参考微波遥感

1、Fundamentals of Microwave Remote Sensing Theory and Techniques（微波遥感理论与技术基础）(04)龙课件地址：mwrs2009：ucas20135. Solid-­surface sensing: microwave emission5-­15-­25-­35-­45-­5Power-­Temperature CorrespondenceSimple Microwave Radiometry MsApplicaMons and Use in Surface Sens

2、ing DescripMon of Microwave RadiometersExamples of Developed Radiometers5-­1 Power-­Temperature Correspondences Concepts, deniMons and units Blackbody emissions and Plank formula Low-­frequency approximaMons Brightness temperatureConcepts, deniMons and units Solid angle Basic radiomet

3、ric quanMMes and unitsdA = rdq × r sinqdjdAW = ASolid angler2= sinqdqdjdW =r2An object's solid angle is equal to the area of the segment of unit sphere (centered at the vertex of the angle) restricted by the object.A solid angle equals the area of a segment of unit sphere in the same way of

4、 unit sphere in the same way a planar angle equals the length of an arc of unit circle.The value of the solid angle is numerically equal to the size of that area divided by the square of the radius of the sphere.The shape of the area doesn't maer at all.The solid angle is the quanMtaMve aspect o

5、f the conical slice of space, that has the center of the sphere as its peak, the area on the surface of the sphere as one of its spherical cross secMons, andextends to in.Any shape on the surface of the sphere that holds the same area will dene a solid angle of the same size.Theum solid angle is 12.

6、57,corresponding to the full area of the unit sphere, which is 4*Pi.Standard unit of a solid angle is theSteradian (sr).(MathemaMcally, the solid angle is unitless, but for pracMcal reasons, the steradian is assigned.)Energy (辐射能量) and energy density(辐射能量密度) Energy (E, 辐射能量) The energy carried by th

7、e electromagneMc waves. Unit: J(Jourl 焦耳)ML2T-­2 Energy density (Ev, 辐射能量密度) The energy in unit volume Ev。 Unit: Jm-­3EV= ¶E¶VPower (辐射功率) Power (radiant ux, 功率, 辐射通量, 发光度) The Mme rate at which radiant energy passes a certain locaMon.P = ¶E / ¶t）(ML2T-­3) Unit: W=

8、Js-­1（ For plane wave, power can be described by PoynMng vectorvvv *12P = kP =E ´ HPower density (辐射功率密度)Power (ux) density (辐射通量密度, 辐照度) The radiant ux intercepted by a unit area of a plane surface.S = ¶P ¶A Unit: Wm-­2=Jm-­1m-­2, MT-­3Irradiance (辐照度): The d

9、ensity for ux incident upon a surface;Emiance (出): The density of ux leaving a surface.或发Intensity (辐射强度) Intensity(radiant intensity, 辐射强度; luminance辐亮度)The radiant intensity of a point source in a given direcMon is the radiant ux per unit solid angle leaving the source in that direcMon)F = ¶P

10、 / ¶WUnit: Wsr-­1=Js-­1sr-­1ML2T-­3Brightness (亮度) The brightness of a point source in a specied direcMon is the power density per unit solid angle in that direcMon.B = ¶2 P¶W¶A Unit: Wm-­2sr-­1=Js-­1m-­2sr-­1MT-­3 Generally, the

11、brightness of a object has direcMvity.B = B(q,j )Spectral brightness (谱亮度) Spectral brightness (brightness spectral density, 谱亮度, 亮度谱密度) is dened as the brightness per frequency (spectrum) interval.Bv = ¶B ¶v Unit: Wm-­2sr-­1f-­1=Js-­1m-­2sr-­1f-­1,MT-

12、73;2 The received power can be represented as:dP = Bv (q,j )dAdWdvP = òòò Bv (q,j )dAdW dvOther radiometric quanMMes Pf（Spectral Power, 谱功率） Radiant power within unit spectral interval.Pf= ¶P ¶ f Unit: WHz-­1 Sf（Spectral Flux Density, spectral emiance, 谱流（通）量密度） Spectra

13、l power per unit area.S= ¶P¶A = ¶2 P ¶ f ¶AffBlackbody emissions and Plank formula Scaering, absorpMon and emission Black body Planck formula Stefan-­Boltzmann principle Wien shij principle Kirchho principleScaering, absorpMon and emission Scaering (散射)The physical proc

14、ess where the electromagneMc waves are forced to deviate from a straight trajectory by one or more localized non-­uniformiMes in the media through which they pass.Change of propagaMon direcMon, same frequency. AbsorpMon (吸收)The physical process where energy of the electromagneMc waves is taken

