Non-intrusive Methods of Temperature Measurement ( Radiation Thermometry )

Radiation Thermometry
Non-intrusive Methods of Temperature
Measurement

Temperature Measurement Using Radiation
A radiation thermometer is an instrument which collects
radiation from a target and produces an output signal,
usually electrical, related to the radiance, which is used to
infer the temperature of the target.

Hemispherical Black Surface Emission
π
σ
π
4
Te
I b
b ==
Emissive Intensity
The radiation emitted by a body is spatially distributed:
),,( ϕθrfIb =

Spherical Black Volumetric Emission
π
σ
π 44
4
Te
I b
b ==
The radiation emitted by a body is spatially distributed:
),,( ϕθrfIb =

Planck Radiation Law
• The primary law governing blackbody radiation is the Planck
Radiation Law.
• This law governs the intensity of radiation emitted by unit surface
area into a fixed direction (solid angle) from the blackbody as a
function of wavelength for a fixed temperature.
• The Planck Law can be expressed through the following equation.
( ) 112
5
2
,
1
12
, −−−
−
= msrWm
e
hc
TI
kT
hcb µ
λ
λ
λ
λ
h = 6.625 X 10-27
erg-sec (Planck Constant)
K = 1.38 X 10-16
erg/K (Boltzmann Constant)
C = Speed of light in vacuum

The behavior is illustrated in the
figure.
The Planck Law gives a
distribution that;
peaks at a certain wavelength,
the peak shifts to shorter
wavelengths for higher
temperatures, and
the area under the curve grows
rapidly with increasing
temperature.

Emissivity
• A black body is an ideal emitter.
• The energy emitted by any real surface is less than the
energy emitted by a black body at the same temperature.
• At a defined temperature, a black body has the highest
monochromatic emissive power at all wavelengths.
• The ratio of the monochromatic emissive power Iλ to the
monochromatic blackbody emissive power Ibλ at the same
temperature is the spectral hemispherical emissivity of the
surface.
λ
λ
λε
bI
I
=)( ),,:,(, ϕθελλ rfIb =

Basic Ideas for Radiation Thermometers
• The wavelength of maximum emission varies between
10.6 µm at 0°C and 1.3 µm at 20000
C.
• For most measurement applications, radiation is emitted
predominantly in the visible, near- and middle-infrared
regions of the electromagnetic spectrum.
• A radiation thermometer is an instrument which collects
radiation from a target and produces an output signal,
usually electrical, related to the radiance, which is used to
infer the temperature of the target.

• The radiant flux, Eλ falling on the detecting element of a
thermometer in the incremental waveband dλ will be
λλλλλ dPABIdE =
where A is the throughput of the optical system, describing the
geometric extent of the beam of radiation falling on the detector; Bλ is
the spectral transmission of the optical system: Pλ, is the spectral
transmission of the medium between the instrument and the target.

For a radiation detector whose responsivity, Rλ is independent
of all variables but wavelength
λ
λ
dE
dV
R =
where dV is the output in response to the radiant flux. dEλ:
λλ dERdV =
Therefore λλλλλ dPABIRdV =
∫
∞
=
0
λλλλλ dPABIRVand

In practice, the range of wavelengths contributing to the
output of the thermometer is restricted by the transmission of
the optical system, the spectral response of the detector and
the nature of the Planck function.
This equation is known as the 'radiometer measurement equation' and
relates the output signal to the target radiance and hence its
temperature.
∫
∞
=
0
λλλλλ dPABIRV

Design features
The basic measurement system for a radiation thermometer
comprises the following elements.
(1) The target of measurement.
(2) An optical system which collects and directs the radiation.
Elements of the optical system may also be used to modify the
spectral response of the thermometer.
(3) A sensor which produces a signal, usually electrical,
related to the incident energy flux.
(4) A reference source which may be physically situated in
the instrument itself or located in a calibration laboratory.
(5) A means of signal processing and display.

