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Fourier Transform Infrared
(FTIR)
Spectrometer
Subhashree Mishra
ATMS Grad Student, UNR
W. P. Arnott
Physics, UNR
Introduction to Atmospheric Instrumentation (ATMS 360)
University of Nevada Reno
Energy Levels: Basic Ideas
Basic Global Warming: The C02 dance …
About 15 micron radiation
Wavelength and Wavenumber
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Wavelength = 1 / Wavenumber
For the IR, wavelength is in microns.
Wavenumber is typically in 1/cm, or cm-1.
5 microns corresponds to 2000 cm-1.
20 microns corresponds to 500 cm-1.
15 microns corresponds to 667 cm-1. Much
‘terrestrial’ IR energy at the wavenumber.
Carbon Dioxide Concentration
Example Problem: Instantly Double CO2 Concentration.
What is the effect on the infrared spectrum at the surface?
Consequence: The Earth’s surface warms because of the additional IR coming
to the surface from the Atmosphere.
Example Problem: Instantly Double CO2 Concentration.
What is the effect on the infrared spectrum from space?
Satellite with FTIR
Looking Down
B(Te)
Te
Consequence: The less IR radiation escapes to space when the atmosphere has 800 ppm
CO2 because the atmosphere is less transparent to IR emitted by the Earth’s surface. The
Earth’s surface temperature must increase to again balance the outgoing IR with the
incoming solar radiation.
LEDs As Detectors
Each photon with enough energy will normally free exactly one electron, and
result in a free hole as well. If this happens close enough to the electric field, or if
free electron and free hole happen to wander into its range of influence, the field
will send the electron to the N side and the hole to the P side. This causes further
disruption of electrical neutrality, and if we provide an external current path,
electrons will flow through the path to their original side (the P side) to unite with
holes that the electric field sent there, doing work for us along the way. The
electron flow provides the current, and the cell's electric field causes a voltage.
With both current and voltage, we have power, which is the product of the two.
From http://science.howstuffworks.com/solar-cell3.htm
LEDs As Detectors: Thermal Noise
FTIRs Often Use MCT Detectors:
Mercury Cadmium Telluride
HgCdTe or Mercury cadmium telluride (also Cadmium Mercury Telluride, MCT or
CMT) is an alloy of CdTe and HgTe and is sometimes claimed to be the third
semiconductor of technological importance after Silicon and Gallium(III) arsenide.
The amount of cadmium (Cd) in the alloy (the alloy composition) can be chosen so
as to tune the optical absorption of the material to the desired infrared wavelength.
(from http://en.wikipedia.org/wiki/Mercury_cadmium_telluride)
Outline
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Introduction
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Theory
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Design
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Applications
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Measurements
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Discussions
What is a FTIR Spectrometer?

A spectrometer is an optical instrument used to measure
properties of light over a specific portion of the
electromagnetic spectrum, 5 microns to 20 microns.
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FTIR (Fourier Transform InfraRed) spectrometer is a obtains
an infrared spectra by first collecting an interferogram of a
sample signal using an interferometer, then performs a Fourier
Transform on the interferogram to obtain the spectrum.

