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C H A P T E R 1
Overview of Radiation Thermometry
Zhuomin M. Zhang1 and Graham Machin2
Contents
1. Introduction 12. Basics of Radiometric Temperature Measurements 4
2.1. Total radiation thermometry 52.2. Spectral radiation thermometry 62.3. Design considerations 9
3. Types of Radiation Thermometers 113.1. Classical radiation thermometry 113.2. Emissivity correction methods 133.3. Fiber-optic radiation thermometry 18
4. Terms Commonly Used in Radiation Thermometry 215. Summary 24References 24
1. Introduction
An intuitive understanding AU :1of temperature, associated with thesensations of hot and cold, has been recognized since ancient times.However it was not until 1592, when Galileo invented the airthermoscope, that quantitative thermometry began. Extensive investiga-tions of various types of liquid-in-glass thermometers in the 17th centuryled to the establishment of the Fahrenheit temperature scale (first reportedin 1724) and the Celsius (or Centigrade) temperature scale (174221744).Some 100 years later in the middle of the 19th century, based on theprinciples of thermodynamics, Lord Kelvin (William Thomson) laid thefoundation of the thermodynamic temperature scale. Today the reliable
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AU:2
1 George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta,GA 30332-0405, USA
2 Division of Industry and Innovation, National Physical Laboratory, Teddington, Middlesex, TW11 0LW, UK
Experimental Methods in the Physical Sciences, Volume 42 r 2009 Elsevier B.V.ISSN 1079-4042, DOI 10.1016/S1079-4042(09)04201-5 All rights reserved.
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measurement of temperature has become an essential component of nearlyevery field of science and industry, including agriculture, biomedicine,chemical and materials processing, earth and atmospheric sciences,manufacturing, and remote sensing [1,2].
Since the early 1900s there have been tremendous advances in all areasof science and technology, e.g., in microelectronics, materials processing,fiber optics, laser, and imaging. Consequently, there has been a surge ofresearch and development activities in temperature measurement, either bymodifying earlier methods or by developing novel techniques. Thiscontinuous progress in thermometry is readily seen from the paperspresented at the symposia on Temperature: Its Measurement and Control inScience and Industry. The first symposium was held in 1919, and the twomost recent ones were held in 1992 (seventh) and 2002 (eighth) [3,4]. Inaddition, the tri-annual TEMPMEKO symposia on temperature andthermal measurements in industry and science [5], organized by theTechnical Committee (TC12) on Temperature and Thermal Measure-ments of the International Measurement Confederation (IMEKO), havealso charted the developments of thermometry, since their inception in1961. The most recent proceedings of these symposia (TEMPMEKO 2007,tenth symposium) were published as special issues in International Journalof Thermophysics (200722009) [6].
Every object emits thermal radiation when it is at a temperature aboveabsolute zero. When its temperature approaches 1,000 K, the object beginsto emit visible light. A sound understanding of electromagnetic waves,especially thermal radiation, was developed by Maxwell, Kirchhoff, Stefan,Boltzmann, Rayleigh, Jeans, Wien, and Planck in the late 19th century andat the beginning of the 20th century. As the temperature of an object rises,it begins to glow, firstly dull red (near 900 K) progressing through light red,orange, yellow, white, blue, and so on. In previous times, metalworkersand glassblowers relied heavily on this incandescence to determine theworking temperature ranges by color in order to properly temper, anneal,and/or shape the work pieces. In essence, the human eye was the firstradiation thermometer. Relying on subjective measurements by the eyebegan to be superseded when the first optical pyrometer was introduced bythe French chemist Le Chatelier in 1892. A United States patent wasgranted to Morse in 1899 for the disappearing filament optical pyrometerfor noncontact temperature measurements. Total radiation thermometersbased on the Stefan2Boltzmann fourth-power law were also developedduring the earlier part of the 20th century. The Morse pyrometer used thehuman eye as the photodetector to compare the brightness temperature ofthe object with that emitted by a tungsten filament, the device becameknown as the disappearing filament pyrometer. It was the dominantinstrument for high-temperature measurements in the first half of the 20thcentury [7]. In the 1950s, several national laboratories began to employ
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Zhuomin M. Zhang and Graham Machin2
photomultipliers (based on the photoelectric effect and secondary electronemission) as the physical detector for the calibration of optical pyrometers[8]. More recently, significant advances in optoelectronics, photodetectors,and radiometers have led to the production of a wide variety of detector-based luminous intensity scale and detector-based radiation thermometers[9]. Detector-based radiation thermometers have been the prevailingtechnologies for noninvasive temperature measurement since the mid-1980s. These devices generally measure infrared radiation, and hence theterm infrared thermometer is commonly used for radiation thermometers.Line scanners and/or infrared cameras/imagers have been used to obtainthermal images that map the surface temperature distribution of the object.For specialist applications, thermal radiation can be used to measuretemperatures down to a few kelvins. Indeed, measurement of the cosmicmicrowave background radiation allows the determination of thetemperature of the universe to be 2.7 K [10].
