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
π M = πL z θ θ 2 θ 2 dS = r dΩ = 2 r sinπ d dS 2 π Ω d Φ = LdAsin dΩ = 2 LdAsinθ cos d θ θ θ π / 2 θ θ dθ θ dΩ dΦ = 2 LdA ∫sin cos d =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 E0λ = 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 opticalλ domain λ s su sdλ sp L = L + L + 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)
τ surface normal φ • Irradianceλ at theλ earth’s surface θ β 0 E = s ( )Eλ cos[θ (x, y)]
• τs … solar path atmospheric transmittance
λ • Radiance of a Lambertianρ surface (on the earth) λ τ λ E0 L ()x, y = x, y (, s )λ cos()[]θ ()x, y π • ρ … diffuse spectral reflectance su Component Lλ (2) λ • At-sensorτ radiance from unscattered, surface λ λ reflectedλ radiation su L (x, y)= ρv ( )L (x, y) λ τ λ () ( )()τ λ ()E0 Lsu x, y = x, y, v s λ cos[]θ ()x, y 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
λ • Radiance measured at satellite caused down scattered, ρsurface reflected λ τ (λ)E d Lsd ()x, y = F x, y ()(x, y, v )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 λ
Total radiance at sensor λ
τ ρ π λ s τ v (λ) 0 λd sp L ()x, y = x, (y,λ ){s ()E cos[]θ x, y (+ F() )x, y E }+ Lλ
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