The nature of electromagnetic radiation.

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1 Lectue 3 The natue of electomagnetic adiation. Objectives: 1. Basic intoduction to the electomagnetic field: Definitions Dual natue of electomagnetic adiation lectomagnetic spectum. Main adiometic quantities: enegy, flux, and intensity. 3. Concepts of extinction (scatteing + absoption) and emission. 4. Polaization. Stokes paametes. Requied eading: G:.1,..1,..,.3,.4, 4.1, Appendix 1. Additional/advanced eading: Online tutoial: Chapte 1, Sections Basic intoduction to electomagnetic field. lectomagnetic adiation is a fom of tansmitted enegy. lectomagnetic adiation is so-named because it has electic and magnetic fields that simultaneously oscillate in planes mutually pependicula to each othe and to the diection of popagation though space. lectomagnetic adiation has the dual natue: its exhibits wave popeties and paticulate popeties. 1

Wave natue of adiation: Radiation can be thought of as a taveling tansvese wave. Figue 3.1 A schematic view of an electomagnetic wave popagating along the z axis.

2 Wave natue of adiation: Radiation can be thought of as a taveling tansvese wave. Figue 3.1 A schematic view of an electomagnetic wave popagating along the z axis. The electic and magnetic H fields oscillate in the x-y plane and pependicula to the diection of popagation. Poynting vecto gives the flow of adiant enegy and the diection of popagation as (in the cgs system of units) S c ε H [3.1] hee c is the speed of light in vacuum (c.9979x1 8 m/s 3.x1 8 m/s) and ε is vacuum pemittivity (o dielectic constant). S is in units of enegy pe unit time pe unit aea (e.g., W m - ) NOT: H means a vecto poduct of two vectos. S is often called instantaneous Poynting vecto. Because it oscillates at apid ates, a detecto measues its aveage value <S> ove some tome inteval that is a chaacteistic of the detecto. Waves ae chaacteized by fequency, wavelength, speed and phase.

3 Fequency is defined as the numbe of waves (cycles) pe second that pass a given point in space (symbolized by ~ ν ). Wavelength is the distance between two consecutive peaks o toughs in a wave (symbolized by the λ). Relation between λ and ν ~ : λ ν ~ c [3.] Since all types of electomagnetic adiation tavel at the speed of light, shotwavelength adiation must have a high fequency. Unlike speed of light and wavelength, which change as electomagnetic enegy is popagated though media of diffeent densities, fequency emains constant and is theefoe a moe fundamental popety. Wavenumbe is defined as a count of the numbe of wave cests (o toughs) in a given unit of length (symbolized by ν): UNITS: Wavelength units: length Angstom (A) : 1 A 1x1-1 m; Nanomete (nm): 1 nm1x1-9 m; Micomete (µm): 1 µm 1x1-6 m; Wavenumbe units: invese length (often in cm -1 ) ν ν ~ /c 1/λ [3.3] NOT: Convesion fom the wavelength to wavenumbe: 1 1 1,cm µ m ν [ cm ] [3.4] λ[ µ m] 3

4 Fequency units: unit cycles pe second 1/s (o s -1 ) is called hetz (abbeviated Hz) Table 3.1 Fequency units Unit Hetz, Hz 1 Kilohetz, KHz 1 3 Megahetz, MHz 1 6 Gigahetz, GHz 1 9 Fequency, (cycles/sec) Paticulate natue of adiation: Radiation can be also descibed in tems of paticles of enegy, called photons. The enegy of a photon is given as: photon h ~ ν h c/λ hcν [3.5] whee h is Plank s constant (h 6.656x1-34 J s). q. [3.5] elates enegy of each photon of the adiation to the electomagnetic wave chaacteistics (ν ~ and λ). Photon has enegy but it has no mass and no chage. NOT: The quantized natue of light is most impotant when consideing absoption and emission of electomagnetic adiation. PROBLM: A light bulb of 1 W emits at.5 µm. How many photons ae emitted pe second? Solution: negy of one photon is photon hc/λ, thus, using that 1 W 1 J/s, the numbe of photons pe second, N, is N 1 ( Js ) λ ( m) ( s ) h( Js) c( ms ) NOT: Lage numbe of photons is equied because Plank s constant h is vey small!!! 1 4

accoding to the wavelength o fequency. NRGY INCRASS WAVLNGTH INCRASS Figue 3.

