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geoinformatics:thermal-infrared

Thermal Infra-red Remote Sensing

Using special sensors and the thermal radiation properties of physical bodies, we can measure surface temperature from a distance. In this project, we'll be using thermal infra-red (TIR) techniques to estimate surface temperatures of an iceberg using thermal camera ground measurements and a land parcel using satellite sensors.

Theoretical foundation

Some basic notes on blackbody radiation:

  • All bodies with temperature above 0 K emit radiation.
  • 0 K = ‒273,15 °C
  • A blackbody is a theoretical object that completely absorbs all wavelengths of electromagnetic radiation incident on it.
  • When a blackbody is heated to a temperature above 0 K, it emits radiation.
  • Blackbody radiation at temperatures comparable to the temperature of the earth’s surface (~300 K) is the thermal infrared (TIR)
  • “Good absorbers are good emitters”, meaning that a blackbody emits 100% of the radiation it absorbs (so the absorbed radiation has no effect on the blackbody’s temperature)

Basic principles:

PrincipleDescription
Planck’s Law of blackbody radiationDescribes the electromagnetic radiation of a blackbody of a defined temperature
Stefan-Boltzmann LawCalculates the total electromagnetic radiation as function of a blackbody’s temperature
Wien’s Displacement LawCalculates the wavelength at which maximum spectral radiant exitance (emitted radiation) occurs
Kirchhoff’s Law• Emittance at a given wavelength = absorbance at the same wavelength
• Blackbodies are theoretical; the behaviour of real objects can be described based on how close to being a blackbody they are.
• Emissivity (ε):
     ε = 1 ⇒ blackbody
     ε < 1 ⇒ real-life material

Plank's law

This law describes how blackbody radiation can be calculated by the object’s (absolute) temperature:

$$ M_\lambda=\frac{2\pi hc^2}{\lambda^5\left(e^{\displaystyle\frac{hc}{\lambda kT}}-1\right)} $$

Where: $M_λ$ = radiation, $λ$ = wavelength, $T$ = absolute temperature.

Therefore, at any given wavelength, we can have a spectral radiant exitance curve (“radiation”) according to the absolute temperature:

Fig. 1; Source: http://ozonedepletiontheory.info/Images/plancks-law-basic-extended.jpg

Stefan-Boltzmann Law

Describes the total electromagnetic radiation as a function of the absolute temperature:

$$ T_\mathrm{RadBB}=\sigma T{}_\mathrm{kin}^4 $$

where $T_\mathrm{RadBB}$ is the radiant flux, and $T_\mathrm{kin}$ the kinetic temperature.

If kinetic temperature is measured in degrees Kelvin, then the temperature value is directly proportional to the average kinetic energy of the molecules in the substance.

Wien's Law

Describes the wavelength at which maximum spectral radiant exitance occurs.

$$ \lambda_\max=\frac AT $$

In Figure 1, the dotted line connects the peak radiances of the temperature curves.

Therefore, hot lava is red because it radiates the red wavelengths more than other wavelengths.

For example:

Kirchhoff’s Law & Relevance of Emissivity

  • Perfect blackbodies are nowhere in this world!
  • For a given wavelength, the emittance is equal to the absorbance

$$ \varepsilon_{\left(\lambda\right)}=\alpha_{\left\{\lambda\right\}} $$

  • Conservation of energy: [absorption] + [reflection] + [transmission] = 1 (for a given wavelength)

$$ \varepsilon_{\left(\lambda\right)}+\rho_{\left(\lambda\right)}+\tau_{\left(\lambda\right)}=1 $$

  • For opaque objects that do not transmit radiation: [absorption] + [reflection] = 1

$$ \varepsilon_{\left(\lambda\right)}+\rho_{\left(\lambda\right)}=1 $$

  • It is therefore calculated that:

$$ T_{\mathrm{rad}}=\varepsilon^{\left(\frac14\right)}\cdot T_{\mathrm{\kappa\iota\nu}} $$

For real materials, ε < 1, so the radiance temperature will always be lower than the actual kinetic temperature on the surface of the material!

geoinformatics/thermal-infrared.txt · Last modified: 2020/08/04 14:34 by sotosoul