A Radar Eye on the Moon: Potentials and Limitations for Earth Imaging

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1 PIERS ONLINE, VOL. 6, NO. 4, A Radar Eye on the Moon: Potentials and Limitations for Earth Imaging M. Calamia 1, G. Fornaro 2, G. Franceschetti 3, F. Lombardini 4, and A. Mori 1 1 Dipartimento di Ingegneria Elettronica e Telecomunicazioni (DET), Università di Firenze, Italy 2 Istituto per il Rilevamento Elettromagnetico dell Ambiente (IREA), Italy 3 Dipartimento di Ingegneria Biomedica Elettronica e delle Telecomunicazioni Università di Napoli Federico II, Italy 4 Dipartimento di Ingegneria della Informazione, Università di Pisa, Italy Abstract Among the next space missions goals the exploitation of the Moon, the natural Earth satellite, is gaining an increasing interest. Colonization of the Moon is along the usual track of human civilization and economic expansion; it is also related to a large number of scientific issues, including Earth Observation (EO). With respect to standard LEO satellite commonly used in remote sensing, Moon has specific features. In this work we analyze the potentials as well as the limitations related to active microwave remote sensing with Synthetic Aperture Radar in terms of imaging characteristics and potential applications. 1. INTRODUCTION The exploitation of the Moon, the natural Earth satellite, is gaining an increasing interest. Calls for ideas are being recently coordinated by several international space agencies, in order to evaluate themes and objectives related to lunar missions. Colonization of the Moon is along the usual track of human civilization and economic expansion; it is also related to a large number of scientific issues, including Earth Observation (EO). EO is traditionally carried out by means of sensors mounted on artificial satellites mainly orbiting on sun-synchronous Low Earth Orbits (LEO). With respect to standard LEO satellites, Moon has specific features: a longer distance between the sensor and the imaged area, non sun-synchronous orbits, a large surface for the installation of sensors and equipments, etc. In this work we analyze the potentials as well as the limitations related to active microwave remote sensing with Synthetic Aperture Radar (SAR), giving particular emphasis to its distinguished characteristic from LEO satellites in terms of imaging characteristics and potential applications. One of the major expected problems of Lunar EO with respect to standard LEO satellites is associated with the considerable increasing distance between the scene and the sensor. For a passive system the increasing distance leads to an unavoidable resolution loss. On the contrary, for a SAR system the increase of the distance could, in principle, drastically impact the power budget [1] leading to a transmitted power level demand that could be hardly provided with standard technology. Nonetheless, there are many expected advantages related to the use of a lunar SAR system that make worth further investigations. First of all, the system would be characterized by a large ground swath, thus allowing the imaging of large portions of the Earth surface as well as a reduction of the revisiting time, down to one day. Secondly, a steering of antenna in elevation would lead to quasi-global scene accessibility. Differently from standard stripmap SAR sensors, a Moon-borne SAR can overcome the limit of half antenna length azimuth resolution [2] due to a peculiar imaging effect associated with the Earth rotation, leading to very high resolution imaging capabilities and hence small pixel size. This feature allows the use of large antennas to partially compensate for power limitations, without to lower the resolution to values unacceptable for some applications; and allows to avoid the need to implement any electronic or mechanical steering of the beam along the azimuth direction typical of more complex acquisition modes aimed at increasing the integration time to achieve very high resolutions. Finally, for a Moon-borne SAR system, the synthetic aperture integration time for full focusing is rather large: this on one side can prevent the possibility to effectively image fast moving scenes, such as the sea surface, but on the other side it can allow implementation of fast moving target detection, even starting from single antenna data [3]. Moon orbits may in principle allow the implementation of one day repeat pass differential interferometry [4]: due the large variation of the elevation angle from day to day, the number of usable