5 Spectum of electomagnetic adiation: The electomagnetic spectum is the distibution of electomagnetic adiation accoding to enegy o, equivalently, accoding to the wavelength o fequency. NRGY INCRASS WAVLNGTH INCRASS Figue 3. The electomagnetic spectum. Figue fom 5

4 A genealized diagam showing elative atmospheic adiation tansmission at diffeent wavelengths.

6 Figue 3.3 Visible egion of the electomagnetic spectum. NOT: In emote sensing, senso s spectal bands in the visible ae often called by thei colo (e.g., blue, geen, and ead channels) ffects of atmospheic gases (will be discussed in Lectue 6-7) Figue 3.4 A genealized diagam showing elative atmospheic adiation tansmission at diffeent wavelengths. Blue zones show low passage of incoming and/o outgoing adiation and white aeas denote atmospheic windows, in which the adiation doesn't inteact much with ai molecules and hence, isn't absobed. 6

7 In this couse we study the UV, visible, infaed and micowave adiation. Table 3. Relationships between adiation components. Name of Wavelength Spectal equivalence spectal egion egion, µm Sola.1-4 Ultaviolet + Visible + Nea infaed Shotwave Teestial 4-1 Fa infaed Longwave Infaed.75-1 Nea infaed + Fa infaed Ultaviolet Nea ultaviolet + Fa ultaviolet UV-A + UV-B + UV-C + Fa ultaviolet Shotwave.1-4 Sola Nea infaed + Visible + Ultaviolet Longwave 4-1 Teestial Fa infaed Visible Shotwave - Nea infaed - Ultaviolet Nea infaed.75-4 Sola - Visible - Ultaviolet Infaed - Fa infaed Fa infaed 4-1 Teestial Longwave Infaed - Nea infaed Themal 4-1 Teestial Longwave Fa infaed (up to 1) Micowave Micowave Radio > 1 6 Radio Table 3.3 Micowave fequency bands used in emote sensing Bands Fequency Old New [GHz] L D 1- S, F -4 C G, H 4-8 X I, J 8-1 Ku J 1-18 K J 18-6 Ka K 6-4 XAMPL: L-band is used onboad Ameican SASAT and Japanese JRS-1 satellites. 7

8 . Basic adiometic quantities: intensity and flux. Solid angle is the angle subtended at the cente of a sphee by an aea on its suface numeically equal to the squae of the adius s Ω [3.6] UNITS: of a solid angle steadian (s) A diffeential solid angle can be expessed as Ω ds s d Ω sin( θ ) dθdφ, using that a diffeential aea is ds ( dθ) ( sin(θ) dφ) XAMPL: Solid angle of a unit sphee 4π XAMPL: What is the solid angle of the Sun fom the ath if the distance fom the Sun fom the ath is d1.5x1 8 km and Sun s adius is R s 6.96x1 5 km. Ω π d R s 6.76 x1 5 s Intensity (o adiance) is defined as adiant enegy in a given diection pe unit time pe unit wavelength (o fequency) ange pe unit solid angle pe unit aea pependicula to the given diection: I λ d λ ds cos( θ ) dωdtdλ [3.7] I λ is efeed to as the monochomatic intensity. Monochomatic does not mean at a single wavelengths λ, but in a vey naow (infinitesimal) ange of wavelength λ centeed at λ. NOT: same name: intensity specific intensity adiance UNITS: fom q.[3.7]: (J sec -1 s -1 m - µm -1 ) (W s -1 m - µm -1 ) 8

9 Figue 3.5 Intensity is the flow of adiative enegy caied by a beam within the solid angle d Ω. Popeties of intensity: a) In geneal, intensity is a function of the coodinates ( ), diection ( Ω ), wavelength (o fequency), and time. Thus, it depends on seven independent vaiables: thee in space, two in angle, one in wavelength (o fequency) and one in time. b) In a tanspaent medium, the intensity is constant along a ay. If intensity does not depend on the diection, the electomagnetic field is said to be isotopic. If intensity does not depend on position the field is said to be homogeneous. Flux (o iadiance) is defined as adiant enegy in a given diection pe unit time pe unit wavelength (o fequency) ange pe unit aea pependicula to the given diection: dλ F λ [3.8] dtdsdλ 9

10 UNITS: fom q.[3.8]: (J sec -1 m - µm -1 ) (W m - µm -1 ) Fom qs. [3.7]-[3.8], the flux is integal of nomal component of adiance ove some solid angle Ω F λ I λ cos(θ ) dω [3.9] ach detecto measues electomagnetic adiation in a paticula wavelength ange, λ. The intensity I λ and flux F λ in this ange ae detemined by λ integating ove the wavelength the monochomatic intensity and flux, espectively: λ λ I λ I λdλ F λ Fλ dλ [3.1] λ 1 λ λ 1 NOT: Many satellite sensos have a naow viewing angle and hence measue the intensity (not flux). To measue the flux, a senso needs to have a wide viewing angle. 3. The concepts of extinction (scatteing + absoption) and emission. lectomagnetic adiation in the atmosphee inteacts with gases, aeosol paticles, and cloud paticles. xtinction and emission ae two main types of the inteactions between an electomagnetic adiation field and a medium (e.g., the atmosphee). Geneal definition: xtinction is a pocess that deceases the adiant intensity, while emission inceases it. NOT: same name : extinction attenuation 1

