CHAPTER 2 FUNDAMENTALS Basic Definitions And Laws Of Electromagnetic Radiation
Sensors collect electromagnetic energy ΔQ emitted from a surface area ΔΑ (pixel), during a time interval Δt, arriving at the sensor aperture with a solid angle ΔΩ Το characterize the intensity of electromagnetic radiation we must get rid of ΔΑ, Δt and ΔΩ! P ΔΑ ΔΩ Basic definitions (Q = energy) radiant flux Φ(t): radiant exitance M(t,P): irradiance E(t,P): illuminance / radiance L: ΔQ ΔΦ = Δt ΔΦ ΔM = ΔA ΔΦ ΔE = ΔA Φ M E dq = dt dφ = da dφ = da L = E ΔΩ (power) (emitted) (incident)
Electromagnetic signals x(t) consist of sines and cosines sin( ωt) = sin(2 πt/ T) = sin(2 πtc/ λ) cos( ωt) = cos(2 πt/ T) = cos(2 πtc/ λ) with varying periods T, or angular frequencies ω = 2π/Τ, or wavelengths λ = ct (c = light velocity) Fourier representation: x(t)= 1! 2π iωt + 0 X(ω )e iωt dω e = cos( ωt) + isin( ωt)
Signal power: 1 P = lim τ τ +τ [x(t)] 2 dt = P ω (ω )dω = P λ (λ)dλ τ + 0 + 0 Pw (ω) = power spectral density function Radiant flux (power): L λ dl dλ Exitance Irradiance Φ = M = L = + Φ ω (ω )dω = Φ λ (λ)dλ 0 + + 0 M ω (ω )dω = M λ (λ)dλ 0 + M λ + 0 L ω (ω )dω = L λ (λ)dλ 0 + 0 dm = dλ = Spectral irradiance Spectral exitance
The Electromagnetic Spectrum A cm λ 0.1 1 10 10 2 10 3 10 4 10 5 10 6 0.1 1 10 10 2 10 3 10 4 10 5 10 6 10 7 A µ cm m km 0.3 0.2 3 30 300 0.3 3 30 300 0.3 3 30 3 30 300 3 30 300 γ RADAR RADIO AUDIO AC Χ MICROWAVES UV IR VISIBLE UV (Ultraviolet) Violet Red IR (Infrared)
The laws of the electromagnetic radiation A body surface can 1. absorb incident radiation, 2. reflect incident radiation, a) as a mirror 3. transmit incident radiation, 4. emit radiation. b) with spherical symmetry (Lambert) The characteristics are a function of the wavelength of the radiation.
Laws of Electromagnetic Radiation black body : an idealized body absorbing all wavelengths of incident radiation or emitting radiation at all wavelengths Physical approximation = sun! T = temperature Law of Plank: (spectral exitance of black body) M λb, ( λt, ) = c 1 c2 λt 5 λ ( e - 1) Law of Stefan-Bolzman: (total spectral exitance) M b (T)=! Law of Wien: (λ of maximal spectral exitance) λ max = M λ,b (λ,t)dλ =σt 4 0 c 3 T M ( λ, T) = max M ( λt, ) λb, max λb, λ
The Solar Electromagnetic Radiation solar irradiance below atmosphere atmospheric absorption
The real body The exitance is not equal to the black body: the emissivity of the body is defined as e( λ) = M ( λ)/ M ( λ) 0 e( λ) 1 λ λ, B In case of incident energy, a body reflects, absorbs and transmits ρλ ( ) = E ( λ)/ E( λ) 0 ρλ ( ) 1 r i αλ ( ) = E ( λ)/ E( λ) 0 αλ ( ) 1 a i τλ ( ) = E ( λ)/ E( λ) 0 τλ ( ) 1 t i reflectivity absorptivity, trasmittivity, ρλ ( ) + αλ ( ) + τλ ( ) = 1 Energy conservation law e( λ) α( λ) = Kirchhoff law
Some definitions Optical window 0.1 µm (10-4 mm) - 20.0 µm (2 10-3 mm) Ultraviolet, 0.38 µm: atmospheric diffusion Visible, 0.38 µm - 0.75 µm: reflected by the earth surface Near infrared, 0.75 µm 1.5 µm: reflected by the earth surface Near/mean infrared, 1.5 µm 7.0 µm: reflected / emitted by the earth surface Mean infrared, 5.0 µm 7.0 µm: absorbed by the water vapor in the atmosphere Thermal infrared,7.0 µm 20.0 µm: emitted by the earth surface Radar window 0.2 cm - 100.0 cm
The spectral signature of a surface The function ρλ ( ) that describes the reflectivity of a surface / material as a function of the wavelength of the incident radiation.
Examples of typical spectral signatures Non vegetated areas: concrete more reflective, Concrete can be clustered: roadways, parking lots, swimming pools, buildings Vegetated areas: a completely different behavior, Tree can be clustered: deciduous, oaks, maples, evergreen
Remote sensing: the ideal case A set of sensors measures the irradiance reflected by a pixel, on all the wavelengths. The pixel spectral signature has been observed. The observed spectral signature is compared with a library of known spectral firms. The pixel is classified in the class whose known spectral signature is equal to the observed spectral signature.
The real case Sensors behavior Atmosphere and shadows Class heterogeneity and mixed pixels
Sensors respond to exitance only within a spectral band λ 1 λ λ: Ideal sensor:! M [λ1,λ 2 ] = λ 2 λ 1 M λ (λ)dλ Actual sensor:! M [λ1,λ 2 ] = λ 2 λ 1 M λ (λ)w(λ)dλ w(λ) = sensor sensitivity response function response functions for the 4 sensors of the Landsat satellite Multispectral Scanner
Spectral Bands of Landsat Satellite - Thematic Mapper (T1, T2, T3, T4, T5) and SPOT4 Satellite HRVIR (S1, S2, S3, S4) 1. water 2. vegetation 3. bare soil 4. snow
The heterogeneity of a class and the mixed pixels The Tree class: different species of trees, different ages of the same species: spatial heterogeneity; different humidity, different foliations: temporal heterogeneity. Often, in the same pixel, different classes: building and garden, highway and crops To solve the absolute classification problem: the spectral firm library should be complete for all the classes / all the conditions, the pixel spatial resolution should be very fine.
Class heterogeneity The same class can present great variability
Mixed pixels Intermediate classes don t exist. A pixel containing different classes is classified in the majority class.
Seasonal variability The same landscape assumes completely different aspect in summer and winter