Since 1990 radiation thermometers, whose operation is based onPlanck’s law of thermal radiation, have been used to establish thetemperature scale above 961.781C using the freezing point of silver, gold,or copper as a reference temperature according to the InternationalTemperature Scale of 1990 (ITS-90) [11213]. In addition, becauseradiation thermometry is based on a fundamental physical law, primaryradiation thermometers have been used to realize the temperature scale inthe range from 1,000 to 3,000 K [14]. The development of high-performance cryogenic radiometers has made it possible to accuratelycharacterize narrowband filter radiometers for low uncertainty radiometrictemperature measurements [15220].
Radiation thermometers belong to the noninvasive class of temperaturemeasurement techniques. It has several unique advantages such as the abilityto reliably follow rapid temperature changes. In some cases, it can measuresmall objects or map the temperature distribution with a spatial resolution ofa few micrometers. It can be used in a harsh environment where the hightemperature, high pressure, corrosion, and/or contaminations would prohibitthe use of other types of thermometers. Traditionally, radiation thermo-meters have been used in determining flame and furnace temperatures forcombustion and materials processing, glass, aluminum, plastics, and steelindustries. More recently, radiation thermometers have also been used forsemiconductor processing, asphalt and cement industry, paper industry, foodindustry, and advanced manufacturing such as laser welding and laser cutting.Furthermore, thermal imaging has been used for remote sensing of earthsurface and sea temperatures, monitoring the thermal performance ofbuildings, tracking forest fires, homeland security, medical diagnostics, as wellas diagnostics of hot spots in microelectronic circuit boards.
This two-volume set is devoted to radiometric temperature measure-ments. Part 1 (Vol. 42) focuses on the fundamental aspects and Part 2
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Overview of Radiation Thermometry 3
(Vol. 43) deals with various industrial and scientific applications. Thischapter provides an overview of the theory (Section 2), classification(Section 3), and common terminology (Section 4) related to this importantfield.
2. Basics of Radiometric Temperature
Measurements
A schematic setup for radiometric temperature measurement isillustrated in Figure 1. The source of thermal emission is the target forwhich the temperature is to be measured. A lens confines the field of viewand a bandpass optical filter determines the spectral region within which thethermal radiation is to be measured. An aperture is placed in front of thedetector to avoid stray light being detected. The output signal (voltage orcurrent) from the detector is amplified and measured by a signal processor.When a radiation thermometer is used to measure the temperature of a realsurface, two issues arise. The first is the unknown emissivity of the surface(which affects the emitted radiation from the target), and the second is theinfluence of the emission from and absorption by the environment (whichcan significantly influence the radiation reaching the detector). Theseeffects are shown in Figure 1. In addition, thermal or other electromagneticradiation from nearby objects can also be reflected from the target to theradiometer, causing additional uncertainty. Methods, with varying degreesof success, have been developed in an attempt to overcome these problems;examples of such approaches are the creation of a blackbody cavity on thesurface, two-color and multiwavelength methods, and the use of acontrolled reference source. In addition, the development of optical fibershas allowed radiometric temperature measurements for surface locationsotherwise inaccessible by imaging radiometers. In the rest of this section,different general techniques of radiation thermometry are described.
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dΩt
At
Target AtmosphereEmis. & Abs.
Lens
Filter
Aperture
Detector Assembly
To Signal Processor
Figure 1 Schematic diagram of a radiometric temperature measurement system.
Zhuomin M. Zhang and Graham Machin4
2.1. Total radiation thermometry
The fundamental theory and methodology of radiation thermometry havebeen well established. Total or broadband radiation thermometry is basedon the Stefan2Boltzmann law of thermal radiation (more details are givenin Chapter 3). For a blackbody, the total energy leaving the surface per unitarea (W/m2) is proportional to its temperature to the fourth power. Sinceemission from a blackbody is diffuse, the exitent radiance from a blackbodyat temperature T0 can be expressed as the total radiant exitance divided byp, such that,
Lb ¼sT 4
0
p(1)
where s is the Stefan2Boltzmann constant (given in Appendix A). A realsurface has an emissivity between 0 and 1, hence, the exitent radiancewithout considering reflection from an object at temperature T becomes
Lem ¼ sT 4
p(2)
Here, e is the directional-total emissivity since it is assumed that theemission is confined within a small solid angle (see Chapter 3 for moredetails). The total radiance temperature Tt (or apparent temperature) isdefined as the temperature at which a blackbody would emit the sameradiance toward the detector as that given in Equation (2). It can be easilyseen from Equations (1) and (2) that
T t ¼ ðÞ1=4T (3)
which is always smaller or at most equal to the true surface temperature.The difference between the true temperature and the radiance temperaturebecomes
DT ¼ T ð1 1=4Þ (4)
Equation (4) gives the error of reading without emissivity correction. Therelative error DT/T is 33% for e ¼ 0.2, 12% for e ¼ 0.6, and 4% fore ¼ 0.85. Suppose the emissivity is estimated and correction for the totalradiance temperature is made to deduce the measured temperature. Then,from Equation (3), we can see that a variation in is corresponding to avariation in T by
dTT¼
1
4
d
(5)
which is obtained by taking the derivative of Equation (3) with fixed Tt. InEquation (5), d signifies a small variation or uncertainty in the indicatedquantity. When the target temperature is 1,000 K, a 4% uncertainty in
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Overview of Radiation Thermometry 5
emissivity will result in a temperature uncertainty of 10 K. It should benoted that unless the environment is well controlled, the uncertaintybecomes much larger than that indicated by Equation (5). For this reason,total radiation thermometers are not particularly suited to industrialapplications. On the other hand, broadband devices, that approximate tototal radiation thermometers, based on thermopile or pyroelectric detectors,are deployed to measure near ambient temperatures. In special cases, such asin the infrared ear thermometer, the measurement area is similar to ablackbody cavity, i.e., the emissivity of the tympanic membrane/ear canalcombination is almost unity. The measurement with such devices isessentially based on radiative heat exchange between the source and thereceiver. Reasonable accuracy (0.120.21C), for infrared ear thermometersand other broadband devices can be obtained through calibration.
