Title: Radiation Thermometry
1Radiation Thermometry
- P M V Subbarao
- Professor
- Mechanical Engineering Department
Non-intrusive Methods of Temperature Measurement
2Temperature 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.
3Hemispherical Black Surface Emission
Emissive Intensity
The radiation emitted by a body is spatially
distributed
4Spherical Black Volumetric Emission
The radiation emitted by a body is spatially
distributed
5Planck 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.
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
6The 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.
7Emissivity
- 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 Il
to the monochromatic blackbody emissive power Ibl
at the same temperature is the spectral
hemispherical emissivity of the surface.
8Basic Ideas for Radiation Thermometers
- The wavelength of maximum emission varies between
10.6 mm at 0C and 1.3 mm at 20000C. - 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.
9- The radiant flux, El falling on the detecting
element of a thermometer in the incremental
waveband dl will be
where A is the throughput of the optical system,
describing the geometric extent of the beam of
radiation falling on the detector Bl is the
spectral transmission of the optical system Pl,
is the spectral transmission of the medium
between the instrument and the target.
10For a radiation detector whose responsivity, Rl
is independent of all variables but wavelength
where dV is the output in response to the radiant
flux. dEl
Therefore
and
11This equation is known as the 'radiometer
measurement equation' and relates the output
signal to the target radiance and hence its
temperature.
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.
12Design 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.
13Anatomy of Radiation Pyrometers
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15- 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 dl, centered on wavelength l. - Using the approximate form of Planck's equation
which is valid for most practical circumstances
16we differentiate with respect to T to obtain
The error in measured temperature, dT. created by
an error dIb in measuring Ib can be expressed as
17Precision 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.
18Classification 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.
19Partial 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 500C. - 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.
20- 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.
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22Total 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.
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24Ratio 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 l2 and l2, the radiances Il1 and Il2 will be
equal to el1 Ibl1 and el2 Ibl2
25- The signals from the detectors are processed to
produce an output which is a function of R. - If el1 el2 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 l1
has
26Similarly for a ratio thermometer
The ratio thermometer can therefore be considered
to behave in the same way as a single-channel
instrument whose effective wavelength le is given
by
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.
27Anatomy of Ratio Radiation Thermometer
28Principal components of radiation thermometers
- All radiation thermometers contain the same
principal elements, namely - an optical system.
- a detector and
- signal processing facilities.
29Optical 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.
30Aperture of a Pyrometer
31Effect of Lens
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33Detectors
- 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.
34Thermal 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.
35Photon 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,
where h is Planck's constant, l is the
wavelength, c is the velocity of light, E is the
energy of the photon and Es, is the excitation
energy.
36Spectral response of a photon detector
37Spectral response of commonly used photon
andthermal detectors
38Non 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.
39Pyrometer 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.
40Reference Target
- At a relatively low temperature (up to 260C),
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.
41Black 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.
42Reference 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.
43Merits 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
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45Effect of Ambient Conditions
Typical measuring windows are 1.1--1.7 µm, 2
--2.5 µm, 3.5 µm and 8.14 µm.
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47Point to Field Measurement of Temeprature
48Optical Imaging for Temperature Measurement
- P M V Subbarao
- Professor
- Mechanical Engineering Department
Simultaneous Measurement of Temperature at
Infinite Locations .
49Interferometry 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.
50Idealized Interferometer
Case 1
Physical distance traveled by beam A1, xa1
Physical distance traveled by beam B1, xb1
Beam B1
Beam A1
Beam B2
Physical distance traveled by beam A2, xa2 lt
Physical distance traveled by beam B2, xb2
Beam A2
Case 2
51Idealized Interferometer
Case 1
Optical distance traveled by beam A1, n1 la1
Physical distance traveled by beam B1, n1 lb1
Beam B1
Beam A1
Beam B2
Physical distance traveled by beam A2, n2 la2 lt
Physical distance traveled by beam B2, n2 lb2
Beam A2
Case 2
la1 lb1 la2 lb2
52Schematic diagram of the Mach-Zehnder
interferometer
53Theory
- 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 Dm fringes where
54Index 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
55- r is the density, l is the wavelength, T the
absolute temperature, a0 to a7 are dimensionless
coefficients, and - lr and luv are the effective infrared and
ultraviolet resonances respectively.
The equation holds for the following ranges
56Index 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 s 1/lac and lac is the wavelength in
vacuum of the laser beam in mm. This equation is
valid for wavelengths between 200 nm and 2 mm.
For pressures and temperatures different from
the indicated values, the value of (n -1) has to
be multiplied by
57Experimental Set-up
Test Field
58Rayleigh Benard convection
59Interference Pattern
60Signs of Pure Conduction
61Onset of Convection
Ra 5.0 X 104
Ra 1.4 X 104
62High Rayleigh Number RBC
63Transition to Turbulence
64Natural Convection Fringes