Estimation of lunar surface dielectric constant using MiniRF SAR data Nidhi Verma, Student Member, IEEE, Pooja Mishra, Member, IEEE, Neetesh Purohit, Member IEEE Abstract—A new model has been developed to estimate dielec- 12), 14163 (Apollo 14), 66041 (Apollo 16) are regolith sam- tric constant () of the lunar surface using Synthetic Aperture ples [15], [16]. Dielectric results from laboratory experiments Radar (SAR) data. Continuous investigation on the dielectric revealed the nature of lunar regolith. Another method in 1998 constant of the lunar surface is a high priority task due to future lunar mission’s goals and possible exploration of human outposts. was given by Chyba et al. in terms of energy loss during For this purpose, derived anisotropy and backscattering coeffi- propagation in an absorbing medium [17]. Alan et al. [10] cients of SAR images are used. The SAR images are obtained and Pollack et al. [16] analyzed the relationship between the from Miniature Radio Frequency (MiniRF) radar onboard Lunar dielectric constant and density of large regions using radar Reconnaissance Orbiter (LRO). These images are available in echoes. Campbell gave the formula for estimation of dielectric the form of Stokes parameters, which are used to derive the co- herency matrix. Derived coherency matrix is further represented constant in terms of radar backscattering coefficients. Avik et in terms of particle anisotropy. This coherency matrix’s elements al. [8] gave another method of dielectric constant estimation. compared with Cloud’s coherency matrix, which results in the Hagfor’s observations show a dielectric constant of 2.7 for the new relationship between particle anisotropy and coherency less dense upper regolith [18]. The overall dielectric constant matrix elements (backscattering coefficients). Following this, of the Moon at the centimeter wavelength is 2.7. This is due estimated anisotropy is used to determine the dielectric constant. Our model estimates the dielectric constant of the lunar surface to a mixture in which 95% of the material consists of fine without parallax error. The produce results are also comparable grain (dust) material [19]. with the earlier estimate. As an advantageous, our method Hence, the dielectric constant () estimation model has been estimates the dielectric constant without any apriori information developed as per the current research requirement for future about the density or composition of lunar surface materials. lunar studies using Miniature Radio Frequency (MiniRF) SAR The proposed approach can also be useful for determining the dielectric properties of Mars and other celestial bodies. data onboard Lunar Reconnaissance Orbiter (LRO) [20]. Our Index Terms—MiniRF data, dielectric constant, coherency model has applied to MiniRF SAR data of the Apollo 17 matrix, particle anisotropy. landing site Taurus-Littrow valley and Sinus Iridium area. The avaible MiniRF data is not parallaxe free which can I. INTRODUCTION affect the results from SAR images [21], [22]. For removing the parallax error MiniRF SAR raw data has been process The continuous examination of the lunar surface dielectric using ISIS3 open source software. Further, Stokes parameters constant is a high priority task for many countries due to has been derived [20]. These Stokes parameters have been the ongoing, future lunar missions and exploration of human further used to derive the coherency matrix, which is reflection outposts [1]–[5]. Some of these missions are Chandrayaan-3, symmetric. The derived coherency matrix is further converted Smart Lander for Investigating Moon (SLIM), and Spacebit into particle anisotropy form. Further, derived coherency has mission (first UK robotic lunar mission), etc. The planning of been compared with the coherency matrix given by Cloude these missions is to land their rover on the lunar surface to [23]. This comparison provides a unique relation between explore resources. For landing the rover, these missions require Stokes parameters and particle anisotropy. Finally, the model the knowledge of the regolith materials [6], [7]. The selection has been developed for the estimation of dielectric constant in of landing sites depends on the particular mission objectives. terms of particle anisotropy. One of the common goals is the analysis of the lunar surface’s The developed model for lunar surface dielectric constant material properties, which includes the estimation of lunar measurement has the advantage over laborite’s measurement arXiv:2105.10670v1 [astro-ph.IM] 22 May 2021 surface dielectric constant [5], [8], [9]. dielectric constant. For the estimation of dielectric constant, In past number of methods have been developed for es- density extraction is required; however, in our work, such kind timating lunar surface dielectric constant [8], [10]–[14].The of apriori information is not needed [14], [24], [25]. Here, we dielectric constant estimation is