An interferometer is an instrument that uses the technique of
superimposing (interfering) two or more waves, to detect
differences between them. The FTIR spectrometer uses a
Michelson interferometer.
FOURIER TRANSFORMS
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Fourier transform defines a relationship between a
signal in time domain and its representation in
frequency domain.
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Being a transform, no information is created or lost in
the process, so the original signal can be recovered
from the Fourier transform and vice versa.
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The Fourier transform of a signal is a continuous
complex valued signal capable of representing real
valued or complex valued continuous time signals.
Fourier Transforms cont.
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The Continuous Fourier Transform, for use on continuous
signals, is defined as follows:
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And the Inverse Continuous Fourier Transform, which allows
you to go from the spectrum back to the signal, is defined as:
F(w) is the spectrum, where w represents the frequency, and
f(x) is the signal in the time where x represents the time. i is
sqrt(-1), see complex number theory.
Fourier Transforms cont.
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A computer can only work with finite discrete signals, not with
continuous signals. Thus, we need to define the Discrete
Fourier Transform (DFT).
In DFT, the infinite borders of the integrals can be replaced by
finite ones, and the integral symbol can be replaced by a sum.
So the DFT is defined as:
And the inverse DFT is defined as:
FTIR Theory
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The spectrometer described here is a modified Bomem MB100 FTIR.
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The heart of the FTIR is a Michelson interferometer (figure 2).
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The mirror moves at a fixed rate. Its position is determined
accurately by counting the interference fringes of a collocated
Helium-Neon laser.
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The Michelson interferometer splits a beam of radiation into
two paths having different lengths, and then recombines them.
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A detector measures the intensity variations of the exit beam as
a function of path difference.
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A monochromatic source would show a simple sine wave of
intensity at the detector due to constructive and destructive
interference as the path length changes (refer figure 3).
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In the general case, a superposition of wavelengths enter
spectrometer, and the detector indicates the sum of the sine
waves added together.
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Figure 3 shows some idealized light sources, and the
interferograms that they would theoretically produce.
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The difference in path length for the radiation is known as the
retardation d (OM = OF + d) in figure 1 and 2.
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When the retardation is zero, the detector sees a maximum
because all wavenumbers of radiation add constructively.
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When the retardation is l/2, the detector sees a minimum for
the wavelength l. An interferogram is the sum of all of the
wavenumber intensities.
Figure 1.
Schematic of Michelson Interferometer
Figure 2.
Source: MS thesis submitted by Carl George Schmitt, UNR , 1998.
Wave Interference
Figure 3.
Sample interferograms and their theoretical source intensity
Source: MS thesis submitted by Carl George Schmitt, UNR , 1998.
Calibration of the FTIR spectrometer
Source: MS thesis submitted by Carl George Schmitt, UNR , 1998.
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The spectrometer produces a complex voltage at each
wavenumber. A linear model for the spectrometer response is
assumed, where A is an instrument offset, and C is a scaling
factor,
V= A+CI
(1)
If the spectrometer views a perfect blackbody, Eq. (1) gives
V = A+ CBT
(2)
where BT is the Planck emission curve for a blackbody of
temperature T.
The two unknowns (A and C) can be determined from
blackbody measurements at two different temperatures,
V1 = A+ CBT1
V2 = A+ CBT2
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Solving for the unknowns yields
C = (V1-V2)/(BT1-BT2)
and
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A = {V1(BT1-BT2)-BT1 (V1-V2)}/(BT1-BT2)
Returning to Eq (1), The FTIR voltage of another target
(Vtarget) is related to the target radiance (Itarget) by
Itarget=[(BT1-BT2)Vtarget–BT1V2+BT2V1]/(V1-V2)
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Thus, with measurements of blackbodies at two temperatures,
the calibrated radiance from a target (cloud) can be
determined.
APPLICATIONS
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Identification of inorganic compounds and organic
compounds
Identification of components of an unknown mixture
Analysis of solids, liquids, and gasses
In remote sensing
In measurement and analysis of Atmospheric Spectra
- Solar irradiance at any point on earth
- Longwave/terrestrial radiation spectra
Can also be used on satellites to probe the space
Source : UV thoughts from http://uvb.nrel.colostate.edu/UVB/publications/uvb_primer.pdf
MODIS Solar Irradiance
Source : http://en.wikipedia.org/wiki/Image:MODIS_ATM_solar_irradiance.jpg
Theoretical Absorption Cross Sections
Theoretical Absorption Cross Sections for the indicated gases, averaged to 1 cm-1 resolution for clarity.
Measurement Example from Reno
FTIR Radiance: Atmospheric IR Window
13 microns
8 microns
DEFINITION OF THE BRIGHTNESS TEMPERATURE
TB
Measured Radiance at wavenumber v
=
Theoretical Radiance of a Black Body at temperature TB
FTIR Brightness Temperatures
Atmosphere
Emission
Measurements,
Downwelling
Radiance
Notes:
1.
Wavelength
range for CO2,
H20, O3, CH4.
2.
Envelope
blackbody
curves.
3.
Monster
inversion in
Barrow.
4.
Water vapor
makes the
tropical window
dirty.
Which day is more moist?
Which day is warmer
near the surface?
RENO FTIR
SPECTRA
Ideal Weighting Function Wi: Where in the atmosphere the main
contribution to the radiation at wavenumber i comes from.
Downwelling Intensity Emitted by the Atmosphere to the Detector
(Radiance)
=cosq
z dz emissivity=absdz/cosq
q
emission
q
B[T(z)]
blackbody
radiance,
T = temperature.
ftir
transmission
weighting
function
Weighting Functions for
Satellite Remote Sensing using
the strong CO2 absorption
near 15.4 um. (from Wallace
and Hobbs, 2nd edition)
I  B(T )exp 
s
i
All Atmos
abs

 (surface)
  B[T (z)]exp( abs (z)) abs (z) dz (atmos)
0
or
I  B(T )exp 
s
i
All Atmos
abs

 (surface)
  B[T (z)]Wi (z) dz (atmos)
0
Satellite with FTIR
Looking Down
B(Te)
Te