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Radiation Thermometry

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Title: Radiation Thermometry


1
Radiation Thermometry
  • P M V Subbarao
  • Professor
  • Mechanical Engineering Department

Non-intrusive Methods of Temperature Measurement
2
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.
3
Hemispherical Black Surface Emission
Emissive Intensity
The radiation emitted by a body is spatially
distributed
4
Spherical Black Volumetric Emission
The radiation emitted by a body is spatially
distributed
5
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.

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
6
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.
7
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 Il
    to the monochromatic blackbody emissive power Ibl
    at the same temperature is the spectral
    hemispherical emissivity of the surface.

8
Basic 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.
10
For 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
11
This 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.
12
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.

13
Anatomy of Radiation Pyrometers
14
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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

16
we 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
17
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.

18
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.

19
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 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.

21
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22
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.

23
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24
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 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

26
Similarly 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.
27
Anatomy of Ratio Radiation Thermometer
28
Principal components of radiation thermometers
  • All radiation thermometers contain the same
    principal elements, namely
  • an optical system.
  • a detector and
  • signal processing facilities.

29
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.

30
Aperture of a Pyrometer
31
Effect of Lens
32
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33
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.

34
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.

35
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,

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.
36
Spectral response of a photon detector
37
Spectral response of commonly used photon
andthermal detectors
38
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.

39
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.

40
Reference 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.

41
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.

42
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.

43
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

44
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45
Effect of Ambient Conditions
Typical measuring windows are 1.1--1.7 µm, 2
--2.5 µm, 3.5 µm and 8.14 µm.
46
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47
Point to Field Measurement of Temeprature
48
Optical Imaging for Temperature Measurement
  • P M V Subbarao
  • Professor
  • Mechanical Engineering Department

Simultaneous Measurement of Temperature at
Infinite Locations .
49
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.

50
Idealized 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
51
Idealized 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
52
Schematic diagram of the Mach-Zehnder
interferometer
53
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 Dm fringes where

54
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
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
56
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 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
57
Experimental Set-up
Test Field
58
Rayleigh Benard convection
59
Interference Pattern
60
Signs of Pure Conduction
61
Onset of Convection
Ra 5.0 X 104
Ra 1.4 X 104
62
High Rayleigh Number RBC
63
Transition to Turbulence
64
Natural Convection Fringes
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