2 PIERS ONLINE, VOL. 6, NO. 4, coherent interfering images is rather limited. However, lunar surface allows the installation of multiple SAR sensors (only one transmitting) partially compensating the above mentioned drawback and also implementing single pass interferometry [4] on a systematic basis, as well as along-track interferometry and advanced 3D imaging [5, 6]. 2. THE MOON AND ITS ORBIT The main orbital and the physical characteristics of the Moon are summarized in Table I. The Moon is in synchronous rotation around the Earth with a sidereal period T M of about 27 days (sidereal month), resulting in an average angular velocity of Ω M = 2π/T M = rad/s. The Moon also rotates around its axis with a period equal to T M. As a consequence the same side of the Moon is always facing the Earth (tidal locking), so that an antenna pointed towards the Earth center approximately maintains its orientation, but for higher order effects such as lunar libration. The Moon orbits around the Earth in a plane which is tilted by 5 from the Ecliptic, and the angle between the Earth rotational axis and the direction perpendicular to the Ecliptic is about 24. As a consequence, a large variation of the elevation of the Moon over the horizon can be observed. For a latitude of 40, the minimum elevation of the Moon over the horizon is = 21 degrees, whereas the maximum elevation is = 79 degrees, with an excursion of more than 50 degrees, limiting the implementation of one day ineterferometry. The Earth rotates with a period T E of 1 day at an angular velocity of Ω E = 2π/T E = rad/s. Ω E Ω M, so, in the following, for sake of simplicity, we assume that the Moon is fixed and the Earth is rotating; and we neglect higher order motions associated with librations (also causing a variation of the angular velocity very low when compared to Ω E ). Obviously, such effects must be considered for data processing in order to achieve fully focused images. Table 1: Orbital and physical parameters of the Moon. Description Value Symbol Semi-major axis 384,748 km Mean eccentricity Average distance from the Earth 377,700 km D M Sidereal orbital period 27.3 days T M Average angular velocity around the Earth rad/s Ω M Average orbital speed 1.04 km/s V M Inclination to ecliptic Inclination to Earth s equator plane Mean radius 1,738 km R M Figure 1: Moon-Earth reference geometry in the equatorial plane used for the calculation of the azimuth resolution.

3 PIERS ONLINE, VOL. 6, NO. 4, QUALITATIVE ANALYSIS In the following, we briefly describe the main characteristics of a Moon based SAR system. For sake of simplicity, we refer to the geometry sketched in Figure 1, neglecting the inclination of the Earth and the inclination of the axis connecting the Moon center to the Earth center. The Moon is still assumed to be fixed whereas the Earth is rotating along an axis orthogonal to the Ecliptic Resolution Range resolution is governed by the transmitted pulse bandwidth B. It depends also on the elevation angle that, for the Moon-borne SAR case, can vary considerably in the sidereal month. To evaluate the azimuth resolution, let Lbe the size of the SAR antenna. The 3-dB antenna aperture is 2ϑ = λ/l, where λ is the radiation wavelength. With simple geometrical considerations, we have: ϕ D M ϑ, (1) R E showing that the Earth angular semi aperture ϕ is amplified by a factor D M /R E with respect to the antenna aperture ϑ. Denoting with v E the scatterer velocity vector and with ˆr the scatterer l.o.s., the Doppler Bandwidth (B D ) is given by: B D = 2 2 λ (v E ˆr) max = 4 λ v E sin (ϕ M + ϑ M ) 4 λ v E sin ϕ M 4 λ v D M E ϑ M = 2v E D M, (2) R E L R E assuming ϕ 1. The azimuth resolution y for the Moon-borne case is then given by: y = v E = L R E, (3) B D 2 D M and thus it is D M /R E 60 times better than that of the LEO space-borne case (L/2). This resolution gain effect has been also highlighted in the study of Medium Earth Orbit SAR systems [7] Ambiguity and Power Constraints In any SAR system the Pulse Repetition Frequency (PRF) f p is down- and up-bounded. The first limitation is related to the sampling of the azimuth bandwidth: for a correct sampling of the scene f p 2v E L D M R E 2v Ma L, (4) where v Ma is the equivalent Moon velocity with respect to a fixed Earth (almost D M /R E higher than the velocity of the scatterers on the ground). The second limitation is associated with the necessity to avoid that echoes backscattered by successive pulses are received simultaneously. We must ensure that [1] f p c/2w, where W = (λ/l r )D M cot ϑ el is the swath extension in the slant range direction, and L R is the antenna size in the direction orthogonal to the azimuth and slant range. It follows that LL r 4 v Ma c D Mλ cot ϑ el = 4 v E DM 2 λ cot ϑ el, (5) c R E Table 2: Parameters of three selected Moon-borne SAR systems compared to the Envisat ASAR system. L-band C-band X-band ASAR Azimuth Footprint [km] Integration time [s] Az. resolution [m] Doppler Bandwidth [Hz] ,400 Min antenna area [m 2 ] 20,987 6,529 3,614 2 Max ground range swath [km] Min average power [kw] Coverage rate [km 2 /day]

