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1 韓國電磁波學會論文誌第 17 卷第 9 號 2006 年 9 月論文 식물층에서의편파별후방산란측정과산란모델의비교 Comparison between Measurements and Scattering Model for Polarimetric Backscattering from Vegetation Canopies 홍진영 오이석 Jin-Young Hong Yisok Oh 요약 본논문은후방산란계수및지표면특성 (ground truth) 에대한측정방법을기술하며후방산란계수측정값과 radiative transfer 이론을적용하여개발된산란모델을비교함으로써산란모델의정확성을검증한다. R 밴드 (1.7~2.0 GHz) 의주파수대역에서 polarimetric scatterometer 시스템으로한강생태공원의수풀지형에서의후방산란계수를입사각도의변화와지표면수분함유량의변화에따라측정한다. 이측정결과를지표산란모델과비교한결과동일편파의경우비교적잘일치하며교차편파의경우보정을해줌으로써산란모델의정확성을얻을수있다. Abstract In this paper, we describe a measurement technique for the backscattering coefficient and ground truth of a vegetation canopy in detail. A simple microwave backscattering model for vegetation canopies is verified by being compared with this measurement. An R-band(1.7~2.0 GHz) scatterometer system is used to measure the backscattering coefficient of a vegetated area in the Han-river park for various incidence angles and a wide range of the soil moisture contents. It is found that the model agrees quite well with the measurements for co-polarized radar backscatter, and needs a correction for cross polarized radar backscatter. Key words : Polarimetric Scatterometer System, Radiative Transfer Theory, Backscattering Coefficient Ⅰ. 서론지표면은일반적으로맨땅, 수풀지형, 숲등과같은다양한환경으로이루어져있으며이로인한전자파의복잡한상호작용을계산하는산란모델을만드는데많은연구가진행되고있다. 본논문의목적은 radiative transfer 이론을적용하여개발된지표면산란모델을 [1] 수풀지형의후방산란계수측정값과비교함으로써산란모델의정확성을검증하고자한다. 기존의지표면측정데이터들이많이발표되어있지만 [2], 편파별측정데이터들이아니든지, 지표면데이터 (ground truth) 가충분하지않아서이용하기에문제점이있고, 본연구실의측정데이터가일부있지만 [1],[3], 여러입사각과여러수분함유량정도에따른데이터가필요하였기에본측정이필요하게되었다. 우선, 측정을위해 R-밴드 polarimetric scatterometer 시스템을구성했으며한강생태공원의수풀지형을한달간 2~3일간격으로측정하였다. 입사각도는 30 ~60 까지이며 1.7~2.0 GHz의주파수대역에서측정하였다. 측정잡음을제거하기위해 time gating 방법을적용했으며보정 target은자체제작한 홍익대학교전파통신공학과 (Department of Radio Science and Communication Engineering, Hongik University) 논문번호 : 수정완료일자 : 2006 년 7 월 31 일 804