11 Radiation is emitted by all bodies that have a tempeatue above absolute zeo ( O K) (often efeed to as themal emission). xtinction is due to absoption and scatteing. Absoption is a pocess that emoves the adiant enegy fom an electomagnetic field and tansfes it to othe foms of enegy. Scatteing is a pocess that does not emove enegy fom the adiation field, but may ediect it. NOT: Scatteing can be thought of as absoption of adiant enegy followed by eemission back to the electomagnetic field with negligible convesion of enegy. Thus, scatteing can emove adiant enegy of a light beam taveling in one diection, but can be a souce of adiant enegy fo the light beams taveling in othe diections. lastic scatteing is the case when the scatteed adiation has the same fequency as that of the incident field. Inelastic (Raman) scatteing esults in scatteed light with a fequency diffeent fom that of the incident light. 4. Polaization. Stokes paametes. Polaization is a phenomenon peculia to tansvese waves. lectomagnetic adiation tavels as tansvese waves, i.e., waves that vibate in a diection pependicula to thei diection of popagation NOT: In contast to electomagnetic waves, sound is a longitudinal wave that tavels though media by altenatively focing the molecules of the medium close togethe, then speading them apat. 11

12 Polaization is the distibution of the electic field in the plane nomal to the popagation diection. Vetically polaized wave is one fo which the electic field lies only in the x-z plane. x y Hoizontally polaized wave is one fo which the electic field lies only in the y-z plane. x y Hoizontal and vetical polaization ae an example of linea polaization. Mathematical epesentation of a plane wave popagating in the diection z is whee is the amplitude; k is the popagation (o wave) constant, k π/λ ω is the cicula fequency, ω kc πc/λ cos( kz ω t + ϕ ) [3.11] ϕ is the constant (o initial phase) ϕ kz ωt + ϕ ) is the phase of the wave ( 1

13 Intoducing complex vaiables, q.[3.11] can be expessed as exp( i ) [3.1] ϕ NOT: In q.[3], we use exp( ± i ϕ) cos( ϕ) ± isin( ϕ) The electic vecto may be decomposed into the paallel l and pependicula components as l l + We can expess l and in the fom l cos( kz ω t + ϕ ) l l Then we have cos( kz ω t + ϕ ) l / l l l cos( ζ )cos( ϕ ) sin( ζ )sin( ϕ ) / cos( ζ )cos( ϕ ) sin( ζ )sin( ϕ ) whee ζ kz ω t. Pefoming simple mathematical manipulation, we obtain ( / ) ( / ) ( / )( / ) cos( ϕ ) sin ( ) [3.13] l l + l l ϕ whee ϕ ϕ lo ϕ called the phase shift. q.[3.13] defines an ellipse > elliptically polaized wave. If the phase shift ϕ n π (n, +/-1, +/-, ), then sin( ϕ ) and cos( ϕ ) ± 1, and q.[3.13] becomes l l ± o ± o l [3.14] lo q.[3.14] defines staight lines > linealy polaized wave 13

14 If the phase shift ϕ n π / (n +/-1, +/-3, ) and l, then sin( ϕ ) ± 1 and cos( ϕ ), and q.[3.13] becomes l q.[3.15] defines a cicle > cicula polaized wave + [3.15] NOT: The sign of the phase shift gives handedness: ight-handed and left-handed polaization Unpolaized adiation (o andomly polaized) is electomagnetic wave in which the oientation of the electical vecto changes andomly. If thee is a definite elation of phases between diffeent scattees > adiation is called coheent. If thee is no elations in phase shift > light is called incoheent Natual light is incoheent. Natual light is unpolaized. The state of polaization is completely defined by the fou paametes: two amplitudes, the magnitude and the sign of the phase shift (see q.[3.13]). Because the phase diffeence is had to measue, the altenative desciption called a Stokes vecto is often used. Stokes Vecto consists of fou paametes (called Stokes paametes): intensity I, the degee of polaization Q, the plane of polaization U, the ellipticity V. 14

15 Notation U V Q I o { I, Q, U, V } Stokes paametes ae defined via the intensities which can be measued: I total intensity Q I -I 9 diffeences in intensities between hoizontal and vetical linealy polaized components; U I +45 I -45 diffeences in intensities between linealy polaized components oiented at +45 and -45 V I cl I lc diffeences in intensities between ight and left cicula polaized components. Stokes paametes can be expessed via the amplitudes and the phase shift of the paallel and pependicula components I + o lo Q [3.16] o lo U V lo o cos( ϕ ) lo o sin( ϕ ) XAMPL. Stokes paametes fo the vetical polaization: Fo this case l Q I U V o o

16 Fo a light beam, we have I Q + U + V Fo unpolaized light: Q U V The degee of polaization P of a light beam is defined as 1 / P ( Q + U + V ) / I The degee of linea polaization LP of a light beam is defined by neglecting U and V Q LP I NOT: Measuements of polaization ae actively used in emote sensing in the sola and micowave egions. Polaization in the micowave mainly due to eflection fom the suface. Polaization in the sola eflection fom the suface and scatteing by molecules and paticulates. 16

Black Body Radiation and Radiometric Parameters:

Black Body Radiation and Radiometic Paametes: All mateials absob and emit adiation to some extent. A blackbody is an idealization of how mateials emit and absob adiation. It can be used as a efeence fo