A very specialized example of using a total radiation thermometer is inexperiments for measuring Stefan2Boltzmann constant and the tempera-ture of a blackbody source with an absolute cryogenic radiometer [21] (seealso Chapter 2). In this case, very high accuracy can be achieved understrictly controlled environmental conditions.
2.2. Spectral radiation thermometry
The measurement equation of a bandpass spectral radiation thermometer isgiven by
Sl ¼ AtdOt
Z lþDl=2
lDl=2tlRðlÞLlðlÞdl (6)
where Sl is the detector output signal (in volts or amperes), At the targetarea perceived by the radiometer through a solid angle dOt (referring toFigure 1), tl the spectral transmittance of the optical system (e.g., lens andfilter), R(l) the detector responsivity, Ll(l) the spectral radiance thatreaches the detector from the target and the environment within the opticalpath and field of view, and Dl the bandwidth of the filter. It is assumed thatthere is no transmission outside of the bandwidth of the filter. Forsimplicity, the emission by and reflection from the detector are neglected inEquation (6). For a narrowband filter, Equation (6) can be approximated asfollows
Sl ¼ CILlðlÞ (7)
where CI is an instrument constant that is independent of the targetmaterial or temperature. For a freely radiating target (i.e., with coldsurroundings and negligible environment emission and absorption), theexitent spectral radiance is due purely to emission, therefore,
LlðlÞ ¼ Lem;lðl;T Þ ¼ lLb;lðl;T Þ (8)
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Zhuomin M. Zhang and Graham Machin6
where Lb;lðl;T Þ is the blackbody spectral radiance given by Planck’s law[13]:
Lb;lðl;T Þ ¼c1L
l5ðec2=lT 1Þ
(9)
where c1L ¼ 2hc20 is the first radiation constant for spectral radiance, and
c2 ¼ hc0=k the second radiation constant. Note that vacuum conditions areassumed for simplicity, while in practice the effect of the refractive index ofthe air may have to be considered for very high-accuracy applications. Inradiation thermometry practice, Wien’s formula
Lb;lðl;T Þ ¼c1L
l5ec2=lT(10)
is appropriate in most cases because c2=lT is usually much greater than 1.The radiance temperature Tl is defined by equating the blackbody radianceat Tl with the exitent radiance of the object at T; hence,
Lb;lðl;T lÞ ¼ lLb;lðl;T Þ (11)
Using Wien’s approximation given in Equation (10), the surfacetemperature is related to the spectral radiance temperature by
1
T¼
1
T lþ
lc2
ln l (12)
The difference between the true temperature and the radiance temperatureis
DT ¼ TlT l
c2
ln l (13)
As an example, Figure 2 shows the temperature difference for a targettemperature at 1,000 K at different wavelengths, along with that calculatedfrom Equation (4) to total radiation thermometer. It can be seen that as thewavelength decreases, the difference between the true temperature and theradiance temperature decreases. Furthermore, the difference becomessmaller when the emissivity is closer to unity. The uncertainty in themeasured temperature due to the uncertainty of emissivity can be obtainedby differentiating T with respect to el using Equation (12) for fixed Tl,resulting in
DTT¼
lTc2
Dll
(14)
It can be seen from Equation (14) that the impact of an uncertainty in theemissivity, given the measurement conditions, on the temperature accuracydecreases as l decreases. Now according to Wien’s displacement law, thewavelength at which Lb;lðl;T Þ is maximum is given by lmax ¼ c3=T ,
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Overview of Radiation Thermometry 7
where c3 is the third radiation constant. From Appendix A, we see thatc2=c3 4:965 5. Equation (14) can be further approximated by
DTT
l5lmax
Dll
(15)
The significant advantage of using spectral over total radiationthermometry at lolmax becomes clear when the influence coefficientsin Equation (15) are compared with those of Equation (5). It should benoted that the error due to Wien’s formula to Planck’s distribution is 0.7%at lmax and smaller at lolmax. Hence, Wien’s approximation is acceptablefor most radiometric temperature measurements.
If the target is not a blackbody and the surrounding radiation is notnegligible, LlðlÞ in Equations (6) and (7) is the sum of the emitted (by boththe target and the environment) and reflected spectral radiances:
LlðlÞ ¼ tenv½lLb;lðl;T Þ þ Lr;lðlÞ þ Lem;lðl;T envÞ (16)
where the term tenv accounts for the transmittance through the atmosphere(see Figure 1) and Lem;lðl;T envÞ is the contribution by the atmosphericemission (which is usually negligible unless in the case of hot gases orplasmas) that reaches the radiometer. The reflected spectral radiancedepends on the distribution of the surrounding radiation incident on thetarget and the bidirectional reflectance distribution function (BRDF) of the
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0
100
200
300
400
500
0 0.2 0.4 0.6 0.8 1
λ = 0.65 µm
λ = 0.95 µm
λ = 1.5 µm
λ = 2.4 µm
Total
∆T =
T -
Tλ
(K)
Emissivity
T = 1000 K
Figure 2 The difference between the true temperature and the radiance tempera-ture, as a function of emissivity, for both spectral and total radiation thermometers.
