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Light Optical 1, Radiative Transfer Basics

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Light Optical 1, Radiative Transfer Basics Light Optical 1 Markéta Potůčková Charles University in Prague [email protected] 29 June 2009, D1Lb1 Introduction to Optical RS (1) • Optical RS • Radiation principles – Radiation terms and units – Basic radiation laws • Sources of radiation • Sensors for optical RS • Observation geometry • Interaction of radiation with surface • Radiative transfer in the optical domain Optical RS Wavelength Spectral band range Visible (V) 0.4 – 0.7 μm Near Infrared (NIR) 0.7 – 1.1 μm Short Wave Infrared 1.1– 2.5 μm (SWIR) MidWave Infrared 3.0 –5.0 μm (MWIR) Thermal or LongWave Infrared 8.0 –14 μm (TIR or LWIR) Microwave 1 mm – 1 m Optical RS: λ∈〈0.4;2.5〉μm Radiation terms and units Term Symbol Unit Radiant Energy Q J Radiant flux Φ W Irradiance E=dΦ/dA Radiant flux density Wm-2 Radiant exitance M=dΦ/dA Radiant intensity I=dΦ/dΩ Wsr-1 Radiance L=d2Φ/(dAcosθ)dΩ Wm-2sr-1 E -2 -1 Spectral radiant flux density λ Wm μm Mλ -2 -1 -1 Spectral radiance Lλ Wm sr μm Geometric characteristics Area projected to the viewing Incoming radiation direction . θ ir d g in w Apparent object area ie v surface normal surface A’=Acosθ A Outgoing radiation A’ . ir d Solid angle Ω g in w e Ω =A/r2 vi surface normal surface θ Hemispherical Directional A r measurement Ω Irradiance E Radiance intensity I Radiance excitance M Radiance L Radiance of Lambertian surface • Lambert’s cosine law dΦ = dΦ n cosθ • Radiance of Lambertian surface M = πL z dS = r 2dΩ = 2πr 2 sinθ dθ dS 2 Ω d Φ = LdAsinθdΩ = 2πLdAsinθ cosθ dθ π / 2 θ dθ dΩ dΦ = 2πLdA ∫sinθ cosθ dθ =πLdA 0 dΦ dM = dA dA x y Sources of radiation • Main sources of natural radiation –Sun • Observation of reflected solar energy • Optical domain (VIS + NIR + SWIR) –Earth • Observation of emitted energy • Thermal radiation (MWIR + TIR) Lillesand (2004) Sources of radiation Radiance excitance of natural sources of radiation Planck’s law 2hc2 1 M = λ5 ehc / λkT −1 Stefan-Boltzmann law M = σT 4 Wien’s displacement law A λ = m T Lillesand (2004) c=299 792 458 ms-1 h=6.62606896 10-34 Js k=1.3806504 10-23 JK-1 σ=5.670400 10-8 Wm-2K-4 A=2898 μmK T[K], λ [μm] Sensors for optical RS SPOT, IKONOS, ETM+, MODIS, … QuickBird, … Cross-track (“whiskbroom”) scanner Along-track (“pushbroom”) scanner Multispectral scanners Material of detectors Approx. spectral range [nm] Silicon 190 - 1100 Germanium 800 -1700 Indium, Gallium, Arsenide 500 - 1700 Indium Antimonide 1000 - 3000 Spectral characteristics (1) Type of sensor Number of bands* Band width* [nm] Example Multispectral 2-10 100 ETM+, QuickBird Superspectral 10 - 100 50 MODIS, Meris Hyperspectral > 100 10 Hyperion * presented values only for a rough orientation y λ x Multispectral image Hyperspectral image Spectral characteristics (2) Spatial characteristics Observation geometry z Lr Li θ dΩ dΩi r r θi φi dA y φr x Observing geometry components Satellite orbits • Polar, sun synchronous • Geostationary Solar elevation angle and earth-sun distance Irradiance on the earth surface E cosθ E = 0 0 d 2 E … normalized solar irradiance E0 … solar irradiance at mean earth-sun distance θ 0… sun’s zenith angle d … earth-sun distance [au] Interaction of radiation with surface (1) • Surface reflectance ρλ= Mrλ /Eλ • specular x diffuse reflectance • Bidirectional reflectance distribution -1 BRDF=Lλ(θi,φi)/Eλ(θr,φr) [sr ] Interaction of radiation with surface (2) • Reflectance of basic materials Interaction of radiation with surface (3) • Hyperspectral sensing Radiative transfer • Spectral irradiance at the top of the atmosphere M solar disk area E0 = λ λ π (distance to earth)2 TOA Schovengerdt (2007) Radiative transfer • Atmospheric effects – Absorption –Scattering • Rayleigh scattering Schovengerdt (2007) – On small particles, wavelengths λ»2πa – Power of scattered radiation proportional to λ-4 • Mie scattering – On aerosols and particles with the size comparable to or larger than the wavelength • Non-selective scattering (water vapor) Radiative transfer • Total radiance measured at sensor in optical domain s su sd sp Lλ = Lλ + Lλ + Lλ su • Lλ unscattered, surface reflected radiation sd • Lλ down-scattered, surface reflected skylight su • Lλ up-scattered path radiance Radiation components su sd sp Lλ Lλ Lλ 0 Eλ su Component Lλ (1) surface normal φ • Irradiance at the earth’s surface θ β 0 Eλ =τ s (λ)Eλ cos[θ (x, y)] • τs … solar path atmospheric transmittance • Radiance of a Lambertian surface (on the earth) τ ()λ E0 L ()x, y = ρ (x, y,λ )s λ cos[]θ ()x, y λ π • ρ … diffuse spectral reflectance su Component Lλ (2) • At-sensor radiance from unscattered, surface reflected radiation su Lλ (x, y) =τ v (λ)Lλ (x, y) τ ()λ τ ()λ E0 Lsu ()x, y = ρ (x, y,λ )v s λ cos[]θ ()x, y λ π • τs … view path atmospheric transmittance – Simplification, in case of real materials a diffuse spectral reflectance ρ is replaced with a Bi-directional Reflectance Distribution Function (BRDF) sd Component Lλ • Radiance measured at satellite caused down scattered, surface reflected τ (λ)E d Lsd ()x, y = F ()(x, y ρ x, y,λ )v λ λ π d • Eλ irradiance at the surface due to skylight • F(x,y) fraction of the sky hemisphere that is visible from the position (x,y); influence of topography; F(x,y)=1 for flat terrain sp Component Lλ • Radiance measured at satellite caused by up scattered path radiance – Combined effect of Rayleigh and Mie scattering – Can vary within a scene (e.g. rural x urban area, difference in view angle - wide FOV) – For scenes of homogeneous landscapes and relatively small FOV (e.g. ETM+) is assumed to be constant Total radiance at sensor τ (λ) Ls ()x, y = ρ (x, y,λ )v {τ ()λ E0 cos[]θ (x, y )+ F()x, y E d }+ Lsp λ π s λ λ λ s • Total at-sensor radiance Lλ – Linearly proportional to the surface reflectance – Modified by • a multiplicative factor dependent on terrain shape, position (x,y) and wavelength (λ) • an additive spectrally variant factor due to view path scattering.
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