗〉
〈 〈
∗〉
∗〉
〈 〈
∗〉
(1)
=
The coherency matrix can be represented in terms of Stokes parameters as in (2): [ ]=
1 2
+ −
+ −
(2)
where * denotes complex conjugate, E is the subscripted polarized complex voltage and 〈… 〉 indicates ensemble averaging by assuming a stationary wave [6]. In the above equation (1), intensities are represented by the diagonal elements while off diagonal elements depict the complex cross correlation. Furthermore, Stokes parameters (S) could be represented as in (3): = 〈|
| 〉 + 〈|
| 〉= 〈
∗〉
+〈
∗〉
= 〈|
| 〉 − 〈|
| 〉 =〈
∗〉
−〈
∗〉
= 2| = 2|
|| ||
| |
∅ ∅
= 〈
∗〉
= 〈
∗〉
+〈 + 〈
∗〉 ∗〉
+
=
cos(2 ) cos(2 ) sin(2 ) cos(2 ) sin(2χ)
ISBN 978-3-8007-4636-1 / ISSN 2197-4403
−180 ≥
= tan
sin 2 =
−
− 45 ≥
≥1
=
(4)
~
795
1−
≥ 180
≥ 45
0 ≥ α ≥ 90
α = 2| |
= =
0≥
(3)
The above four parameters are expressed in terms of power rather than amplitudes and phases. The first term S1 gives the total intensity while S2 provides the polarization state (horizontal or vertical) of the wave. The third and fourth terms relate to phase difference with S3 describing the eccentricity of the wave and S4 denoting the handedness or rotation (left or right handed) [7]. The Stokes parameters can also be expressed in the form of ellipticity parameter (χ) and orientation angle (ψ), as in (4):
[ ]=
+
− +
>1 + − , ~0.74
(5)
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EUSAR 2018
1.3 Hybrid Decomposition Approaches
2 Dataset and Study Area
In order to characterize the lunar surface based on scattering pattern retrieval, several hybrid-pol decomposition modelling approaches are investigated. The total contribution of surface, volume and double bounce scattering is denoted by s, v and d respectively, in the following approaches.
In this study, hybrid polarimetric data from Chandrayaan – 1 MiniSAR and LRO MiniRF were utilized. Table 1 gives a brief description of datasets. Datasets Incidence Angle Wavelength Swath Width Azimuth Resolution GRD Polarization
1.3.1 m- Decomposition This technique offers a robust solution for distinguishing even and odd bounce scattering [13], [14]. The applicability of this in hybrid pol data for lunar surface has been first demonstrated by Raney et al. [13] for Mini-SAR data (6).
= = =
(1 +
Six study areas have been selected in order to carry out the research, ranging from two in the North Pole, two in the mid latitude Equatorial region and two in the South Pole. The major objective behind selecting these craters is to understand the spatial distribution of the polarization scattering behavior of different targets, globally. Table 2 gives a brief description of the study areas, their locations and diameters.
2 )
(1 −
) 2
(6)
1.3.2 m-χ Decomposition This method is useful for characterizing backscatter contribution of double bounce from surface scattering [11]. Comparatively, this proved to be more efficient than m- approach in scattering property retrieval (7).
S.No.
Feature Name
Location
1.
Shackleton Crater
2.
Von Baeyer Crater
3.
Near Apollo 15 Landing Site Part of Cassini Crater Erlanger Crater
89.9o S, 0.0o E (South Pole) 81.6o S, 61.3o E (South Pole) 26.1o N, 3.6o E (Equatorial) 40.2o N, 4.6o E (Equatorial) 86.9o N, 28.6o E (North Pole) 85.2o N, 155.4o W (North Pole)
4. 5.
= = =
(1 −
2 )
6.
2 (1 −
2 ) 2
= =
2α) 2
(1 −
27.9, by Lunar Rover 57 10.94 177
Figure 1 shows the flow chart of the methodology. Data products along with their intensity images, in dB, are extracted by processing the LRO MiniRF (for South Pole and Mid-latitude equatorial) and Chandrayaan – 1 MiniSAR (for North Pole) CTLR datasets. Stokes child parameters are calculated based on the derived Wolf’s coherency matrix upon which hybrid polarimetric decomposition modelling is performed. The scattering patterns retrieved are then compared and analyzed by polarization parameters in order to characterize the selected craters on the lunar regolith.
As compared to previous techniques, this method forms a basis of Eigenvector analysis of hybrid pol data, similar to H/α decomposition of fully pol data [6], [7]. The α describes the scattering mechanism (8). (1 +
13.8
3 Methodology
(7)
1.3.3 m-α Decomposition
=
Part of Rozhdestvenskiy Crater
Diameter (km) 20.93
Table 2: Brief Description of the Study Areas.
)
(1 +
LRO MiniRF ~ 48o 12.6 cm (S-Band) 18 Km 150 m (S-Band) 7.5 m/pixel Right CTLR
Table 1: Description of the Datasets.
)
(1 −
Chandrayaan – 1 MiniSAR ~ 35o 12.6 cm 13 Km 150 m 75 m/pixel Left CTLR
)
(1 −
2α) 2
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(8)
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EUSAR 2018
Figure 2: Comparison of LH and LV Intensity (in dB) between inside and outside the selected craters.
4.2 Polarimetric Properties of Lunar Surface For enhancing the quality of information and interpretation aiding to scattering component retrieval, several polarization parameters were estimated as plotted in Figure 3. Higher values of CPR were observed in the South Polar Regions, with a mean CPR of 0.851 near Shackleton crater. This may attribute to increased double bounce scattering due to several peaks towards the western end of the inner crater rim of Shackleton. Previous studies showed no evidence of exposed ice as the surface albedo of the permanently shadowed crater floor correlated with the lunar far side [2]–[4]. It was characterized by a comparatively lower entropy value and moderate coherency, signifying low degree of randomness in the backscattered signals. North Polar regions were identified with high coherency leading to more sub surface scattering phenomena and moderately high CPR values indicating the presence of volumetric scattering in the floor of Erlanger. This was well demonstrated by having a higher entropy value, relating to the previous works for evidence of water ice patch inside the crater [2], [3], [9]. Being at the eastern end of Mare Imbirium, Apollo 15 landing site witnessed a mean entropy value of 0.611 due to the basaltic volcanic deposits and a more dominant odd bounce scattering. Furthermore, moderate degree of surface roughness provided it to be a good site for exploring the evolution of volcanic processes that produced Hadley Rille. However, the Cassini crater was characterized by intermediate levels of CPR, coherency and randomness, which is evident to its highly matured lunar soil grains enriched in higher FeO and TiO2 concentrations of the lava flooded crater floor [16].
Figure 1: Flow Chart of Proposed Methodology.
4 Results and Discussions 4.1 Transect Analysis of dB Scale Intensity for North Polar Region The polarization behavior of LH and LV received signals were plotted by investigating transects of 100 samples taken inside and outside the North polar craters, Rozhdestvenskiy and Erlanger. It was observed that Chandrayaan – 1 MiniSAR captured more intensity in the linear coherent horizontal receive mode as compared to linear vertical. This is contradictory to the scattering theory, which states that the vertical polarized component of the received signal should be always greater than the horizontal component over rough surfaces, for incidence angle greater than 15o [15]. For the regions outside the crater, this effect was more dominant with a mean LH intensity of -14.56 dB as compared to mean LV intensity of -17.64 dB, for Rozhdestvenskiy crater. Similar intensities were observed for Erlanger, with less effect inside the crater. This inconsistent behavior of Chandrayaan – 1 MiniSAR may be due to the varying incidence angle for different scattering mechanisms allowing stronger intensity at lower incidence [5], [7], [15]. This effect was not noticed in LRO MiniRF data of South Polar Regions. Figure 2 gives a quantitative approach for comparing the LH and LV intensities showing variability in the backscatter observed.
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Figure 3: Polarimetric Properties of Selected Regions.
4.3 Retrieval of Scattering Patterns
Figure 4: Comparison of m- , m-χ and m-α decomposition for all the regions.
The results of scattering mechanisms, as illustrated by m- , m-χ and m-α decomposition, are shown in Figure 4. The m-χ for Cassini crater proved to be more evident in detecting ejecta deposits and demonstrated the potential in differentiating materials within the ejecta. Cassini M and Cassini B craters were found to have more dominant even bounce scattering in their eastern end of the rim, leading to the interaction of EM wave with a double bounce tendency near the crater rim wall. Along with this, several craters and secondary craters were seen to have reddish hue on one side and meanwhile bluish purple on the other. Raney et al.[11] explained this defect to be one of the shortcomings of m. Due to the change in the sign of from one side to other, the axis of the crater floor wall gets oriented relative to the orthogonal linear component of radar incoming signal and thus, this change of color is observed. Because of this, m- is inconsistent in retrieving the exact scattering power due to elliptical (imperfect) transmit polarization [5], [11]. Furthermore, m-α decomposition technique showed a relatively larger amount of even bounced scattering power in all the six features used in the study. Therefore, for an efficient scattering characterization, m-χ proved to be a reliable model for lunar surface.
The m-α derived scattering patterns as observed at the interior rocks of the Shackleton (Figure 4) provided a much reliable even bounce as compared to other decomposition approaches. However, the surrounding lunar regolith of all the selected crater sites was more pronounced in m-χ technique. Quantitative analysis in the form of transects of 50 samples inside and outside the craters was performed to examine the proportion of volume, even bounce and single bounce scattering patterns, as shown in Figure 5. Erlanger crater showed a much higher amount of volume scattering within the local crater surface, aiding to the interpretation by several studies on detecting water ice. Comparatively, a more fraction of single bounce Bragg scattering was observed in the Apollo 15 landing site, suggesting the presence of mineral grains. Shackleton crater noticed more random scattering in its rim rather inside it, where almost an aggregate mixtures of all patterns were seen. The overall analysis concludes in characterizing different regions of the lunar surface on the basis of scattering mechanism.
Significantly, higher CPR is evident for the surface ejecta that may appear smooth in hyperspectral and optical imagery but actually has a rough texture, may be at centimeter and decimeter scales [7], [13]. These ejecta deposits may have derived from oblique directed impacts [11]. Particular to the case of Cassini crater, one probable reason of having variations in the CPR within the ejecta may be due to the locations of the craters as Cassini B resides inside the primary Cassini crater which is evident to have lava flooded floor giving rise to more CPR value as compared to its outside. Additionally, the polar craters are characterized by high CPR values inside their rim at the floor, attributing to the presence of water ice as studied by [3], [4].
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Figure 5: Quantitative Transect Analysis for selected craters of North Pole, Mid latitude and South Pole.
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5 Conclusions
27, 2011.
In this paper, an attempt has been made to characterize lunar surface on the basis of scattering patterns using CTLR data of Chandrayaan – 1 MiniSAR and LRO MiniRF. Several decomposition techniques were applied for facilitating unambiguous lunar features depending on their polarization behavior. The utility of m-χ decomposition to examine realistic scattering mechanisms for identifying various geomorphic features could be well demonstrated. Along with this, eigen vector based m-α was performed, resulting in more even bounce scattering attributing to false prediction of excessive dihedral structures. Erlanger crater observed higher entropy value within its rim along with increased volume scattering and high CPR value inside the crater. This remained consistent with the previous findings of water ice. Furthermore, higher value of CPR was seen in Shackleton crater, which may attribute to increased even bounce near the peaks inside the western end of the crater. Mid latitude Cassini crater was characterized by moderate level of coherency and randomness with evident basaltic deposits in its ejecta and lava flooded floor. Consequently, most parts of lunar surface except the interiors of the craters were effected by odd bounce scattering. Moreover, inconsistency was observed in Chandrayaan – 1 MiniSAR on received signals from North Polar Regions, with a probable reason of varying incidence angle. Furthermore, the dual frequency SAR data in the ISRO made Chandrayaan – 2 mission may provide a better scattering characterization to understand the EM wave interaction with the lunar surface.