Zhuomin M. Zhang and Graham Machin8
target. Hence, except for well-controlled environment or in some limitedcases, LlðlÞ is difficult to determine and corrections must be made to obtainthe true temperature of the target.
2.3. Design considerations
The central problems in applying radiation thermometry are (1)determining the target emissivity, which depends on temperature, surfaceconditions, and angle of view and (2) reducing the influence of surroundingradiation and environmental effects such as absorption along the viewingpath so that the true surface temperature can be obtained. Anotherimportant issue is the accurate determination of the instrument constant CI
given in Equation (7). Neither of these issues is insurmountable,nevertheless great care and patience are required to perform radiometrictemperature measurements correctly. Calibration of the radiometer using atraceable blackbody source is a necessary first step to determine theinstrument constant and thus provide a sound platform for correct surfacetemperature measurements. Various methods have been developed to dealwith the emissivity problem, including the creation of a blackbody cavity,employing a reflecting mirror, applying a controlled reference source, dual-wavelength pyrometer, multispectral pyrometry, and spectrometric meth-ods or active laser methods. One of the solutions to the second problem isto slightly modulate the surface temperature with a laser source andmeasure the modulated signal. This method is called photothermalradiometry [22]. The optical fiber thermometry based on a sapphirelightpipe has been employed in the semiconductor industry using the‘‘ripple technique’’ [23,24]. Details of how to apply radiation thermometryto particular temperature measurement problems will be discussed insubsequent chapters of this volume and in the companion volume devotedto such measurements [25].
In general, issues that need to be addressed when developing a radiationthermometer are the following: wavelength selection; the optical system(such as lenses, mirrors, filters, and the use of aperture and field stops) tocollect the thermal radiation and to define the field-of-view of the targetand detector area; the detector that matches the spectral band and the signallevel of the emitted thermal radiance, along with the readout electronicsmatched to the detection system. A detailed treatment of the radiationthermometer design will be given in Chapter 4. Briefly, the wavelengthselection should match with the temperature range of the targets to bemeasured. An attempt should be made to reduce the atmospheric effect bychoosing a wavelength band that avoids emission or absorption by gasessuch as carbon dioxide and water vapor. The bandwidth can be selected tomatch with the detector signal requirements and signal-to-noise ratio.
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Overview of Radiation Thermometry 9
The sensitivity of the emitted radiance to temperature can be obtainedby differentiating Equation (11) with respect to T using Equation (10),giving
dLem;l
Lem;l¼
c2
lTdTT
(17)
If at a given T and l, we can approximate Lem;l as proportional to T to themth power, i.e., Lem;l ¼ aTm, we have
dLem;l
Lem;l¼ m
dTT
(18)
Comparison of Equations (17) and (18) suggests that the larger the m, themore sensitive the emitted radiance is to a temperature change of the target.Or put it another way, a small change in temperature results in a largechange in radiance. This is because the Planck curve as a function oftemperature has a very steep slope toward short wavelengths. As anexample, for T ¼ 1,000 K and l ¼ 1mm, we have mE14.4, which is muchgreater than the sensitivity of a total radiation thermometer (fourth power).It can be shown with the long-wavelength approximation of Planck’s law(i.e., the Rayleigh2Jeans limit) that the effective power or influencecoefficient m ¼ 1 when l-N, hence, shorter wavelengths are generallypreferred. This is consistent with the predicted reduction in temperatureuncertainty (when the wavelength of measurement decreases) for a givenemissivity uncertainty as prescribed by Equation (14). On the other hand,since the Planck function decreases rapidly as the wavelength is reduced toshorter than lmax for the same temperature, there is a trade-off in terms ofthe magnitude of the signal and the sensitivity of the radiant power withrespect to the temperature change. In most applications, the properwavelengths of radiation thermometer range from a few tenths of the peakwavelength lmax to slightly above lmax. For example, if a focal plane array isto be used for thermographic imaging near room temperature, theoperating wavelengths should be somewhere between 3 and 12 mm, takingcare to avoid atmospheric absorption bands. Liquid-nitrogen-cooled InSbdetectors with high sensitivity from 3 to 5 mm should have good sensitivity.Also, MCT (a HgCdTe alloy) focal plane array may be used in the spectralband from 8 to 12mm.