15、up bythe maer and transformed to other forms of energy, usually heat. ExMncMon (消光) Both scaering and absorpMon can aenuate energy of the incoming electromagneMcwaves, and are called exMncMon. Emission (radiaMon, 发射)the process by which the energy of electromagneMc waves is released by another enMty

16、.ElectromagneMc emission (radiaMon) of a maer is emied by the element's atomsor molecules when they are returned to a lower energy state. Emission=absorpMon (thermal/energy equilibrium)Blackbody emission (黑体辐射)All maers with temperature above 0K (-­273.15°C) have electromagneMc emissio

17、ns due to the movement of molecules, atoms, electrons, etc.Heat energy is the kineMc energy of random moMon of the parMcles (molecules, atoms, electrons, etc.) of maer.The random moMon results in excitaMon (electronic, vibraMonal, or rotaMonal) due to collisions, followed by random emission of elect

18、romagneMc waves during decay. Because of its random nature, this type of energy transformaMon leads to emission over a wide spectral band.A black body is dened as an idealized, perfectly opaque material that absorbs all the incident radiaMon at all frequencies, reecMng none.A blackbody transforms he

19、at energy into radiant energy with theum ratepermied by thermodynamic laws, and the spectral emiance is given by Plancks formula.Blackbody Total absorpMon, no reecMon/ scaering It is a theoreMcal object that absorbs 100% of the radiaMon that hits it. It reects no radiaMon and appears perfectly black

20、.Planck formulaPlanck describes the frequency (spectral) distribuMon of blackbody, and the relaMonship between the spectral emiance and frequency and temperature of a blackbody.32hfBf (T ) =c e- 12hf /( KT )2hc2Bl (T ) =l e- 15hc/(lKT )dB = Bvdvv = cÞ dv = - c dlll 2dB = Bl dlwhere :Planck cons

21、tant h = 6.626 ´ 10-34 J × sBoltzmann constant K = 1.3806 ´10-23 J × K1Stefan-­Boltzmann principle The relaMonship between the radiance and the temperature of a blackbody can be obtained by integraMon of Planck formula over the total temperature range:+¥B(T ) = ò0B

22、f (T )df32hf+¥ò0=dfehc/( KlT )- 1c2= s T 4ps = 5.673 ´ 10-8Wm-2sr-1Wien shij principle Wien principle describes the frequency withum radiance.¶Bf (T ) = 0¶ fÞ fm = 5.87 ´10T (Hz)10B ( f ) = c T3fm1c = 1.37 ´10-19Wm-2sr-1Hz-1K -31Planck equation = f(frequency,T

23、emperature)Planck radiation at20,000 GHz is 36,000 times greater than at 37 GHz,so pixels at lower frequenciesmust be biggerRegionWavelength (centimeters)Energy(eV)Blackbody Temperature(K)Radio> 10< 10-5< 0.03Microwave10 - 0.0110-5- 0.010.03 - 30Infrared0.01 - 7 x 10-50.01 - 230 - 4100Visib

24、le7 x 10-5 - 4 x 10-52 - 34100 - 7300Ultraviolet4 x 10-5 - 10-73 - 1037300 - 3 x 106X-Rays10-7- 10-9103 - 1053 x 106 - 3 x 108Gamma Rays< 10-9> 105> 3 x 108Some Blackbody TemperaturesLow frequency approximaMons and brightness temperatureHigh-­frequency approximaMon (Wien distribuMon):L

25、ow frequency approximaMon (Rayleigh-­Jeans distribuMon):2 f 2KT2KTBf (T ) »=l22chf / KT << 12h3 - hf /KTBf (T ) »f ef< 3.9 ´ 108 HzK -1for2cTthe deviation between Rayleigh - Jeans approximation and Planck formula is less than 1%for T=300K, the highest frequency is 117GHz

26、hf / KT >> 1S( f ) = 2pkT= 2kTWf 2l2m2Hzc2Kirchho principle)： Emissivity (发射率, ef Is the relaMve ability of its surface to emit energy by radiaMon. It is the raMo of energy radiated by a material to energy radiated by a blackbody ate same temperature.AbsorpMvity (absorptance 吸收率, a f): The fra

27、cMon of radiaMon absorbed by a surface to the total radiaMon incident on the surface.ef = 1 for all frequencyef < 1 黑体（black body） 灰体（grey body） Kirchho principle describes the energy conservaMon under thermal equilibrium. In the state of thermal equilibrium, the emissivity of a medium is equal t

28、o the absorpMvity.ef= a fRayleigh-­Jeans approximaMons Thermal radiaMon from natural surface occurs mainly in the far infrared region, it extends throughout the EM spectrum in to submilimeter and microwave region. For low frequency approximaMons:RelaMons between spectral radiant emiance S(f) an