2 식물층에서의편파별후방산란측정과산란모델의비교 Trihedral corner reflector를사용하였다. 또한, 지표면의특성 (ground truth) 을측정하기위해 surface profilometer를제작하여지표면의거칠기변수인 RMS 표면높이 s와표면상관길이 l을측정하였고, 토양샘플을취득하여토양의수분함유량을측정하였으며, 여러종류의식물층샘플을취득하여잎의밀도, 길이, 폭, 수분함유량등을측정하였다 [4]. 입사각도의변화와지표면수분함유량의변화에따른후방산란계수측정값을얻을수있었으며지표산란모델과비교한결과동일편파의경우비교적잘일치했으며교차편파의경우보정을해줌으로써산란모델의정확성을얻을수있었다. Ⅱ. 후방산란계수측정후방산란계수를측정하기위해우선 R 밴드 scatterometer 시스템을구현하였다. 본 scatterometer의송수신기로는네트워크분석기 (HP8753D) 를사용하였고, R 밴드표준혼안테나두개를동축선으로송수신기에연결하여간단하게 full polarimetric scatterometer 시스템을그림 1과같이구성하였다. 측정주파수로는 1.85 GHz를중심으로 0.5 GHz의대역폭에서측정함으로써, Fourier 변환을이용하여 time gating 기능을이용할수있었고, 이기능으로수풀에대한후방산란이외의잡음 ( 안테나어댑터, 안테나지지대등에서의반사파들 ) 을제거하여마치전파무반향실측정과같은효과를볼수있었다. 측정장소로는측정이용이하고비교적한적한한강생태공원의수풀지형으로선정하였고, 여기 에타워를설치하였으며, 안테나세트를삼각대에고정하여타워위에설치한후에각도별로 30번씩다른지역들에서의전파산란을 vv-, hh-, vh-, hv- 편파별로측정하였다. 지표면에서안테나까지의높이 (h) 는 4.8 m이었으며입사각 30, 40, 50, 60 에서측정하였다. 보정용 target으로는 Trihedral 전파반사기를사용하였으며전파반사기측정은잡음을제거하기위해스티로폼위에올려놓고빔이지면에도달하는중심거리 (r 0 ) 만큼의거리에서측정하였다. 그림 2는수풀에대한각도별 hh(horizontal to horizontal)-편파측정값의한예를시간영역에서나타낸그림이다. 수풀지면에대한각도별시간영역에서의응답을확인하기위해안테나의방향을허공 (air) 으로향하여측정한결과를기준으로, 40, 50, 60 의입사각도별로측정한시간영역에서의측정결과를함께보여주고있다. 안테나어댑터에서의반사가 62.5 ns에서나타나는것을볼수있으며입사각을 40 로하고거리를시간으로환산하였을경우, 지면까지의왕복거리 (2r 0) 는 104 ns이고또한, 안테나패턴을고려한 footprint는 97~122 ns이다. 입사각 50, 60 에서도같은방법으로시간영역을예측할수있으며그림 2에서예측값과측정값이같음을확인할수있었다. Footprint를확인한후네트워크분석기의 time gating 기능으로지면산란이외의잡음을제거하여측정함으로써보다정확한데이터를얻을수있었다. 측정데이터보정은계산의편의성을위해위상 그림 1. Scatterometer 시스템 Fig. 1. Polarimetric scatterometer system. 그림 2. 시간영역에서의측정데이터 (hh- 편파 ) Fig. 2. Measured data at time domain(hh-pol.). 805

3 韓國電磁波學會論文誌第 17 卷第 9 號 2006 年 9 月 은고려하지않고크기만을보정하여식 (1) 과같이 계산하였다. 식 (1) 에서 σ t 는 trihedral 전파반사기의 pq dm 이론적 radar cross section(rcs) 값이고 S pq, S tm은각 pq 각수풀지역과전파반사기에의한전파반사측정값이며 pq는 vv, hh, vh, hv 편파를나타낸다. Illumination integral(a ill) 은식 (2) 에의해계산할수있고 [5] R은안테나와전파반사지점까지의거리함수이며, g 2 (θ, φ) 는안테나의표준화된이득 (normalized gain) 함수인데, 적분변수에따라변하는값들이다. 식 (2) 의안테나이득함수는모든각도별로얻어야하므로, principal E-면과 H-면에서얻은측정패턴들을 interpolation하여 3차원으로안테나이득함수를계산하였고, 그림 3은이 3차원안테나패턴을보여준다. Standard 혼안테나의 H-plane HPBW(Half-Power Beam- Width) 는 30 이고, E-plane의 HPBW는 28 이다. σ t pq σ 0 pq = S dm pq 2 S dm pq 2 r 4 oa ill A ill = s g 2 (θ,φ) R 4 (θ,φ) ds 측정은독립적인지표면샘플을얻기위해측정타워를중심으로회전하면서각각도별로 30번씩측정하였다. 그림 4는 30번의측정중한번의결과를나타내는것이며입사각이 40 이고 time gating 후 1.6~2.1 GHz의주파수대역에서의측정결과이다. 