Radiation detectors can be divided into photon detectors (nonthermal)and thermal detectors. In photon detectors, direct interaction of electro-magnetic radiation (or photons) with electrons in a material may result inphotoelectric, photoconductive, or photovoltaic effect. For example, in aphotoconductive process, the absorption of incoming photons causeselectronic transitions from the valence band to the conduction band and,subsequently, generates free carriers (electrons and holes) that vary the
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Zhuomin M. Zhang and Graham Machin10
conductivity of the semiconductor material. Photon detectors are moresensitive and have a faster response than thermal detectors, which rely on thetemperature change of the detector material caused by the absorption of theincoming photons. Typical photon detectors that are used widely inradiation thermometers are based on silicon (Si) and indium gallium arsenide(InGaAs) photodiodes. On the other hand, thermal detectors are commonlycharacterized by a broadband absorption and excellent linearity. Typicalthermal detectors are thermopiles, pyroelectric detectors, and bolometers[26]. The bolometer was first invented by the American astronomer Langleyin 1878 based on the resistance change of a Pt metal strip (lampblack coated)due to a temperature change associated with the absorption of the incomingthermal radiation. Modern bolometers based on superconducting materialsoperate in the transition region between superconducting and normal statesand, hence, can be much more sensitive than those manufactured fromnormal metals [27]. Uncooled microbolometer arrays have recently beenfabricated using microfabrication techniques and commercially applied forthermal imaging and remote sensing [28].
3. Types of Radiation Thermometers
In this section the common, and many of the less common, types ofnoncontact thermometry methods are briefly described. Classical radiationthermometry is based on single-spot devices, with some restrictions inspectral band and with a single detector. Line scanners and thermal imagerswhich are extensions of the basic method are also discussed. Some morespecialized methods for emissivity correction are also described, such as thetwo-color pyrometry, multiwavelength radiometry, and polarimetry, aswell as active compensation methods such as reflectometry, increasing theapparent emissivity using multiple reflections, and some modulationtechniques. Finally, the use of fiber optics in thermometry is outlined,including lightpipes, phosphor, Fabry2Perot interferometry, and Bragggrating thermometry.
3.1. Classical radiation thermometry
Classical radiation AU :3thermometers comprise essentially three components:
(1) A means for collecting the radiation, either a lens that transmits in thesensitivity band of the detector, or a mirror, or even just an aperture.
(2) A means for restricting the spectral band of radiation sensed by thedetector; this could be an interference filter, a colored glass filter or theintrinsic bandpass of the detector, or a combination of the latter two.
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Overview of Radiation Thermometry 11
(3) A detector that is sensitive to the radiation emitted by the object ofinterest; its selection would be governed by the thermal emissionspectrum at the temperature of the object as well as concerns for therequired speed and sensitivity.
Single-spot thermometers are extensively used in industry over a verywide temperature range, from process control to quality control anddiagnostics (spot checks). More details are given in the companion volume[25]. These thermometers can be grouped into three types according to thetemperature of the object being measured.
3.1.1. High-temperature radiation thermometersUsed for temperature measurements typically above 6001C. Si photo-detectors are almost universally used due to its excellent linearity with alarge dynamic range, low noise, fast response, low cost and easy to fabricatedetectors with large areas, and wide spectral response (for wavelengths fromapproximately 400 to 1,050 nm) [29]. Lens optics is commonly adopted.This type of radiation thermometer is extensively used for process controland for heavy industry, such as glass and steel manufacturing.
3.1.2. Mid-temperature radiation thermometersUsed for typically temperatures from 1001C to 6001C. There exist a widervariety of technologies for detector choices since the operating wavelengthsare usually between 1 and 3mm. Examples are uncooled InGaAs or Gephotodiodes and PbS photoconductive detectors, as well as LN2-cooledInSb and InAs photodetectors of high detectivity. Thermal detectors such aspyroelectric detectors and bolometers are also used. Lens optics is mostlyemployed and the target sizes are generally larger compared with thosemeasured by high-temperature radiation thermometers in order to obtainsufficient radiant fluxes. This type of detectors is commonly used for Al,galvanneal, and other metals process.
3.1.3. Low-temperature radiation thermometersTypically for temperature measurements and thermal imaging from 01C upto 1001C. Since the wavelength range of interest is from 3 to 15mm,wideband or unfiltered thermal detectors are frequently used, includingbolometers, pyroelectric detectors, and thermopiles. LN2 or thermoelec-trically cooled MCT detectors are also common. Replica optics and mirroroptics are mostly used instead of lens optics. This type of radiationthermometer finds a wide range of applications in spot checks, paper andplastics industry.
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Zhuomin M. Zhang and Graham Machin12
An extension of low-temperature radiation thermometers are thermalimagers. In recent years, old scanning systems with cryogenic cooleddetectors (usually InSb or MCT) have largely given way to focal plane arraysand uncooled detector arrays for thermal imaging and remote sensing [30].
3.2. Emissivity correction methods
The biggest issue when trying to measure temperature by radiationthermometry is the emissivity of the surface. Various strategies have beenproposed to overcome the effect of emissivity with various degrees ofsuccess. Some of these are discussed below and are classified into two types:passive methods relying only on the emitted radiation from the surface oractive approaches reliant upon determining the emissivity by otherindependent means.