4 PIERS ONLINE, VOL. 6, NO. 4, showing that the minimum antenna area of a lunar SAR increases with respect to standard satellite systems for an increase of the distance and a scaling of the velocity (v Ma in place of v E ). With the same notation of [1], the basic constraint on the achievable SNR for lunar SAR system satisfying the constraint on the antenna minimum effective area is: P T λ SNR KT 0 σ 0 v Ma cos ϑ el F B πd M c sin 2 ϑ el P T KT 0 F B λ σ 0 v E πr E c cos ϑ el sin 2 ϑ el. (6) On the basis of the previous analysis, Table 2 provides the quantitative parameters of the three lunar system configurations with reference to an average value of the elevation of 50 degree at 40 latitude; the Envisat ASAR satellite of the European Space Agency is reported for comparison. The transmitted power budget has been also evaluated accordingly to (6) by assuming: T 0 = 290 K, SNR = 13 db, F = 3 db at L-Band, F = 4 db at C-Band and F = 5 db at X-Band. Moreover we considered σ 0 = 15 db at L-Band, σ 0 = 9 db at C-Band, and σ 0 = 6 db at X-Band corresponding to average values of agricultural fields Integration Time The three example systems of Table 2 exhibits a long integration time. As a consequence, it greatly enlarges the well-known imaging artefacts of non stationary or partially coherent scatterers. For a scatterer having a line of sight motion with a velocity of v t, the azimuth position in the final image is misplaced by ey = v t D M /v Ma. For v t = 1 m/s the scatterer would be misplaced of about 14 km. If τ c is the coherence time of a scatterer, the effective azimuth resolution ye is degraded by a factor which is approximately the ratio of the integration time T over the coherence time: ye = y T /τ c. For instance, in case of a forest canopy, the azimuth resolution will degrade up to several kilometers. The blurring effects from non stationary and partially coherent scatterers can also cause clutter power problems, due to the energy spreading over adjacent areas of stable scatterers. Analyzing the possible sources of clutter, the water can be considered to be not of great concern, unless for very windy days, being the scattering level significantly less (at least, a few db less) than other area, e.g., urban or agricultural fields. Clutter from strong windblown forest might exhibit higher power. Except high wind velocity, it can be estimated that even the forest clutter would not constitute a significant limitation. However, to reduce the possible criticalities in the vicinity of non fully coherent areas, a synthetic aperture processing robust to energy leakage may be achieved by resorting to presumming, as hinted in [8] Cross-track Interferometry With respect to existing LEO satellites a main peculiarity of Moon-borne SAR imaging is related to the one day site accessibility. The elevation angle has a large excursion in the sidereal month, and the acquisitions useful for one day repeat pass interferometry could be quite limited. However, the Moon surface offers the possibility to install different antennas allowing collection of simultaneous radar images from different elevation angles, single pass cross-track interferometry, and even 3D tomographic imaging [5, 6]. ACKNOWLEDGMENT The authors are grateful to Giovanni Vulpetti, of the Galileian Plus Italy for providing the Moon orbits via the computer program S.M.A.C. (Copyright, G. Vulpetti 1983, 2007). This work has been partially financed by the Italian Space Agency under the contract Italian Vision for Moon Exploration Earth observation from the Moon (n.i/042/06/0). REFERENCES 1. Franceschetti, G. and R. Lanari, Synthetic Aperture Radar Processing, CRC Press, Curlander, J. C. and R. N. McDonough, Synthetic Aperture Radar: Systems and Signal Processing, John Wiley & Sons, New York, Dias, J. M. B. and P. A. C. Marques, Multiple moving target detection and trajectory estimation using a single SAR sensor, IEEE Trans. Aerosp. Electron. Sys., Vol. 39, No. 2, , April Rosen, P. A., S. Hensley, I. R. Joughin, F. K. Li, S. N. Madsen, E. Rodriguez, and R. M. Goldstein, Synthetic aperture radar interferometry, Proc. IEEE, Vol. 88, No. 3, , March 2000.

5 PIERS ONLINE, VOL. 6, NO. 4, Reigber, A. and A. Moreira, First demonstration of airborne SAR tomography using multibaseline L-band data, IEEE Trans. Geosci. Remote Sens., Vol. 38, No. 5, , September Fornaro, G., F. Lombardini, and F. Serafino, Three-dimensional multipass SAR focusing: Experiments with long-term spaceborne data, IEEE Trans. Geosci. Remote Sens., Vol. 43, No. 4, , April Raney, K., Consideration for SAR image quantification unique to orbital systems, IEEE Trans. Geosci. Remote Sens., Vol. 29, No. 5, , September Prati, F., F. Rocca, D. Giancola, and A. Monti Guarnieri, Passive geosynchronous SAR system reusing backscattered digital audio broadcasting signals, IEEE Trans. Geosci. Remote Sens., Vol. 36, No. 6, , November 1998.

ERS-ENVISAT Cross-interferometry for Coastal DEM Construction

ERS-ENVISAT Cross-interferometry for Coastal DEM Construction Sang-Hoon Hong and Joong-Sun Won Department of Earth System Sciences, Yonsei University, 134 Shinchon-dong, Seodaemun-gu, 120-749, Seoul, Korea