Origin of TIR Spectral Features

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Origin of TIR Spectral Features

• Lecture VEH2
• 8-28-03

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Vibrational Motions

• displacements of atoms from equilibrium positions
  produce vibrations
• of modes depends on number and type of atoms,
  molecular geometry, and bond strength
• think of masses on springs oscillate with
  harmonic frequencies (spring/force constant) and
  at discrete, quantized energies
• Spring constant high strong bond high
  frequency oscillation
• Spring constant low weak bond low frequency
  oscillation
• If frequency of photon (electric field)
  frequency of oscillation of atoms, then photon
  gets absorbed

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Vibrational Motions

• Fundamental vibrational modes of geologic
  materials coincide with TIR region (gt3 µm)
• Weaker overtone and combination bands can be
  observed in VNIR (lt3 µm, some out to 5 µm)
• IR activity
• there must be a dipole moment (an unequal
  distribution of charge) that changes upon
  vibration
• Molecules like N2, O2 do not have a net dipole
  moment, and are therefore IR inactive
• CO2, H2O do exhibit dipole changes during
  vibration they are IR active

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Heat, Temperature, Radiant Flux

• Kinetic energy ? radiant energy by particle
  collisions that produce changes in energy state
  (and thus the emission of EM radiation)
• EM energy radiated is the radiant flux (F) and
  has units of Wcm-2
• The kinetic temperature (Tkin)of a material is
  the surface temperature, whereas the radiant
  temperature (Trad) is what is measured remotely
• Trad usually less than Tkin because of emissivity

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Thermal Properties of Materials

• Radiant energy incident on a material is partly
  reflected (R), partly absorbed (A), and partly
  transmitted (T) R A T 1
• For materials where transmissivity is negligible,
  this equation reduces to R A 1

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Blackbodies, Emissivity, and Radiant Temperature

• A blackbody material radiates/emits energy in a
  pattern that is dependent only on Tkin
• A blackbody absorbs all incident energy (A 1)
• The radiant flux of a blackbody (Fb, the
  integrated flux over all wavelengths)
  is Fb sTkin4
• where s the Stefan-Boltzmann constant (5.67 x
  10-12 Wcm-1K-4)

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Blackbodies, Emissivity, and Radiant Temperature

• Emissivity is the ratio between the radiant flux
  of a real material (Fr) and that of a blackbody
  (Fb) at the same temperature e Fr/Fb

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Blackbodies, Emissivity, and Radiant Temperature

• So, the radiant flux of a real material
  is Fr esTkin4
• For a blackbody, emissivity 1
• A material with wavelength-constant emissivity lt1
  is called a greybody
• For real materials, emissivity is wavelength
  dependent
• Materials with high e radiate large amounts of
  kinetic energy and absorb large amounts of
  incident energy

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Blackbodies, Emissivity, and Radiant Temperature

• Most thermal IR remote sensing systems measure
  the radiant temperature (Trad) of the
  surface FbsTrad4

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The Planck Function

• The hotter a material is, the more photons that
  are radiated/emitted as energy
• The emitted energy is a function of wavelength
  (?), temperature (T), and emissivity (?), in the
  general form E(l,T) elEo(l,T)and
  specifically as the Planck function

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The Planck Function
whereh Planck constantk Boltzman constantc
speed of light
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The Planck Function
Radiance
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Wiens Displacement Law

• Describes variation in Planck function with
  temperature lmax 2987K/T(where T is in
  Kelvin)
• So, with increasing T, there is a shift of lmax
  to shorter l

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Wiens Displacement Law
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Reflection and Emission

• Reflectance is a measure of how much incident
  energy is reflected from a surface vs. how much
  is transmitted R(l) Rref/Rinc
• For a perfect reflector, R 1, and for a perfect
  absorber, R 0
• Recall that optical properties (n, k) and
  physical properties will control R as a function
  of wavelength

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Reflectance and Emission

• Emitted energy is equivalent to absorbed energy,
  so, from above (and assuming no surface
  scattering) R 1 Atherefore,
  E 1 R

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Reflectance and Emission

• Recall that radiance of real materials is
  wavelength dependent
• Planck function includes information on both the
  emitted energy and the temperature of the
  material
• Because temperature may vary over a planetary
  surface, comparing Planck functions is not very
  convenient
• Examine emissivity independent of temperature
• convert radiance to emissivity using the
  relationship between the radiant flux of a
  blackbody and a real material (above)

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Radiance of Real Materials
Radiance
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Radiance of Real Materials
Radiance
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Radiance