3.2.1. Dual-wavelength or ratio pyrometersThe essential measurement performed by a dual-wavelength pyrometer (alsocalled two-color pyrometer) is the emitted radiant flux from the same surfaceat two different wavelengths. The underlying assumption is that for thesurfaces whose temperatures are being measured, the emissivity is indepen-dent of wavelength (at least from l1 to l2, which are the wavelengths ofconcern). This is true for gray surfaces. By applying Equations (7), (8), and(11) to both wavelengths, we see that the ratio of the signals becomes
r ¼Sl1
Sl2
¼CI;11l
52ec2=l2T
CI;22l51ec2=l1T
l5
2
l51
expc2
l2T
c2
l1T
(19)
Usually CI;1 CI;2 due to the closeness of the two wavelengths. Thetemperature obtained from Equation (19) is called the ratio temperature:
Tr ¼c2ðl12 l1
1 Þ
lnðrl51=l
52Þ
(20)
This strategy is only successful if the emissivity of the surface is the same(which is rarely true for real surfaces) at the wavelengths of operation of thepyrometer. For surfaces whose emissivity varies linearly with wavelength,the slope of e(l) can in principle be used to correct Equation (20), but theslope itself is also difficult to determine. Hence, if the surface does notexhibit a flat emissivity, then it is always better to use a single-spotpyrometer and correct for the known emissivity.
The benefits of dual-wavelength pyrometry lie not so much in its abilityto correct for emissivity, as surfaces with emissivity which is invariant withwavelength are rare, but in the fact that it can perform reliable thermometryin situations which are unsuited to single-spot pyrometry. These are where
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Overview of Radiation Thermometry 13
the target is smaller than the spot size, or where wavelength neutral, butabsorbing gas or smoke obscures the field of view. In fact targets that onlyfill a few percent of the field of view can have their temperaturedetermined successfully by this method.
More sophisticated types of dual-wavelength pyrometry have beenimplemented for specific situations. For instance the aluminum and steelindustries present particular challenges for noncontact thermometry thatcan be addressed using dual-wavelength pyrometry, not in simple ratioform as described above but where an a priori known mathematical functiondescribes the relationship of emissivity at two different wavelengths.A successful implementation of this technique to the galvanneal process isdescribed in Ref. [31] while its application in the aluminum industry isoutlined in Refs. [32,33].
3.2.2. Multiwavelength pyrometersMultiwavelength pyrometry has been, and is periodically proposed, as thesolution to the emissivity problem. Suppose the emissivity can be expressedin terms of a given function of l with m unknown constants. If the radiancetemperature is measured at more than m wavelengths, the m constantstogether with the unknown surface temperature can be determined usingthe measured blackbody radiance or radiance temperature at eachwavelength. This is the principle of the multiwavelength (or multicolor)radiation thermometer. The least-squares method is often used if themeasured radiance temperature is at more than (m+1) wavelengths.Detailed discussions have been given in the literature [34236].
Classic examples of this are given in Gebbie et al. [37] and Svet [38]. It isproposed that by using the spectral radiance at a number of wavelengths (oreven the full emitted spectrum), coupled with an assumed model ofemissivity, it is possible to deduce both the temperature and the surfaceemissivity from the radiance data alone. However it has been shown[34,35,39] that, when there is no a priori knowledge of the emissivityvariation with wavelength, multiwavelength pyrometry has distinctdisadvantages and generally results in much larger temperature uncertaintiesthan those possible by much simpler methods, e.g., single-spot pyrometrywith a reasonable estimate of the emissivity [35].
As with dual-wavelength pyrometry, there are some specific situationswhere multiwavelength pyrometry can convey advantage, providedadditional information is known, in particular the functional relationshipof the emissivity function with wavelength. This has been demonstrated,e.g., on measurements of SiC samples [35] and also in the aluminum processindustry [38]. In both cases, a reasonable understanding of the variation ofemissivity with wavelength was achievable [35,38].
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In summary, multiwavelength pyrometry alone cannot solve the surfaceemissivity problem. For proper implementation a priori knowledge of atleast the functional form of the emissivity with wavelength is required toconstrain the uncertainties in temperature estimates. For some specificsituations, multiwavelength pyrometry might convey a measure ofadvantage, while on the whole single-spot pyrometry, armed with areasonable estimate of the surface emissivity is likely to be a simpler solutionand is likely to yield lower uncertainties for the temperature estimates.
3.2.3. Fourier-transform infrared spectrometryFourier-transform infrared (FTIR) spectrometry has been used extensivelyin chemical analysis, remote sensing, and the measurement of radiativeproperties. Since FTIR measurement is in a broad spectral region, theemissivity function can also be obtained through modeling, similar tomultiwavelength pyrometry. Some dielectric materials (e.g., SiO2, Al2O3,MgO) exhibit blackbody behavior at a single wavelength, called theChristiansen wavelength. This allows determination of the sampletemperature as well as emissivity by measuring the emission spectrum[40]. More discussion on the Christiansen wavelength will be given inSection 5.2 of Chapter 3. Markham et al. [41] used the FTIR emissionspectra at three slightly different sample temperatures (DTE501C) tomeasure the surface temperature at about 8001C in a flame environment.This ratio-difference method eliminates the background radiation effectand does not require a priori knowledge of the surface emissivity, as long asthe change in el is negligible at a given l. Large modifications of the sampletemperature, however, may cause the emissivity to vary and/or affect theprocess condition. Another apparatus used a hemi-ellipsoidal mirror tomeasure the radiative properties as well as temperature of the surface [42].A diffusely radiating near-blackbody source and the sample were mountedin the two foci of the hemi-ellipsoidal mirror; therefore, the radiationleaving the source was reflected diffusely onto the sample. This apparatuswas used to measure the spectral radiative properties (within 223%uncertainty) and surface temperature (within 101C uncertainty) [42].Hanssen and coworkers [43245] have developed an FTIR facility forcharacterization of materials emissivity and used the FTIR to determinesurface temperatures through a separate measurement of the reflectancewith integrating spheres. An FTIR spectrometer was also used togetherwith optical fibers to measure the temperature of a high-flux solar furnace[46]. Generally speaking, using an FTIR for thermometry is moreexpensive than traditional radiation thermometers, and thus it is not usedroutinely. The only reason for using an FTIR is because the additionalinformation such as gas emission and surface properties that may be inferredfrom the measurements is of value to the investigator.