29、dsurface radiance (brightness) Bfp2p2S(f) = òò Bv (q,j )cosq dW = ò ò Bv (q,j )cosq sinq dq djW00 Lambert surfaceB(q,j ) is independent of q,jS(v) = p B(v) Surface radianceB (f) = 2KT= 2KT v2( W)l 2m2HzSrvc222p KTc2S(v) =vFor a narrow-­band system, blackbody emissiondP= 2KT

30、dvdAdWl 2bbdv << vv+Dv2KTl 21ò òòFn (q,j )dW dv=Ar2Pbbv4pfactor 2 considering unpolarized emissionl 2Dv << v,W p =ArP= KT Dv AròòF (q,j )dWl 2bbn4p= KT Dv ArWl 2p= KT DvEmissivity and brightness temperature Blackbody2KTl 2dP= 2KT dvdAdW= Bv Dv =DvBbbl 2bb Graybod

31、ydP = 2KTB2KT (q,j )dvdAdWB(q,j ) =Dvl 2Bl 2 EmissivitydP £ dPbbB(q,j ) = TB (q,j )e(q,j ) =BbbTBrightness temperature :TBPower-­temperature correspondence of grey-­ body (real maer) Pn = kT Dv Nyquist, Noise power of P(v) = 2KT e (q )dsdW¢l 2dW¢ = A / r 2dP(v) = 2kT e (q )

32、G(q ,f) dAdv = AKT e (q )G(q ,f)dWdfl 2dW = ds / r 24p r 2l 22e (q )G(q ,f)dWdvl 2l 2APr = AKT òDv òWW0 = antenna beam solid angleg(q ,f) = 4p AG(q ,f) = antenna gainDv << vl 2= AKT Dve (q )G(q ,f) dWl 2òWPe (q )G(q ,f)r T 4()= T òWòdW =e q g(q ,f) dWTeq= KTeq DvWpW05-

33、­2 Simple Microwave Radiometry Ms RealisMc observaMon m Eects of polarizaMon Eects of the observaMon angle Eects of atmosphere Eects of surface roughnessA realisMc observaMon mExistence and eects of sky emissionThe microwave brightness temperature depends on three independent factors:the surfac

34、e temperature Tgthe sky temperature Tsthe surface dielectric constant or index of refracMon n, which determines the surface reec8vity and also the emissivity.Equivalent microwave temperature (on the surface)Ti (q ) = ri (q )Ts + ei (q )Tgri + ei = 1Ti (q ) = Tg + ri (q )(Ts - Tg )= Ts + ei (q )(Tg -

35、 Ts )Apparent temperature (视在温度) for space-­based observaMonApparent temperature TAPAntenna temperature TAUpward emission of atmosphereTup+S(Tg+ Tsc ) 1 La+Downward emission ofAtmosphereTdown() 1 T= T+T + TScaered emission+APUPgscLfrom skyTscSa= 1 T+Ground emission Tgr + eTTscdowngLaAtmospheric

36、 aenuaMon 1/LaatmosphereAntennaAntenna Radiometric Temperature (天线温度)P = 1 A2K Tòò(q,j )DvF (q,j )dW(Dv << v)lrAPn224pPn = kTA Dv = PArl 2òòT=(q,j )F (q,j )dWTAAPn4p= WsòòTAP (q,j )Fn (q,j )dWTT= 4pWpAAPòò Fn (q,j )dW4p The antenna radiometric temperatur

37、e is apparent temperature weighted by the normalized the weighted antenna paern (solid angle) For a closed blackbody with physical temperature TAP=T For discrete point source (such as the sun), whereantenna beam width is much wider than the angular extension of the source= WsTTASWpEects of polarizaM

38、onThree factors determines the microwave temperature:the surface temperature Tgthe sky temperature Tsthe surface dielectric constant or index of refracMon n, which determines the surface reec8vity and also the emissivity.The fact that the brightness temperature at a certain angle is a funcMon of the

39、 polarizaMon allows us to derive two of these parameters if the third one is known.Expression for polarized emissivity raMoThe measured raMo on the right-­hand plus the theoreMcal expression for polarized emissivity raMo would then allow the derivaMon of the surface dielectric constant.Once the

40、 dielectric constant of the surface is known, the emissivity at each of the two polarizaMons can be calculated.Using this informaMon, the surface temperature can then be derived fromSky temperature In the case of planets with no atmosphere or if the atmosphere is transparent at the frequency of obse

