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Frequency and time dependece of
signals
Frequency Domain Spectroscopy – radiant power
data are recorded as a function of frequency (or
wavelength).
Time Domain Spectroscopy – concerned with
changes in radiant power with time. Achieved by Fourier
transform.
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Chemistry Department, University of Isfahan
Non-Dispersive Methods
 Fourier-Transform Interferometry
What if we could measure the oscillating
wavefunction of EMR directly?
Fourier
Transform
Time Domain
Frequency Domain
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Chemistry Department, University of Isfahan
Fourier composition of a square
wave
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Chemistry Department, University of Isfahan
Direct Measurement:
Feasible?
 Suppose we had EMR with λ = 10 μm
3.00 10 m/s
Freq    

10 10 6 m
8
c
  3 10 Hz
That’s 1 cycle every 33 x 10-15 s
(33 femtoseconds!)
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Upshot: we can’t measure the oscillating
EMR field directly for optical radiation
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Chemistry Department, University of Isfahan
Enter Interferometry
 We need a signal that is much slower, so
that it can be measured . . . How?
High Freq.
~ 1013 Hz
h
Interferometer
Low Freq.
~ 102 Hz
Detector
Computer
h
@f
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Chemistry Department, University of Isfahan
Michelson Interferometer
Movable mirror
Beam splitting mirror
Fixed Mirror
Sour
ce
-1

Detector
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2
3
Resulting Interferogram
δ = pathlength difference
(retardation)
δ = 2(M-F)
δ = 2x (mirror displacement)
So, we get maxima when δ = nλ and minima when
δ = ½nλ (recall that the actual mirror movement is ½δ)
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Chemistry Department, University of Isfahan
Modulation Frequency
•
Moving Mirror moves continuously at a fixed
velocity (VM), so the signal at the detector will
oscillate at a related frequency (f):
f = 2VM/λ
Or:
f = (2VM/c)ν
If VM = 0.1 cm/s, λ = 10 μm EMR will be modulated
at: f = 2(1.0 x 10-3 m/s)/(10 x 10-6 m) = 200 Hz
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Chemistry Department, University of Isfahan
To the Frequency Domain!
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Chemistry Department, University of Isfahan
Chemistry Department, University of Isfahan
From Interferogram to
Spectrum
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Why Bother with
FT-Interferometry?
1. Signal-to-Noise Enhancement
 Multiplex Advantage (“Fellgett’s Advantage”)
-All wavelengths viewed simultaneously, so
measurement time/resolution element is
greater
If measurement is limited by detector noise:
S/N enhancement ∝ (n)1/2
where n = number of resolution elements
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Chemistry Department, University of Isfahan
Multiplex Advantage: Time
 Suppose we spent 6000 seconds acquiring the
spectrum and we really don’t need the enhanced
S/N:
We can get the same S/N as with a
dispersive system in 1/(n)1/2 of the time
In this case, this means it would take:
6000 s/54.8 ≈ 110 s
So, 100 minutes (dispersive) versus 2 minutes
(FT-interferometry)!
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Chemistry Department, University of Isfahan
Summary of Advantages of Fourier
Transform Spectroscopy
Fellgett Advantage – all of the resolution elements for a
spectrum are measured simultaneously, thus reducing the
time required to derive a spectrum at any given signal-tonoise ratio.
Jacquinot Advantage – the large energy throughput of
interferometric instruments (which have few optical elements
and no slits to attenuate radiation.
High wavelength precision, making signal averaging feasible.
Ease and convenience that data can be computermanipulated.
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Chemistry Department, University of Isfahan
Optical instrument
Five components
1. a stable source of radiant energy
2. a transparent container for holding the sample
3. a device that isolates a restricted region of the
spectrum for measurement
4. a radiation detector
5. a signal processor and Fiber Optics
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Chemistry Department, University of Isfahan
Detectors for spectroscpic instruments
, nm
100
200
VAC
400
UV
700 1000
VIS
2000
Near IR
4000 7000 10,000 20,000 40,000
IR
Far IR
Spectral region
Detectors
Photographic plate
Photomultiplier tube
Phototube
Photon
detectors
Photocell
Silicone diode
Charge transfer detector
Photoconductor
Thermocouple (voltage) or barometer (resistance)
Thermal
detectors
Golay pneumatic cell
Pyroelectric cell (capacitance)
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Chemistry Department, University of Isfahan
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Radiation Detectors
Detectors convert light energy to an
electrical signal.
 In spectroscopy, they are typically placed
after a wavelength separator to detect a
selected wavelength of light.
 Different types of detectors are sensitive in
different parts of the electromagnetic
spectrum.