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3.2.4. Polarization pyrometryThe technique known as polarization pyrometry is a possible method, formetallic surfaces, of overcoming the emissivity problem, even if it is varyingdue to oxidation or scale growth. The surface temperature is determined byexamining the polarization of the sum of the radiation emitted by thesurface and thermal radiation emitted by a blackbody reflected from thesurface [47,48]. The method is a relatively straightforward application ofKirchhoff’s law for individual polarization. The surface is irradiated at highangle of incidence, around 701, with unpolarized blackbody radiation; adetector then measures the specularly reflected radiation, which is partiallypolarized, since the reflection for p polarization exhibits a dip around thisangle. The radiation emitted from the surface is also partially polarized(higher for p polarization than for s polarization). It can be shown that thetotal radiation will not be polarized if the temperatures of the blackbodyand surface are equal, so that the unknown temperature of the surface canbe inferred from the blackbody temperature when the measured radiation isunpolarized. No quantitative response of the detector is needed since oneonly needs to find the temperature when the detector response isindependent of the analyzer (a polarizer between the sample and thedetector).
Experiments have shown that this technique is feasible [49,50].However, these early versions were limited in measurement time becausethe temperature of the blackbody had to be the same as that of the surface,this was time-consuming to achieve. One way of reducing the measure-ment time would be to fix the temperature of the blackbody and place avariable attenuator in front of the cavity. By changing the radiance bymeans of the attenuator, the null polarization position can be found rapidly[49]. More recent measurements have been made of very low emissivitymetals near room temperature [50] using this technique. However, ingeneral polarimetry has not been implemented on a wide scale. Additionaldiscussion of the use of ellipsometry for temperature and film thicknessmeasurements will be presented in Chapter 7.
3.2.5. Emissivity-enhancement methodsSeveral methods have been used to increase the apparent emissivity of thesurface and, consequently, to alleviate the emissivity problem. Oneimportant method that has been used extensively over the years for thecorrection of emissivity is the so-called ‘‘gold-cup’’ method [51,52]. In thismethod, a conventional single-spot radiation thermometer is used, butthe surface is not imaged directly. Instead, a metallic hemisphere bowl(usually cooled) is coated with a highly reflective material (e.g., gold, whichearns the name of this method). This hemispherical mirror is then broughtclose to the radiating surface and a quasi-blackbody radiation field is
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generated in the region enclosed by the ‘‘cup.’’ This radiation field is thenmeasured through a small hole in the cup by the detector either directly orthrough the intermediary of a fiber-optic bundle. The surface temperaturecan thus be inferred from the radiance temperature of the effectiveblackbody at the same temperature.
Different shapes of reflecting cavity type have been modeled [53] andoptimized for particular situations; e.g., aluminum sheet that has a very lowsurface emissivity. Another design [33] allows the temperature measure-ment of aluminum billets, which have to be conditioned to a particulartemperature, before they are extruded. The ‘‘cup’’ in this case has aparticular form that allows for some variation in the position of the billetwith respect to the cup while maintaining a high and fixed emissivity.
In some industrial processes it is not possible to deploy an activeemissivity-enhancement method. However through the use of thegeometry of the situation it is still possible to greatly reduce the emissivityeffects. This is done through positioning a conventional pyrometer so that itviews into a wedge made by two surfaces of the same temperature (e.g., thewedge generated where steel is being coiled from a flat sheet) [54] or whereit measures the radiation field between two slabs of material [55,56]. Inrapid thermal processing of silicon wafers, a reflective shield can be used toenhance the emissivity [23], and models have shown that the effectiveemissivity can be significantly enhanced but care must be taken to addressthe BRDF [57,58].
3.2.6. In situ emissivity determinationA straightforward method for emissivity correction is to directly measurethe reflectance by a build-in reflectometry. A pulsed or cw laser AU :4source canbe used to measure the reflectance of the target and the emissivity can beinferred by the use of Kirchhoff’s law [59].
Another method, first proposed and trialed by DeWitt and Kunz [60],involves the introduction of a small thermally induced perturbation to thethermal radiation emitted by a (hot) surface. This is done by employing thephotothermal effect whereby a modulated laser beam, with sufficientpower hence the use of a class 4 type, is used to introduce a periodic changein the emitted radiation. The perturbation is small usually of order of adegree or so on surfaces that can be in excess of 1,0001C. The basic methodworks as follows: two high-powered lasers operating at wavelengths l1 andl2 are modulated at frequencies o1 and o2 respectively. The criticalmeasurement is that of the modulated thermal radiance at l1 arising fromlaser l2 and the modulated thermal radiance at l2 arising from laser at l1.