41、rvaMon, Ts is basically the temperature of space. This can be directly measured with the sensor by looking away from the planet. In the case in which the atmospheric contribuMon is signicant, a m for Ts must be used.Tv = Tg Brewster angle qBTv - Th isum near qBTv = Th = Tg for low dielectric constan

42、tsTv = Th = Ts for high dielectric constants Brewster angle: no reflectionEects of observaMon angleThe fact that Th and Tv have dierent dependence on the observaMon angle does allow the derivaMon of all three unknown natural parameters Ts, Tg, and dielectric constant.By looking at Tv() and Tv() Th()

43、, a peak should be observed near the Brewster angleKnowing this angle will allow the derivaMon of the surface dielectric constant.This in turn will provide surface reecMvity for both polarizaMons. Then Tgand Tscan be derived.In reality, the above approach most likely will be iteraMve. For instance,

44、if it is found that the derived Tg varies with , then a mean value can be taken and another iteraMon made.Eects of the atmosphere The Earths atmosphere absorpMon is relaMvely small at frequencies lower than 10 GHz. Clouds are also transparent at these frequencies. At higher frequencies, the absorpMo

45、n increases appreciably mainly due to the presence of water vapor and oxygen. The water vapor absorpMon increases from 103 dB/km at 10 GHz to 1 dB/km at 400 GHz for 1 g/m3 density and 1 bar pressure (non-­resonant absorpMon). In addiMon, sharp absorpMon lines are present at 22.235 GHz and near

46、183 GHz. Oxygen has strong absorpMon lines at 60 GHz and 118.8 GHz. The atmospheric absorpMon in the high-­frequency region plays a major role in the behavior of Ts and in the transmission of the surface radiaMon.Eects of surface roughness In a large number of situaMons, natural surfaces have a

47、 rough interface and contain near-­ surface inhomogeneiMes. The surface reecMvity and emissivity are strongly dependent on the surface roughness and subsurface inhomogeneiMes, and their expressions are fairly complex.ContribuMon of sky temperature Assuming that the observaMon frequency is fairl

48、y high so that the subsurface penetraMon is negligible, the sky contribuMon to the microwave brightness can be expressed as Where the integral is over the hemisphere covering the sky. This expresses the fact that incoming sky radiaMon from all direcMons can be parMally scaered into the direcMon of o

49、bservaMonContribuMon from the surfaceObserved microwave temperaturewhich is idenMcal to general expression except that the surface reecMvity has been replaced by its equivalent in the case of a rough surface, that is, the integral of the backscaering cross secMon5-­3 ApplicaMons and use in surf

50、ace sensing ApplicaMons in polar ice mapping ApplicaMons in soil moisture mapping Measurement ambiguityRadiant power and surface properMes Graybody surface: Radiant power emied P(v): funcMon of surface temperature T and emissivity e; Emissivity: funcMon of surface composiMon (dielectric constant) an

51、d roughness; Limited physical temperature variaMon on earth <20% (60K) (centered 300K) Larger variaMons due to surface roughness and composiMonApplicaMons in polar ice mapping Polar ice cover and temporal changes Important measurement for global change research and monitoring The large emissivity

52、 dierence between ice and open water (their dielectric constants are approximately 3 and 80, respecMvely) leads to a strong contrast in the received radiaMon, thus allowing easy delineaMon of the ice cover. The key advantage of the microwave imaging radiometer, relaMve to a visible or near-­inf

53、rared imager, is the fact that it acquires data all the Mme, even during the long dark winter season and during Mmes of haze or cloud cover.Ice cover change monitoring Contrast between ice and open water Tg=272K, Ts=50KèèT=127KDT = Ta - Tb= (ra - rb )(Ts - Tg )= Dr(Ts - Tg )For normal inci

54、dence and specular reflectione - 1ö 2ææ n - 1ö 2r = çr÷= çè÷øn + 1er + 1øèr(water) = 0.64r(ice) = 0.07Dr = 0.57Ice change (sali, ice ages) Slight change of dielectric constant and surface reecMvity:2DerDr rer (er - 1) In ice-­covered r

55、ange, the BT change is mainly due to compound change, which results in slight change of dielectric constant For 20% changeDer = 0.6er = 3Dr / r = 0.34Dr = 0.024DT = 5.4K24 years of mulMyear sea ice observaMonsApplicaMons in soil moisture mapping Water has a high microwave dielectric constant andlow

56、emissivity in comparison to most natural surfaces.For unfrozen soils: BT L band (1.4GHz) change decrease as much as 70K (depending on the vegetaMon cover) as the soil moisture increases from dry to saturated.Soil moisture can be measured radiometrically with an accuracy of beer than0.04 g cm3 under vegetaMon cover