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Chemistry Department, University of Isfahan
Ideal Detectors






high sensitivity
high S/N ratio
constant response over a considerable range of 
fast response
minimum output signal in the absence of
illumination (low dark current)
electric signal directly proportional to the radiation
?
power
S =kP + kd
radiation power (intensity)
dark current
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Chemistry Department, University of Isfahan
Types of radiation detectors
Two major types: one responses to photons,
the other to heat

photon detectors: UV, visible, IR
used for 3 µm or longer , cooling to dry ice
or liquid nitrogen is necessary to avoid interference
with thermal signal)
 signal results from a series of individual events
 shot noise limited
 (when

thermal detectors: IR
 signal
responds to the average power of the
incident radiation
 thermal noise limited
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Chemistry Department, University of Isfahan
Photon detectors
(a) Photovoltaic cells: radiant energy generates a current at
the interface of a semiconductor layer and a metal;
(b) Phototubes: radiation causes emission of electrons from
a photosensitive solid surface;
(c) Phtomultiplier tubes: contain a photoemissive surface as well
as several additional surfaces that emit a cascade of electrons
when struck by electrons from the photosensitive area;
(d) Photoconductivity detectors: absorption of radiation by a
semiconductor produces electrons and holes, thus leading
to enhanced conductivity;
(e) Silicon photodiods: photons increase the conductance
across a reverse biased pn junction. Used as diode array to
observe the entire spectrum simultaneously
(f)
Multichannel photon detector
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Chemistry Department, University of Isfahan
Barrier Layer Cell
Glass Thin layer
of silver
Selenium
Plastic
case
Iron
+
-
Photoelectric Effect
V
Cathode
Wire anode
90 Vdc
Vacuum Phototubes
•
•
•
The number of electrons ejected from a photoemissive
surface is directly proportional to the radiant power of the
beam striking that surface;
As the potential applied across the two electrodes of the
tube increases, the fraction of the emitted electrons
reaching the anode rapidly increases;
when the saturation potential is achieved, essentially
all the electrons are collected at the anode.
•
The current then becomes independent of potential and
directly proportional to radiation power.
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Chemistry Department, University of Isfahan
Photomultiplier Tube
Dynode
Potential(V)
Number of
electrons
1
90
10
2
180
100
3
270
103
4
360
104
5
450
105
9
6
540
106
Quartz
envelope
7
630
107
8
720
108
810
900V
109
Gain =108
5
7
3
4
6
2
1
8
Anode
Grill
Photoemissive
Cathode
9
Anode
900V dc
Photoemissive
Cathode
Dynodes 1-9
Anode
+
_
To readout
Features of Photomplier Tubes
• High sensitivity in UV, Vis, and NIR
– Limited by dark current
– Cooling to -30oC improves response
• Extremely fast time response
• Limited to measuring low-level signals
Silicon Diode
pn junction
Metal contact
Lead wire
p region
n region
Fig. 7.30
Silicon diode under Revese Bias
Reverse bias
Depletion layer
Silicon Diode under Forward Bias
Forward bias
e
e
Photodiode and Photovoltaic Detectors

When a photon strikes a semiconductor, it can
promote an electron from the valence band (filled
orbitals) to the conduction band (unfilled orbitals)
creating an electron(-) - hole(+) pair.

The concentration of these electron-hole pairs is
dependent on the amount of light striking the
semiconductor, making the semiconductor
suitable as an optical detector.
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Chemistry Department, University of Isfahan
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Semiconductor Detector
A reverse-biased
linear diode-array
detector:
(a) cross section
and
(b) top view.
Chemistry Department, University of Isfahan
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Multichannel Photon Detector
Photodiode Arrays
Charge-injection devices
Charge-coupled devices (CCDs)
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Chemistry Department, University of Isfahan
Photodiode Array Detectors (PDA)




A photodiode array (PDA) is a linear array of
discrete photodiodes on an integrated circuit (IC)
chip.
For spectroscopy it is placed at the image plane
of a spectrometer to allow a range of
wavelengths to be detected simultaneously.
In this regard it can be thought of as an
electronic version of photographic film.
Array detectors are especially useful for
recording the full uv-vis absorption spectra of
samples that are rapidly passing through a
sample flow cell, such as in an HPLC detector.
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Chemistry Department, University of Isfahan
Diode Array Detectors
Advantage
speed
sensitivity
The Multiplex
advantage
Disadvantage
resolution is 1
nm, vs 0.1 nm
for normal UV
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Optical instrument
Five components
1. a stable source of radiant energy
2. a transparent container for holding the sample
3. a device that isolates a restricted region of the
spectrum for measurement
4. a radiation detector
5. a signal processor and Fiber Optics
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Chemistry Department, University of Isfahan
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Signal processing
An electronic device that amplifies the electric
signal from the detector
photon counting:
• has a number of advantages over analog signal:
• improved S/N
• sensitivity to low radiation level
• improved precision for a given time
measurement time
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Chemistry Department, University of Isfahan
Fiber Optics
The field of fiber optics depends upon the total
internal reflection of light rays traveling through tiny
optical fibers.
Once the light is introduced into the fiber, it will
continue to reflect almost losslessly off the walls of
the fiber and thus can travel long distances in the
fiber.
Bundles of such fibers can accomplish imaging of
otherwise inaccessible areas.
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Chemistry Department, University of Isfahan
Fiber optic
•
•
•
Optical fibers are circular dielectric waveguides that can
transport optical energy and information.
They have a central core surrounded by a concentric cladding
with slightly lower (about 1%) refractive index.
Fibers are typically made of silica with index modifying
dopants such as GeO2.
•
•
•
•
•
total internal reflection
incident angle larger than critical angle
core material: n1; cladding material: n2
n1 > n2 for total internal reflection
numerical aperture: a measure of the magnitude of the
light gathering ability of the fiber. It also indicates how easy it
is to couple light into a fiber.
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Chemistry Department, University of Isfahan
Fiber Optics
• Good for transmission of light over long distances
• Flexible
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Chemistry Department, University of Isfahan
Chemistry Department, University of Isfahan
Fiber Optics
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