Acknowledgement
[4]
K. Watson, B. Murray, and H. Brown, “On the Possible Pressence of Ice on the Moon,” J. Geophys. Res., vol. 66, no. 5, pp. 1598–1600, 1961.
[5]
R. K. Raney et al., “The Lunar Mini-RF Radars: Hybrid Polarimetric Architecture and Initial Results,” Proc. IEEE, vol. 99, no. 5, pp. 808– 823, 2011.
[6]
W.-M. Boerner, Basics of Radar Polarimetry Introduction : A Review of Polarimetry, no. October. 2004.
[7]
R. K. Raney, “Hybrid-Polarity SAR Architecture,” IEEE Trans. Geosci. Remote Sens., vol. 45, no. 11, pp. 3397–3404, 2007.
[8]
L. Carter et al., “The MiniSAR Imaging Radar on then Chandrayaan - 1 on the Moon,” Lunar Planet. Sci. Conf., vol. 40, no. 1098, pp. 7–8, 2009.
[9]
P. D. Spudis et al., “Initial results for the north pole of the Moon from Mini-SAR, Chandrayaan-1 mission,” Geophys. Res. Lett., vol. 37, no. 6, p. L06204, 2010.
[10]
S. Nozette et al., “The Lunar Reconnaissance Orbiter Miniature Radio Frequency (Mini-RF) Technology Demonstration,” Space Sci. Rev., vol. 150, no. 1–4, pp. 285–302, 2010.
[11]
R. K. Raney, J. T. S. Cahill, G. W. Patterson, and D. B. J. Bussey, “The m-chi decomposition of hybrid dual-polarimetric radar data,” Int. Geosci. Remote Sens. Symp., vol. 117, no. May, pp. 5093–5096, 2012.
[12]
S. Saran, A. Das, S. Mohan, and M. Chakraborty, “Study of scattering characteristics of lunar equatorial region using Chandrayaan-1 MiniSAR polarimetric data,” Planet. Space Sci., vol. 71, no. 1, pp. 18–30, Oct. 2012.
[13]
R. K. Raney, “Decomposition of hybrid- polarity SAR Data,” Proc. 3rd Int. Work. Sci. Appl. SAR Polarim. Polarim. SAR Interferom., pp. 22–26, 2007.
[14]
F. T. Charbonneau et al., “Compact polarimetry overview and applications assessment,” Can. J. Remote Sens., vol. 36, pp. S298–S315, 2010.
[15]
J.-C. Souyris, “The Physics of Radar Measurement,” Remote Sens. Imag., pp. 83–122, 2014.
[16]
S. Shukla, S. Kumar, and S. Agrawal, “Mineral Mapping of FeO and TiO2 of the Cassini crater using Moon Mineralogy Mapper,” in 38th Asian Conference on Remote Sensing, pp. 1–10, 2017.
The authors are grateful to the Lunar PDS Geoscience Node for providing free and open access to S-Band LRO MiniRF and Chandrayaan – 1 MiniSAR data.
References [1]
L. M. Carter, D. B. Campbell, and B. A. Campbell, “Geological Studies of Planetary Surfaces using RADAR Polarimetric Imaging,” Proc. IEEE, vol. 99, no. 5, pp. 770–782, 2011.
[2]
W. Fa, M. A. Wieczorek, and E. Heggy, “Modeling polarimetric radar scattering from the lunar surface: Study on the effect of physical properties of the regolith layer,” J. Geophys. Res., vol. 116, no. E3, p. E03005, 2011.
[3]
T. W. Thompson, E. A. Ustinov, and E. Heggy, “Modeling radar scattering from icy lunar regoliths at 13 cm and 4 cm wavelengths,” J. Geophys. Res. E Planets, vol. 116, no. 1, pp. 1–
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