Anatomy of Radiation Pyrometers

• The design of the instrument must allow a measurement to be
made with acceptable accuracy and repeatability given all the
circumstances of the target, the instrument itself and the
surrounding environment.
• The most important choice which faces the designer, and indeed
the user is that of the operating waveband for the instrument.
• There are several factors, some of them conflicting, which need
to be considered carefully when choosing the span of
wavelengths to be used.
• First of all, consider an instrument sensitive to a narrow
waveband dλ, centered on wavelength λ.
• Using the approximate form of Planck's equation which is valid
for most practical circumstances:
( ) 112
5
2
,
1
12
, −−−
−
= msrWm
e
hc
TI
kT
hcb µ
λ
λ
λ
λ

we differentiate with respect to T to obtain
( ) 112
5
2
,
1
12
, −−−
−
= msrWm
e
hc
TI
kT
hcb µ
λ
λ
λ
λ
( ) dT
e
T
hc
TdI
kT
hcb
1
12
, 26
2
,
−
=
λ
λ
λ
λ
( )
( ) 2
,
,
,
,
T
dT
k
hc
TI
TdI
b
b
λλ
λ
λ
λ
=
The error in measured temperature, dT. created by an error dIb in
measuring Ib can be expressed as
( )
( )
k
hc
T
TI
TdI
T
dT
b
b λ
λ
λ
λ
λ
×=
,
,
,
,

Precision of Radiation Thermometers
• This relationship indicates that the precision with which the
output needs to be measured in order to achieve a required
accuracy increases with wavelength.
• For this reason it is advantageous to work with the shortest
possible wavelength.
• The nature of the Planck's law curve sets a lower practical limit
on the wavelength which can be used at a particular temperature.
• The bandwidth of radiation accepted by the instrument must be
sufficiently wide to create a signal from the detector that can be
measured with acceptable accuracy, in comparison with the
system noise.
• Finally, the waveband chosen must be free from absorption
effects in the sight path of the thermometer.
• There is no single solution which is best for every application and
care must be exercised in choosing the correct waveband.

Classification of Thermometers
• (1) Partial radiation thermometers:
• These use a fraction of the spectrum defined by the spectral
response of the detector and the optical system.
• (2) Total radiation thermometers: These use virtually the whole
of the spectrum.
• (3) Ratio or two-colour thermometers: These use two distinct
wavebands.
• Thermometers of all types may be constructed either as portable,
hand-held devices or as units for permanent installation in a
fixed position.

Partial Radiation Thermometers
• The advantage of using short wavelengths can be conveniently
realised by using an instrument sensitive to all wavelengths
shorter than a limiting value which is set by the characteristics
of the detector or a filter incorporated into the optical system.
• Thermometers of this type are widely used in many
applications for the measurement of temperatures above 500
C.
• Photon detectors such as silicon and germanium photodiodes
are often used because their spectral response is of an
appropriate form, and lies in the part of the spectrum where the
rate of energy emission is high.
• This type of thermometer is the one most frequently
encountered.

• The optical or disappearing filament pyrometer is an example of a
partial radiation thermometer which uses the eye itself as the
detector working in a comparative mode.
• An electrically heated filament is viewed against a background of
the target.
• The current through the filament is adjusted until its brightness is
equal to that of the target, at which point it cannot be seen. hence
the name of the instrument.
• The temperature of the target is inferred from the magnitude of the
current which current flowing through the filament.

Total Radiation : Stefan-Boltzmann Law
• The maximum emissive power at a given temperature is the black
body emissive power (Eb).
• Integrating this over all wavelengths gives Eb.
( ) ∫∫
∞∞








−
=
0
5
2
0
1
12
, λ
λ
λλ
λ
d
e
hc
dTI
kT
hcb
( ) 44
4
42
15
2
TT
k
hc
hc
TEb σ
π
=




=
( ) 44
4
42
15
2
TT
k
hc
hc
TE εσ
π
ε =




=

Ratio Thermometer
• A ratio thermometer is essentially two thermometers sensitive to
different wavebands built into a single body.
• For a thermometer operating at narrow wavebands of λ2and λ2,
the radiances Iλ1 and Iλ2 will be equal to ελ1 Ibλ1 and ελ2 Ibλ2
( )








−
=
1
12
,
1
5
1
2
11
kT
hc
e
hc
TI
λ
λ
λ
ελ ( )








−
=
1
12
,
2
5
2
2
22
kT
hc
e
hc
TI
λ
λ
λ
ελ
( )
( )
R
e
e
TI
TI
kT
hc
kT
hc
=










−
−
=
1
1
,
,
1
2
5
1
5
2
2
1
2
1
λ
λ
λ
λ
λ
λ
ε
ε
λ
λ

• The signals from the detectors are processed to produce an output
which is a function of R.
• If ελ1 = ελ2 i.e., the body is grey, then the output is independent of
emissivity.
• Similarly the output will be unaffected by partial obscuration of the
target provided that both channels are equally affected.
• At first sight the ratio thermometer appears very attractive.
• It does, however, suffer from some limitations.
• First, very few bodies are exactly ‘grey’ and the deviation from
‘greyness’ creates a measurement error if it is not known accurately.
• Furthermore the inherent accuracy of a ratio thermometer is less
than that of a single-wavelength instrument.
• A single-channel thermometer with wavelength λ1 has
( )
( )