주파수의시작부근과끝부근에서는 Fourier 변환과정에서 aliasing 효과로잡음의영향이있기때문에측정데이터에서 1.7~2.0 GHz 대역만선택하여 그림 3. 안테나이득패턴 Fig. 3. Antenna gain pattern. (1) (2) 그림 4. 주파수영역에서의측정데이터 Fig. 4. Measured data at frequency domain. 사용하였고 30 개데이터의평균값을취하였다. Ⅲ. 표면거칠기와수분함유량측정 산란모델과의비교를위해서는정확한후방산란계수측정못지않게, 모델입력변수가되는지표면의특성 (ground truth) 을정확하게측정하는것이매우중요하다. 지표면의특성에는지표면거칠기, 토양수분함유량과풀층특성변수들 ( 밀도, 크기, 각도, 수분함유량등 ) 이있다. 우선, 지표면토양의거칠기를나타내는변수인 s(rms 표면높이 ) 와 l( 표면상관길이 ) 을구하기위해서는일정거리만큼의지표면높이를정확하게측정해야하고, 이를위해지표면높이측정기 (surface profiler) 를제작하였다. 그림 5는제작된 surface profiler를보여주고있다. 이는실제지표면의높이를측정하는장비로써전체의길이가 1 m이며 0.5 cm 간격에 20 cm의길이를갖는철사 201개로구성되어있다. 그림 5에는잘보이지않지만, 철사의윗부분이보이는면에는모눈종이가있어서높낮이를수치로읽을수있다. 디지털카메라로찍은후에그영상에서높이를숫자로얻게되고, 일렬로연속으로 5번반복하면지표면 5 m의길이에대해지표면 profile을얻는다. 이측정된데이터로부터높이분포함수 (PDF) 를얻고, 이 PDF의표준편차를구하면 s(rms 높이 ) 를얻게된다. 다음식 (3) 과같이정규화된자기상관함수 (normalized autocorrelation function) 을구하여그함수의 1/e에해당 806

4 식물층에서의편파별후방산란측정과산란모델의비교 그림 5. 지표면높이측정기 Fig. 5. Surface profiler. 하는값 l(correlation length) 을구하였다 [6]. ρ( x')= L X/2 z(x)z(x+x')dx - L X/2 L X/2 z 2 (x)dx -L X/2 여기서 z(x) 는 x의위치에서의지표면높이 (z) 를의미한다. 측정지역의토양수분함유량을측정하기위해서, 지표면깊이 0~5 cm에서토양샘플 2~3개 ( 약 200 ~300 g) 를채취하여무게를재고, 완전건조시킨후무게를재어, 물의부피와토양의부피비 (ratio) 인 volumetric 수분함유량 m v(cm 3 /cm 3 ) 를다음식처럼계산하였다 [4]. m v = W w W dry ρ b = m g ρ b 여기서 W w 는물의무게, W dry 는흙의무게이고, m g (g/cm 3 ) 는 gravimetric 수분함유량, ρ b 는토양의밀도이다. 측정된토양의밀도는대략 1.2(g/cm 2 ) 이었다. 측정기간동안의측정된수분함유량은 0.17~0.38 cm 3 /cm 3 의범위내의값이었다. 산란모델의입력변수는상대유전율이기때문에수분함유량에서토양의상대유전율을얻으려면토양의성분을알아야한다. 비중계 (hydrometer) 를사용하여토양성분을측정한결과측정지역의토양성분은모래가 33.9 %, 실트가 42.9 %, 점토가 23.2 % 인 loam 토양으로판명되었다 [4]. 비중계방법에서 40초이내에가라앉는성분이모래 (sand), 40초부터 2시간사이에가라앉는성분이실트 (silt), 2시간이후까지떠있는토양성분이점토 (clay) 로간주하였다. 본측정지역은키가큰 ( 약 70 cm 정도 ) 일년생풀들로덮여있는지역이다. 측정일자마다토양위에자란잎의크기 ( 길이와넓이 ), 밀도, 각도, 수분함유 (3) (4) 량등의입력변수를얻기위해균일한곳에서 30 cm 30 cm의샘플 2곳을선정하여, ground truth를측정하였다. 수풀을모두채취한후무게를재고, 완전건조후무게를비교하여수분함유량 (m g) 을구하였으며, 수풀의길이, 폭, 밀도등을측정하였다. Ⅳ. 지표면산란모델검증 Radiative transfer 이론은지표면위의풀, 나무층에의한체적산란을계산할때보편적으로사용하는방법으로써비교적정확한산란값을제공한다고알려져있다. 지표면을구성하는식물층에서부터산란되는전파의세기를계산하기위해전파적분방정식을이용하여전자계를직접계산하는대신에, 여러요소들로이루어진하나의매체 ( 식물층 ) 를통해전달되는전파의세기를이용하여산란계수를계산하는방법이다 [5]. 