Lecture 3. Interaction of radiation with surfaces. Upcoming classes

Transcription

1 Radaton transfer n envronmental scences Lecture 3. Interacton of radaton wth surfaces Upcomng classes

2 When a ray of lght nteracts wth a surface several nteractons are possble: 1. It s absorbed. 2. It s reflected (scattered specular/dffuse). 3. It s transmtted nto the materal. These nteracton are mportant as both the radance feld drectonalty and magntude may change followng ths nteracton. Thermal emsson by the surface (e.g. a source) are sometme also consdered as part of these process. From: wkpeda

3 The ndex of refracton: N=n r +n n r -controls the phase speed of lght relatve to a gven medum (often vacuum). n -descrbes the absorpton by the wave. Note: the two are related (Kramer-Krong relatons) Related to the delectrc constant (relatve permttvty-ε/ε o ). For non-magnetc materals: N 2 =ε/ε o ε s more convenent when we want to compute the ndex of refracton of a mxture. In most problem we are nterested n the relatve ndex of refracton e.g. partcles n water (μ-permeablty). N 2 =ε r μ r The ndex of refracton vares wth wavelength (dsperson) separaton of spectra usng prsm. For most materals the longer the smaller n (normal dsp.).

4 Some mportant concepts/prncples: Durng the nteracton wth surfaces radant energy must be conserved. R f l h f ll h h h ll b k Recprocty: f a lght ray follows a certan path the same path wll be taken n the opposte drecton f we replace the source and recever geometry (very mportant for Monte Carlo smulatons).

5 Refracton (Snell s Law): Effect due to an nterface:

6 Another vew (Feynman s lfeguard): From: Wkpeda

7 Refracton & Reflecton (crtcal angle): Effect due to an nterface Whch h s larger n or n t? Ar and water: n /n t 1.33 c 49

8 Refracton (Snell s cone/wndow): Effect due to an nterface

9 Effect due to an nterface Specular reflecton (Sun glnt): Drectonalty of specularly reflected beam: r = φ r =φ +180

10 Effect due to the nterface Fresnel (specular) reflecton Reflectvtes (derved from Maxwell s equatons translated to plane waves + BCs for nonmagnetc substances Bohren and Huffman 1987): Polarzaton plane R=0.5(R s +R p ) Transmttance (T)=1-R Normal ncdence: From: wkpeda

11 Reflectance and Transmttance for an Ar-to-Glass Interface Perpendcular polarzaton Parallel polarzaton 1.0 T 1.0 T R R Incdence angle Incdence angle Brewster angle: Note that R + T = 1 b =53 ar water

12 Reflectance and Transmttance for a Glass-to-Ar Interface Perpendcular polarzaton Parallel polarzaton 1.0 R 1.0 R T T Incdence angle Incdence angle Note that R+T =1 b =37 water ar

13 Specular reflectance at the ar-sea nterface As a functon of sun angle U=10m s -1 =20 As a functon of sun angle And wnd speed

14 Effect due to the nterface: Imm s ff ts 2 l f d ( s t ) Immerson effects n 2 -law of radance (energy conservaton) φ d d ΔΩ = sn L t t n n sn sn = t t t d n d n = cos sn cos sn 2 2 t t t d n d n Ω = Ω cos cos 2 2 L t ( ) 2 t n t T L = A L ΔΩ Δ Φ ( ) 2 n T L = Note: L t can be larger than L prahl88/node95.html 2 1 A A T t Δ Φ Δ Φ =

15 Reflecton from natural surfaces. R and T defned above apply to rradances. Irradance reflectance s n fact: R E u E d The B-drectonal reflecton dstrbuton functon (BRDF): BRDF L ( ) r Ωr E ( Ω ) Unts? How does one measure t? From: wkpeda

16 Example of lght feld reflected from natural surfaces. Concepts: Shadows specular reflecton Hot spot (backscatterng) Pctures from:

17 Basc models of BRDFs: 1. Lambertan surface: BRDF s ndependent of drecton of observaton and drecton of ncdence: L = E 2. Specular: BRDF δ ( ) δ ( φ ) For more models see e.g. Thomas and Stamnes. L ρ π Calculaton the radance when the BRDF s known: ( Ω ) = BRDF ( Ω Ω ) E ( Ω ) r r 2π ; d Ω

18 What about macro surface features? What ρ should we use? For a Lambertan surface and a collmated source: Zaneveld and Boss

19 Albedo emssvty and reflectvty Untl now all we descrbed are spectral concepts (narrow band). We gnored absorpton and the possblty that the surface emts lght. In general: ( ) ( ) ( ) r r r r r E R E φ φ φ φ = And: ( ) ( ) 1 = + r r r r A R φ φ φ φ Ignorng angular dependence and lambertan reflecton ( ) ( ) d u d d u E A - E E E E R E = = Δ = d u d d u

20 Albedo emssvty and reflectvty Integratng the rradance over a wde band (~ assumng a constant absorptvty grey-body approxmaton) we defne the Albedo : R Δ E u E d Not a bad assumpton f E d ~ flat spectrally (why?).

21 Albedo emssvty and reflectvty In the 1 st lecture we talked about black-body radaton. Natural bodes emt less than a black-body and we defne the rato as the emssvty: ε E πb u ( T ) ( T ) where : B = 5 2hc hc k T 1 B ( ) ( e ) 2 Broadband grey-body emssvty: Wde enough spectral gap: ε Δ π EΔ Δ u 2 1 B ( T ) d E ε σt E u 4

22 Albedo emssvty and reflectvty Krchhoff s law: n local thermodynamc equlbrum: ( ) d A E( ) = 0 ε E 0 d From the prncple of detaled balance (tme reversal symmetry of Maxwell s equ.) t follows that: ε = A It s most common to apply ths law to broad-band radaton.

23 Next week: nteracton of lght wth matter Ranbow tutoral t on U-tube: