FUNDAMENTALS OF RADIOMETRY

Transcription

1 1 FUNDAMENTALS OF RADIOMETRY Lectue 5

2 Radomety 2 Quanttatve measuement of the popetes of EM adaton nteacton wth matte o emsson fom t Radomety deals wth total EM adaton We extend the concept of adans n 3d to explan sold angle

3 Sold angle 3 3D analogue of 2D angle angle l, ccle 2 adans sold angle a, sphee 4 steadans 2 R d dacos R 2 1m 2 subtends a sold angle of 1steadan (s). Sphee 4, hemsphee 2 steadans. Sold angle of a small plana patch of aea da at a dstance R :

4 Radomety 4 Radometc Quanttes : Radant Enegy Q Joules Radant flux Watts Iadance E Watts/m 2 Radant Intensty I Watts/s Radance L Watts/s/m 2 d sndd

5 Radant Enegy 5 Quantty of enegy caed by the EM adaton Quantty of enegy popagated nto/though/emegng fom a specfed suface (RS) n a gven aea n a gven peod of tme All wavelengths contaned n the adaton s ncluded When consdeed at a patcula wavelength Spectal adant enegy dq Q d

6 Radant Flux 6 Radant flux s the ate at whch adant enegy s emtted/tansfeed/eceved n the fom of EM adaton fom a pont/suface to anothe Spectal adant flux dq dt d d

7 Iadance/Radance 7 Iadance: The measue of adant flux pe unt aea Radant Intensty Radant flux leavng a souce pe unt sold angle n a gven decton Radance: d E da d da d I d Radant flux pe unt sold angle n a gven decton pe unt pojected souce aea n that decton dq dt

8 Radance 8 Foeshotened suface n measung adance

9 Radance 9 L x, y,, 2 d x, y,, dda cos Radance s a functon of poston n a defned suface as well as the decton though the pont to the obseve (senso)

10 Radance vs. Iadance E dl, 10 Radance and adance ae vey smla concepts, both descbe an amount of lght tansmtted n space but t s mpotant to ecognze the dstnctons between them. Thee ae seveal ways of thnkng about the dffeence: Radance s a functon of decton; t s powe pe foeshotened suface aea pe steadan n a specfc decton Radance (Ws -1 m -2 ) Iadance (Wm -2 ) Radance descbes lght emtted fom a suface Iadance s ncdent powe pe suface aea (not foeshotened); t s not a dectonal quantty. Iadance descbes lght ncdent on a suface Fom the adance emtted fom one suface we can compute the ncdent adance at a neaby suface.

11 Radomety 11

12 Suface chaactestcs fo adometc measuements 12 Reflecton and emsson fom tagets ae two mpotant phenomenon used n RS Smooth suface Snell s law Specula eflecton Specula eflecton does not mean that the amount of eflected flux s ndependent of the angle of ncdence

13 Suface chaactestcs fo adometc measuements 13 The angula dstbuton of the eflected ay vaes wth the suface popetes Lambetan Suface If the emegent adance s constant fo all decton n a hemsphecal sold angle then the suface s sad to be Lambetan eflecto/emtte The eal suface we encounte s nethe a pefect specula no a pefect Lambetan suface

14 Suface chaactestcs fo adometc measuements 14 Whethe a suface behaves as Lambetan o specula depends on the suface s unevenness (that s heght of vaaton fom efeence suface) elatve to the wavelength of obsevaton Raylegh s ctea h 8cos Faunhofe s ctea h 32cos h RMS heght vaaton above a efeence plane n unts of Wavelength Angle of ncdence h RMS heght vaaton above a efeence plane n unts of Wavelength Angle of ncdence

15 Suface chaactestcs fo adometc measuements 15 The adance n any one decton s, on aveage, the same as any othe; n othe wods, adance s constant at any vewng poston on the hemsphee and s theefoe ndependent of. Howeve, the adant ntensty at any poston wll vay accodng to the elaton. I I 0 cos Ths states that as the angle of ncdent adaton I θ s vaed, the ntensty of outgong adaton also changes. Fo nomal ncdence (fom the zenth), θ s 0 and cosθ s 1, so I θ = I 0. Fo all othe angles cosθ s less than 1 and I 0 s educed.

16 B-dectonal Reflectance Dstbuton (BRDF) 16 The eflectance popety of a suface can be completely descbed by a b-dectonal eflectance dstbuton (BRDF). Reflectance of a taget as a functon of the llumnaton geomety and vew geomety BRDF s a mathematcal epesentaton of ou pactcal expeence that the eflectance fom an object s geneally dffeent when vewed fom dffeent angles and when llumnated fom dffeent dectons

17 BRDF 17 The BRDF f, s gven by dl, f, de o f,, dl, de s 1 BRDF essentally tansfom the ncdent adance nto eflected adance.

18 BRDF 18 de : The elemental adance fom the decton wthn a sold angle d dl, : The elemenatl eflected adance n the decton nto the sold angle d Snce eflecton depends on wavelength de and dl ae spectal quanttes dependent on (omtted) de f L dl,, cos d L cos d

19 Radometes 19 The adometes gves the adance values coespondng to a numbe of boad spectal bands, usually matchng the satellte sensos (MSS, TM, IRS-LISS) chaactestcs BRDF popetes : f, 0 Enegy consevaton :, f, cos 0 d 0

20 BRDF Measuement 20 An example of feld gonometes fo BRDF measuements

21 BRDF Example 21 Bdectonal eflectance effect on a gass lawn, obseved unde dffeent vewng angles fom a mounted camea n the sola pncpal plane. Sola zenth angle s 35, ndcated wth ed aows. The vew dectons ae gven n blue.