그림 6에서식물층에입사하는전파의세기와산란하는전파의세기를보여주고있고, 땅과식물두개의층으로구성된산란모델그림이다. 이모델에서고려한산란방식들에는 (1) 토양-식물-토양, (2a) 토양-식물, (2b) 식물-토양, (3) 식물, (4a) 토양-나무기둥, (4b) 나무기둥-토양, (5) 토양에서의전파산란들이있으나, 본측정에서는나무기둥이없으므로그림 6에나타낸것처럼 5개의산란방식만이있다. 여기서 θ는입사각을나타내고, d는식물층의두께이다 [1]. 산란세기의비로투과행렬값을얻고, 여기서후방산란계수를계산하게되며, 이모델의자세한수식유도는참고문헌 [1] 에있으므로이논문에서는 그림 6. 산란방식들 Fig. 6. Scattering mechanisms. 807

5 韓國電磁波學會論文誌第 17 卷第 9 號 2006 年 9 月 생략한다. 이산란모델은단지 10개의변수들 ( 수분함유량, RMS 표면높이, 풀층높이, 잎의밀도, 잎길이, 잎넓이, 나무줄기밀도, 나무줄기길이, 나무기둥밀도, 나무기둥길이 ) 을입력하면된다. 본연구에서는나무가없는상태이므로나무줄기와나무기둥에대한입력변수는필요없고, 단지 6개의입력변수만있으면된다. 위의모델의검증을위해측정은두가지형식으로진행하였다. 첫번째데이터는일정수분함유량에서여러각도의후방산란계수를얻은것이고, 두번째데이터는일정한각도에서다른수분함유량에서의후방산란계수를얻은것이다. 첫번째데이터는하루동안에얻었고, 두번째데이터는한달동안에 40 에서 11번의측정을수행한것이다. 이기간동안에여러번비가내렸고, 토양의젖고마르는과정이있었다. 첫번째측정에서얻은측정지역의 ground truth 는다음과같다. RMS 표면높이 s는 2.35 cm, 땅의수분함유량 (m v) 은 0.21 cm 3 /cm 3, 수풀의높이는 72 cm, 잎의길이는 60 cm, 잎의폭은 2 cm, 잎의밀도는 800 개 /m 3 이었다. 그림 7은이상의조건을지표면산란모델에적용하여입사각도에따른산란계수의변화를계산한결과로서, 편파별로전체산란에대한각산란방식의기여도를나타낸것이다. 모든편파에서지표면에서의직접산란 (G) 과풀층에서의직접산란 (C) 이산란계수값을결정하는주요변수임을알수있었다. 그림 8은입사각도에따른측정값과산란모델의계산결과를비교한것으로서, vv 편파와 hh 편파에서는측정값과산란모델계산값이잘맞는것을볼수있으며 vh 편파에서는약 2~3 db의차이가있음을알수있다. 이는산란모델계산에서높은차수의다중산란 (multiple scattering) 을고려하지않은영향으로보이며 vv 편파와 hh 편파의경우다중산란에의한영향이크지않지만 vh 편파의경우고차다중산란의영향이크게작용함을알수있었다. 따라서, 지표면산란모델에서교차편파의경우대략 2~3 db 정도의보정이필요함을알수있다. 그림 9는토양수분함유량 (m v) 의변화에따른산란계수측정값과산란모델을비교한것으로서, 측 (a) vv- 편파 (a) vv-polarization (b) hh- 편파 (b) hh-polarization (c) vh- 편파 (c) vh-polarization 그림 7. 산란모델의산란메커니즘별후방산란계수기여도 Fig. 7. Contributions of the scattering mechanisms to the backscattering coefficients. 808

6 식물층에서의편파별후방산란측정과산란모델의비교 결정하기위해서는다양한상태의지표면에대한측정데이터를획득하든지, 몬테카를로방식의수치해석적연구를통해향후에더연구해야할것이다. Ⅴ. 결론 그림 8. 각도별측정값과모델비교 Fig. 8. Comparison between measurements and model at various incidence angles. Backscatt. Coeff. (db) Simple model(vv-pol.) Measured(VV-pol.) Simple model(hh-pol.) Measured(HH-pol.) -35 Simple model(x-pol.) Measured(x-pol.) Soil moisture (Mv) 그림 9. 수분함유량의변화에따른측정값과모델비교 Fig. 9. Comparison between measurements and model for various soil moisture contents. 정은지표수분함유량의변화를얻기위해한달동안 2~3일간격으로입사각도를 40 로고정시켜측정한결과이다. 수분함유량 (m v) 은 0.17~0.38 cm 3 / cm 3 이었으며이는토양의마른정도가중간에서부터비온후의젖은상태까지이며마른흙에대해서는측정을하지못하였다. 측정값과산란모델의결과는 vv-, hh-편파에서비교적잘일치하며, 교차편파는모델이낮은값을보인다. 이는고차다중산란이모델에서배제되었기때문이며, 이경우에약 2~3 db 정도를보정할경우측정결과와잘일치함을알수있다. 교차편파에서의정확한보정정도를 본연구에서는 R 밴드용 (1.7~2.0 GHz) polarimetric scatterometer 시스템을구현하여한강생태공원내수풀지형을후방산란계수를편파별로측정하였다. 고정된각도 (40도) 에서다양한수분함유량상태수풀의후방산란계수와고정된수분함유량에서다양한입사각도의데이터를얻었다. 이전에개발하였던지표면산란모델의정확성을검토하기위해서, 정확후방산란계수를얻는외에지표면의상태특성 (ground truth) 을정확하게추출하였다. 후방산란계수측정값과산란모델을비교한결과동일편파 (vv와 hh 편파 ) 의데이터는비교적잘일치함을확인할수있었으며, 교차편파의경우 2~3 db의편차가있음을알수있었다. 이는산란모델계산에서고차의다중산란 (multiple scattering) 을고려하지않은영향으로보이며 vv 편파와 hh 편파의경우다중산란에의한영향이크지않지만교차편파의경우다중산란의영향이크게작용함을알수있었다. 따라서, 지표면산란모델교차편파의경우 2~3 db 보정을할경우산란모델의정확성을높일수있을것이다. 교차편파의보정정도를정확하게예측하기위해서는향후에다양한환경에서의측정데이터를더확보할필요가있으며, 몬테카를로방식의수치해석적연구등을통해서연구의범위를확대해나갈필요가있다. 감사의글저자들은본연구의측정데이터수집에도움을준홍익대학교전파응용연구실의현종철, 최재원, 김령모, 김상근에감사합니다. 본연구는국방과학연구소지원을받는 KAIST 전파탐지연구센터의도움으로수행되었습니다. 참고문헌 [1] Yisok Oh, Jin-Young Hong, and Sung-Hwa Lee, "A 809

7 韓國電磁波學會論文誌第 17 卷第 9 號 2006 年 9 月 simple microwave backscattering model for vegetation canopies", JKEES, vol. 5, no. 4, pp , Dec [2] F. T. Ulaby, M. C. Dobson, Handbook of Radar Scattering: Statistics for Terrain, Artech House, [3] 이성화, 정구준, 오이석, " 지표면산란모델개발과 JPL AirSAR 측정데이터와의비교 ", 대한원격탐사학회춘계학술대회논문집, pp , 2003년 3월. [4] F. T. Ulaby, R. K. Moore, and A. K. Fung, Mi- crowave Remote Sensing Active and Passive, vol. Ⅲ, Artech House, [5] F. T. Ulaby, C. Elachi, Radar Polarimetry for Geoscience Applications, Artech House, [6] F. T. Ulaby, R. K. Moore, and A. K. Fung, Microwave Remote Sensing Active and Passive, vol. Ⅱ, Artech House, [7] L. Tsang, J. A. Kong, and R. T. Shin, Theroy of Microwave Remote Sensing, John Wiley & Sons, 홍진영 2000년 2월 : 홍익대학교전파공학과 ( 공학사 ) 2002년 2월 : 홍익대학교전파통신공학과 ( 공학석사 ) 2002년 2월~2004년 8월 : 삼성전기중앙연구소 RF Lab. 2003년 3월~현재 : 홍익대학교전파통신공학과박사과정 [ 주관심분야 ] 전파산란, 마이크로파원격탐사, 안테나 오이석 1982년 2월 : 연세대학교전기공학과 ( 공학사 ) 1988년 12월 : University of Missouri- Rolla 전기및컴퓨터공학과 ( 공학석사 ) 1993년 12월 : University of Michigan, Ann Arbor 전기공학및컴퓨터과학과 ( 공학박사 ) 1994년 3월~현재 : 홍익대학교전자전기공학부교수 [ 주관심분야 ] 전파산란, 마이크로파원격탐사, 안테나 810

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