CE 603 Photogrammetry II

Some Definitions (from Elachi, 1987) Radiant : The energy carried by an electromagnetic . It is a measure of the capacity of the wave to do by heating an object or changing its state. Radiant : The at which passes a certain location. Density: The radiant flux intercepted by a unit of a plane . The density for flux incident upon a surface is called . The density for flux leaving a surface is called Emittance or Exitance. Radiant : The of a in a given direction is the radiant flux per unit leaving the source in that direction Solid Angle: 4π per sphere : For an extended source, the radiant flux per unit solid angle in a given direction, per unit projected area in that direction. (If radiance does not change as a function of direction of emission, the source is called Lambertian. CE 603 Photogrammetry II

Radiometry (aggregate quantities) Symbol Quantity Equation Units Q Radiant Energy F Radiant Flux F=dQ/dt (j / s) E Radiant Flux Density E=dF/dA watt / m2 (Irradiance) M Radiant Flux Density M=dF/dA watt / m2 (Emittance or Exitance) I Radiant Intensity I=dF/dW watt / sr L Radiance L=dI/dA cosQ watt / m2 sr Black-body at any temperatureλ (above -273.15 deg. K) radiates over a continuous range of . Strength ofλ contribution to radiance varies with . Quantify this with a function, spectralλ radiance, S(λ), such that, ΔL = S( )Δ or S( )= dL dλ λ CE 603 Photogrammetry II λ λ ΔL = S( )Δ or S( )= dL dλ S()λ

ΔL Radiance over a range of wavelengths λ2λ L λ λ = S()λd S(λ) 1 2 ∫ 1 λ ∞ () L = S λ dλ Total ∫ 0

Δλ λ Spectral radiance of blackbody at a given temperature CE 603 Photogrammetry II

Planck’s formula for spectral radiance λ 2hc2 S()= λ5 ()ehc λkT −1 In which, h = 6.6261×10−34 Js, planck k =1.3807×10−23 JK −1, boltzmann c = 2.9979×108 ms−1, speed of T = temperature in degrees kelvin λ = wavelength in meters CE 603 Photogrammetry II

This is actually a log-log plot of S(λ) vs. wavelength for black-bodies at various temps.

6000 deg K

500 deg K CE 603 Photogrammetry II Convert units of S(λ) by multiplying by 1E-06, convert to spectral exitance, M(λ) by multiplying by .

6000 deg K

500 deg K CE 603 Photogrammetry II

From Rees, 2001 CE 603 Photogrammetry II

From Rees, 2001