= 2
1
1,1
,1
1
TdT
TdI
TI
k
hc
λ
λ
λ

Similarly for a ratio thermometer
















−= 2
21
111
TdT
dR
R
k
hc
λλ
The ratio thermometer can therefore be considered to behave in the
same way as a single-channel instrument whose effective
wavelength λe is given by






−=
21
111
λλλe
The effective wavelength of the thermometer will therefore be longer
than that of at least one of the channel and consequently its sensitivity
will be lower than that of a single waveband thermometer.

Anatomy of Ratio Radiation Thermometer

Principal components of radiation thermometers
• All radiation thermometers contain the same principal
elements, namely
• an optical system.
• a detector and
• signal processing facilities.

Optical system
• The purpose of the optical system is to collect the
incoming radiation and direct it onto the detector.
• Filters may also be included to restrict the
waveband used.
• Depending on the nature of the application, the
desired accuracy of the thermometer and the cost
that can be tolerated, the optical system may be
one of the following types:
(1) Aperture optics
(2) Mirror systems
(3) Lens systems
(4) Fiber optics.

Detectors
• The detector is the key component in a radiation thermometer,
being the means by which the incident radiation is converted to a
measurable parameter.
• parameters by which a detector is selected.
• (i) Spectral responsivity describes in a relative sense the manner
in which the output of the detector varies with the wavelength of
the incoming radiation.
• It can be expressed in terms either of output per unit of incident
energy in a given wavelength interval or of output per photon
arriving in the wavelength interval.
• (ii) Detectivity describes the signal-to-noise ratio of the detector
in relation to incident radiant power, and defines the resolving
power of the detector.
• (iii) Linearity. A linear relationship between the output of a
detector and the incident radiation flux is a useful property.
• (iv) Response time describes the manner in which a detector
responds to changes in the incident radiation.

Thermal Detectors
• The incident radiation causes an increase in temperature of
the detector, thereby creating a change in its temperature-
dependent properties.
• The measurement of one of these will provide information
about the temperature of the detector and, by inference, the
rate of incident energy and the temperature of the source of
the radiation.
• Thermal detectors generally have a spectral response
which is uniform over a broad band, making them
particularly useful for total radiation and wide-band
thermometers.
• The most commonly used thermal detectors are
thermopiles, bolometers and pyroelectric crystals.

Photon Detectors
• Photon detectors are those in which the incidence of a photon
causes a change in the electronic state of the detector.
• The integrated effect of individual photons creates a change of
measurable magnitude.
• There are numerous photon effects of which the photoconductive
and photovoltaic effects are those most commonly used for the
detection and measurement of infrared radiation.
• In either case incident photons excite carriers in the detector
material from a non-conducting to a conducting state.
• The photon must have sufficient energy to overcome the gap
between the bands,
sEE
hc
>=
λ
where h is Planck's constant, λ is the
wavelength, c is the velocity of light, E is
the energy of the photon and Es, is the
excitation energy.

Spectral response of a photon detector

Spectral response of commonly used photon and
thermal detectors

Non Black Bodies : Determining Emissivity
• There are various methods for determining the emissivity
of an object.
• Emissivity of many frequently used materials in a table.
• Particularly in the case of metals, the values in such tables
should only be used for orientation purposes since the
condition of the surface can influence emissivity more than
the various materials themselves.

Pyrometer with emissivity setting capability
• Heat up a sample of the material to a known temperature
that you can determine very accurately using a contact
thermometer.
• Then measure the target temperature with the IR
thermometer.
• Change the emissivity until the temperature corresponds to
that of the contact thermometer.
• Now keep this emissivity for all future measurements of
targets on this material.

Reference Target
• At a relatively low temperature (up to 260°C), attach a
special plastic sticker with known emissivity to the target.
• Use the infrared measuring device to determine the
temperature of the sticker and the corresponding
emissivity.
• Then measure the surface temperature of the target without
the sticker and re-set the emissivity until the correct
temperature value is shown.
• Now, use the emissivity determined by this method for all
measurements on targets of this material.

