Review of Molecular Absorption

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Review of Molecular Absorption Basic properties
of molecular absorption (how why) Absorption
Spectrum Absorption coefficient and pressure
broadening Transmission Applications bases for
estimating column CO2 and O2 (surface
pressure) Spectrometer systems prism
(Dobson), grating and interferometers (contrast
to filter radiometers)
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Molecular absorption
The electric dipole
The electric dipole is a parameter important to
how E-M radiation interacts with matter.
The dipole is an arrangement of opposite
charges where the vector direction is in the
sense of -ve to ve
To a large extent whether a molecule absorbs
radiation is determined by how atoms are arranged
to form the molecule and its associated
ability to create charge separation Homopolar
H2, N2,O2 no permanent dipole, H2O, O3, CH4
polar molecules (permanent) CO2 is special
(induced) O2 ??? permanent mognetic dipole
The fact that the charges are displaced results
in an ? field and oscillations of the dipole
(ie. dp/dt) creates an time varying e- field and
thus EM radiation
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High energy fast oscillations
UV photo- dissociation
The types of interactions that occur in matter
depend on the rate of oscillations that must be
induced (i.e the wavelength of the incident
radiation). On the whole, shorter
wavelength radiation interacts with lighter parts
of matter whereas more sluggish, slower
oscillating radiation affects the larger parts of
matter. We are mainly concerned with mechanisms
affecting electrons, atoms and the more bulky
molecules
Vibration rotation
Depends on mass distribution
Low energy slow oscillations
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Vibration modes of CO2
No radiation
Radiation
Radiation
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vibrations rotations typically occur together -
at least ?lt 20 ?m for example consider the
vibration/rotation modes of a linear
molecule. selection rules (from q-theory)
establish which transitions are
permitted Diatomic molecule ?v ? 1, ?K ? 1
PR
Branch Triatomic (linear) molecule (CO2)
?v ? 1, ?K ? 1
PR Branch
?v 0, ?K 1
Q Branch
Insert 8.7 b 4.8b
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Lamberts Law
optical path length
Calculating the amount of absorption by absorbing
gases Express this in terms of transmission
functions Absorption coefficient amount of gas
- path
Beers Law
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The Absorption Coefficient

• Three important factors define the properties of
  an absorption line
• spectral position - ?o
• strength - S
• shape - f(?-?o)

Defined by factors already described -
ie properties of the given molecule
Line strength depends on the population of the
E-states of the absorbing molecule.
S?(n-nu)/ntotal Populations are generally
determined by the Boltzmann distribution
The lines are not sharp but are fuzzy -
measure the fuzziness in terms of width of the
line
populations
Cross- section
These three properties in turn define the
absorption coefficient k? S
f(?-?o) where
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Pressure Broadening
Collisions between molecules produce a broadening
of the absorption line. There is no exact
solution to the many-body collision problem and
parametric models
Consider rotation
Collision has the effect of spontaneously
rotating the molecule such that the phase of
rotation has changed.
K1
K
absorption
absorption collision
K
K1
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centre
The Lorentz pressure broadening model
wing
where ?L 1/(2?t) with t the mean time between
collisions (which is inversely proportional to
pressure).
Pressure of colliding molecule (e.g N2, O2) which
defined foreign broadening in contrast to self
broadening
In the wings, ?-?0 ??L and
Pressure broadening is the most
important broadening mechanism for the problems
of interest to this class. The proportionality
of the line width on pressure is fundamental
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Insert fig 8.12
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midday
Further example identification of
stratospheric ClO
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Gas path- Optical Mass (contd)
Mass mixing ratio
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N2O
UV
near-IR/far IR
Microwave
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H2O spectrum
O2 A-band spectrum
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• Selected applications
• Aerosol turbidity
• Column gas - O2- surface pressure
• CO2

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Example 1 Sensing the surface pressure
Measure on and off the absorption line ?1 ? ?2
are very close, R ?1 , R ?2 etc are essentially
the same
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Aircraft obs., clear sky, ocean surface (OBrien
et al.,J.A O.T, 1998)
lnI2/I1
adjusted m
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But!!!!
IIsurfIatm and the presence of the atmospheric
contribution introduces an ambiguity.
Tenuous Medium I2 I0 R exp(- ?2 m) I1 I0 R
exp(- ? ?1 m) R grey surface reflection m air
mass factor (1/µo 1/µs) ? path
enhancement lnI2/I1 - (?2 - ? ?1)m
change of slope
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• Aircraft
• Spectrograph
• Measurements

These define X for model A
Basic question can we separate atmospheric
scattering from surface reflection? If so with
what sensitivity? Analysis procedure m1/µo
1/µs 1-(p/p0)2 convenient to introduce
adjusted airmass m ? m (p0/p)2 X ? amb m ?
cXd From X (ratio of spectral radiances), obtain
m and thus p. Compare with measured p. Two
models Coarse band (model A) m cX d, where
X is ratio of 2 3 nm-mean radiances Narrow band
(model B) m ? fjXj gj cX d where Xj are
narrow band radiance ratios (0.03nm).
Thin Cirrus
Aircraft pressure p
Aerosol
OBrien et al, 1998
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Same idea measuring CO2 from Space
Level 1
Calibration
XCO2 Retrieval
Level 2
Source/Sink Retrieval
Level 3

• Inverse Models
• Assimilation Models

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The OCO design

• Sampling Approach - High spatial resolution
• Isolates cloud-free scenes
• Minimizes scene inhomogeneity
• Single space-based instrument incorporating three
  passive near-infrared spectrometers
• CO2 1.58 ?m band
• CO2 column abundances
• CO2 2.06 ?m band
• CO2, cloud, aerosol, water vapor, temperature
• O2 0.76 ?m A-band
• Clouds, aerosols, and surface pressure

2.06
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• Spectrometer Systems
• refraction (prism spectrometers)
• diffraction (grating spectrometers)
• interference (interferometer, etalons)

Elementary Prism Spectrometer
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Dobson Spectrometer
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Basics of a grating spectrometer
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SAGE I optical layout
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OCO A-band Spectrometer Optical Concept
Spectrometer rotated out of the plane by 90o from
the slit back
Solar Calibrator Diffuser
Focal Plane
Camera
Solar Calibrator Collimator
De-polarizer
90o Fold (not shown)
Grating
Slit
Collimator Triplet
Telescope Triplet
Bandpass Filter
Beam Splitter
Nadir Pointing Mirror
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Interferometry basic idea is to use the
interference of radiation of one wavelengths
that experiences two slightly different paths.
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interferogram
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