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 Φ W E=dΦ/dA density Wm-2 M=dΦ/dA 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 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 • (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

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

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