Black Body Reference
• Create a blackbody using a sample body from the material to be
measured.
• Bore a hole into the object.
• The depth of the borehole should be at least five times its diameter.
• The diameter must correspond to the size of the spot to be measured
with your measuring device.
• If the emissivity of the inner walls is greater than 0.5, the emissivity
of the cavity body is now around 1, and the temperature measured in
the hole is the correct temperature of the target.
• If you now direct the IR thermometer to the surface of the target,
change the emissivity until the temperature display corresponds
with the value given previously from the blackbody.
• The emissivity found by this method can be used for all
measurements on the same material.

Reference Black Coating
• If the target can be coated, coat it with a matte black paint.
• "3-M Black" from the Minnesota Mining Company or
• "Senotherm" from Weilburger Lackfabrik, either which
have an emissivity of around 0.95).
• Measure the temperature of this blackbody and set the
emissivity as described previously.

Merits of Radiation thermometers
• No contact or interference with process
• No upper temperature limit as thermometer does not touch
hot body
• Accurate and stable over a long period if correctly
maintained
• Quick response (1 ms to 1 s, according to type)
• Long life
• High sensitivity

Effect of Ambient Conditions
Typical measuring windows
are 1.1--1.7 µm, 2 --2.5 µm,
3.5 µm and 8.14 µm.

Point to Field Measurement of Temeprature

Optical Imaging for Temperature Measurement
P M V Subbarao
Professor
Mechanical Engineering Department
Simultaneous Measurement of Temperature at
Infinite Locations …….

Interferometry for Temperature Measurements
• Interferometry is the technique of diagnosing the properties of
two or more waves by studying the pattern of interference
created by their superposition.
• The instrument used to interfere the waves together is called an
interferometer.
• Interferometry is an important investigative technique in the
fields of astronomy, fiber optics, engineering metrology, optical
metrology, oceanography, seismology, quantum mechanics,
nuclear and particle physics, plasma physics, and remote
sensing.[
• In an interferometer, light from a single source is split into two
beams that travel along different paths.
• The beams are recombined to produce an interference pattern
that can be used to detect changes in the optical path length in
one of the two arms.
• Here we discuss about the use of the Mach-Zehnder
interferometer in measurements of the index of refraction.

Idealized Interferometer
Case 1
Case 2
Beam A1 Beam B1
Beam A2 Beam B2
Physical distance
traveled by beam A1,
xa1= Physical distance
traveled by beam B1,
xb1
Physical distance
xa2 < Physical distance
traveled by beam B2,
xb2

Idealized Interferometer
Case 1
Case 2
Beam A1 Beam B1
Beam A2 Beam B2
Optical distance
n1 λa1= Physical
distance traveled by
beam B1, n1 λb1
Physical distance
n2 λa2 < Physical
distance traveled by
beam B2, n2 λb2
λa1= λb1= λa2= λb2

Schematic diagram of the Mach-Zehnder interferometer

Theory
• In the measurement of the index of refraction using the Mach-
Zehnder interferometer, a sample of thickness d with index of
refraction n0 is inserted in one of the arms of the interferometer.
• The insertion of this sample increases the optical path length in
this arm due to the fact that light travels more slowly in a
medium' as compared to air.
• The optical path length in the sample is equal to n0d.
• When the temperature of the sample changes, the index of
refraction will change to n.
• This corresponds to a change in the optical path length of (n -
n0)d.
• This will result in a shift of the fringe pattern by ∆m fringes
where
( )
λ
dnn
m 0−
=∆

Index of Refraction of Water
• The dependence of the index of refraction n of water on
wavelength, temperature and density hasrecently been studied by
Schiebener et.
• Using a large number of experimental data sets published
between 1870 and 1990 they arrived at the following formula
where

∀ ρ is the density, λ is the wavelength, T the absolute temperature,
a0 to a7 are dimensionless coefficients, and
∀ λr and λuv are the effective infrared and ultraviolet resonances
respectively.
The equation holds for the following ranges:

Index of Refraction of Air
• The index of refraction n of dry air at 15 °C and a pressure of 1.01
3 x 105
Pa has been calculated from the expression
where σ = 1/λac and λac is the wavelength in vacuum of the laser beam in
µm.
This equation is valid for wavelengths between 200 nm and 2 µm.
For pressures and temperatures different from the indicated values, the
value of (n -1) has to be multiplied by

Experimental Set-up
Test Field

Onset of Convection
Ra = 1.4 X 104 Ra = 5.0 X 104

Non-intrusive Methods of Temperature Measurement ( Radiation Thermometry )

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Non-intrusive Methods of Temperature Measurement ( Radiation Thermometry )

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