not a new priority, but it is have used the advantage of microwave scattering information important from several years [10], [11]. In 1975 an empirical for estimating dielectric constant. Our method can also be relationship between the dielectric constant and bulk density relevant for estimating the dielectric constant of other celestial had been derived by Olhoeft and Strangway using lunar bodies such as Mars etc. samples returned by the Apollo missions [12]. During the Apollo missions 11, 12, 13, 14, 15, 16, and 17, various samples II. DATA AND STUDY SITE DETAILS were taken from the lunar regolith. There were seven samples In this work, hybrid polarimetric S-band MiniRF data has of such kind. Four of the 10084 (Apollo 11), 12070 (Apollo been used. This data is obtained by transmitting (Left/right) circular polarization and receiving horizontal and vertical polarization coherently. The available MiniRF data level-2 in 8 2 2 S11 = (Ap − 1)sin θ cos τ + 1 PDS is not orthorectified. Due to the topographic varaions the > S S <>S = (A − 1)cosθ cos 2τ parallax error comes into the existance [21], [22]in the MiniRF [S] = 11 12 = 12 p S21 S22 S = (A − 1)sinθ cos θ cos 2τ data. Some times the SAR data produces 20% or higher like > 21 p > 2 2 50-60% (mostly in case of opposite sens (OC) and same sens :S22 = (Ap − 1)cos θ cos τ + 1 (SC) polarization) [21], [22]. This error effect the results in (1) the previous developed method for estimation lunar surface Where angle θ and τ represent the rotation and tilt angle dielectric constant. Hence, level-1 raw data again reprocess of the spheroid, respectively. The Ap is particle anisotropy, and parallax error has been removed using the process given which is also known as particle polarizability. The value of by Fa et al. [21]. This data is further used for the extration Ap is defined below in equation (2) of Stokes parameters (S , S , S and S ). The selected 1 2 2 3 P article anisotropy (A ) 0 (2) study areas for this paper are Taurus-Littrow valley and Sinus p > Iridium., the S1 (total power) images of which are shown in B. Generation of Coherency matrix Figure 1 (a) and Figure 1 (b) (before parallax correction), The scattering matrix in equation (1) is in complex symmet- respectively. The complete description of these images is given ric form. Hence it can be represented in the form of eigenvalue in Table 1. We have chosen these areas due to the earlier study expansion form as shown in equation (3) [27] suggested that they are more suitable for landing purposes and less affected by roughness. The mass wasting is process which usally present on lunar cosθ sin θ 1 0 cosθ −sinθ [S] = 2 2 surface. This mass wasting some time effect the SAR image −sinθ cosθ 0 sin τ + Apsin τ sinθ cosθ (3) due to high roughness. Hence further to avoid the missinter- The scattering matrix further reformulated into the following preation from SAR images the GDL DTM 100M was used to scattering vector (k) form as given by equation (4) mask the high slope area (slope < 5◦) after parallex correction. 21 0 0 3 22 + Xcos2τ3 k = 40 cos2θ −sin2θ5 4 Xcos2τ 5 (4) TABLE I 0 sin2θ cos2θ 0 DATA DESCRIPTION Parameters Taurus-Littrow valley Sinus Iridium W here X = Ap − 1 Central frequency 2.38 GHz 2.38 GHz Incidence angle 52:21◦ 53:73◦ Further, we have computed the Coherency matrix [T ] (3×3) Center longitude 30:586469◦ 34:821143◦ using k as shown in equation (5) Center latitude 17:234865◦ 41:744494◦ ◦ ◦ Maximum latitude 25:33734 45:443823 1 T Minimum latitude 9:146916◦ 38:046091◦ [T ] = kk* (5) Westernmost longitude 9:146916◦ 324:67553◦ 2 Easternmost longitude 30:154224◦ 325:622395◦ Where k∗ represents complex conjugate of k, T represents the transpose. The final simplified form of coherency matrix is given below 2 j2 + Xcos2τj2 (2 + Xcos2τ)X∗cos2τ cos 2θ (2 + Xcos2τ)X∗cos2τ sin 2θ3 III. METHODOLOGY 1 [T ] = (2 + X∗cos2τ)Xcos2τ cos 2θ jXcos2τ cos 2θj2 X2cos4τ cos 2θ sin 2θ 2 4 5 (2 + X∗cos2τ)Xcos2τ sin 2θ X∗2cos4τ cos 2θ sin 2θ jXcos2τ cos 2θj2 In this paper, we have developed the model for estimating (6) the dielectric constant () of the lunar surface using MiniRF Synthetic Aperture Radar (SAR) data by using the concept Here, we have found that the off-diagonal elements of [T] of particle anisotropy concept. Our model assumes that the will be zero for all possible value of τ and θ. However, non- surface regolith particles are the same as the cloud of randomly diagonal elements maintain scattering information. oriented particles [26]. This assumption states that the regolith particles size is smaller than the S-band wavelength, which is C. Coherency matrix conversion into eigenvalue decomposi- used for the volume scattering mechanism from the “surface tion matrix form regolith” [26].The steps for the development of the proposed Next, equation (6) converted into the Eigenvalue decompo- model are as follows sition form with three diagonal values are , λ11, λ22 and λ33 2 3 2 3 2 3 A.