The ratio of these two thermal radiances, from which temperature can becalculated, is effectively independent of surface emissivity, opticaltransmission, and reflected radiation [61,62].
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Different variations of the basic technique have been developed[61265], some employing optical fibers [62264] to transfer the lasers to themeasurement surface and to capture the emitted signal. Others have usedmirror [64,65] instead of lens optics [61,63]. Most have been demonstratedin the laboratory and uncertainties in the technique have been typicallyfrom 31C to about 101C dependent on the surface under investigation[63265]. Some developments have gone further and been specificallydeveloped for trials in industrial settings [62,64,65]. Typical targetapplications include steel production, reformer tube measurements, andthe heat treatment of turbine blades. However despite this significantactivity no commercial device currently exists and there is resistance to itsintroduction into an industrial setting largely because of safety concernsabout the use of high-powered lasers.
One feature of the method is that it can be used to determinethermophysical properties such as emissivity and thermal diffusivity as wellas surface temperatures [66]. This feature may be useful in the future if online measurement of properties for process control is required.
3.3. Fiber-optic radiation thermometry
This generally falls into two classes. The first is termed ‘‘thermal fiber-opticthermometry.’’ The distinguishing feature of this type of thermometers is thatan optical fiber or optical-fiber bundle is used to convey emitted thermalradiation to a detector. This is often used in very hostile environments orwhere access is limited. Typical areas of applications are in aerospaceengines or the steel industry. A variant on this is the use of lightpipes orincorporated blackbody often used in semiconductor processing. A secondclass of fiber-optics thermometers that do not depend on emitted thermalradiation but on the temperature-sensitive properties of something else,often, but not necessarily, are incorporated into the fiber itself. This groupof techniques is termed for convenience as ‘‘nonthermal fiber-opticthermometry.’’ The most common of these are based on properties such asfluorescence timescales or building into the fiber itself a temperature-sensitive element such as a Fabry2Perot interferometer or a Bragg grating.These second type of fiber-optic thermometers are often, but notexclusively, for relatively low-temperature applications (up to a fewhundred degrees Celsius). They are generally used where electromagneticimmunity is essential such as in microwave processing of materials or inhigh-magnetic fields, e.g., magnetic resonance imaging. One big advantageover the first type of thermometer is that the thermometric performance ofthe device is less, or even not, sensitive to the fiber being bent, changes intransmission losses, or even progressive optical degradation 2 provided, ofcourse, that light can still be transmitted by the fiber. Not all types are
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described in this section and the interested reader is referred to Refs.[2,67269] for a comprehensive outline of methods.
3.3.1. Thermal fiber-optic thermometryThese types of thermometers are simply an extension of the classical radiationthermometry technique. The detector and wavelength-defining filter areusually the same as in conventional radiation thermometry. The maindifference is that instead of free space between the thermometer and theobject a fiber-optic bundle is used to convey the thermal radiation from theobject whose temperature is being determined. The fiber-optic bundle isnearly always heavily armored to protect it from the hostile environment inwhich it needs to operate. This type of thermometer is mostly used eitherbecause of accessibility issues, i.e., no clear line of sight to the target ispossible, or to remove the sensitive detector and electronics from a hostileenvironment. One particular application is monitoring the health of turbineblades in, e.g., the combustor region of a gas turbine engine both on militaryand civil aircraft engines [70,71]. Here, early detection of overheating bladestriggers preventative maintenance ensuring optimal and safe performance ofaircraft and power generation turbines [72].
3.3.1.1. Immersed optical fiber. This type of device is used in the metal-processing industry, primarily the steel industry [73]. Here an optical fiber isprogressively immersed into a vat of molten metal from a large reel of fiber.On immersion the fiber tip forms an equivalent cylindrical cavity with anisothermal wall of molten metal. Since the fiber is so thin (0.125 mm) evena small immersion creates a long cavity compared to its diameter and hencethe conditions for producing a good blackbody are achieved. The fiberitself then conveys this blackbody radiation back to a detection system thatcorrects for the changing length of the fiber reel and determines thetemperature. The original work required the use of special metal clad fibers[73] but subsequent research has shown that with care more ordinary fiberscan be used for the same application [74].
3.3.1.2. Lightpipe and incorporated blackbody types. Fiber optics canbe used as lightpipes. In this case, single-crystal sapphire ‘‘fiber’’ is used. Theadvantage is that it can be used to very high temperatures (above 1,8001C).A variant on this sensor coats the end of the fiber with a refractory metalforming a quasi-blackbody on the tip thereby negating emissivity effectsarising from the target [75]. These types of thermometers, particularly thesingle-crystal lightpipe types, are used extensively in the semiconductorprocessing industry where minimal intrusion, rapid response, and robustnessagainst high temperatures are essential [76278].
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3.3.2. Nonthermal fiber-optic thermometry3.3.2.1. Phosphor-based methods. This ‘‘noncontact’’ method is basedon the use of phosphors. The technique utilizes inorganic compounds thatfluoresce when appropriately stimulated. The excitation usually comesfrom a spectrum that has higher photon energy than the correspondingfluorescence. Typical excitation sources are a xenon flash or a bright lightemitting diode. The brightness of the fluorescence decays exponentiallyover time and it is this fluorescence lifetime (typically W1 ms), which is astrong function of temperature, and hence is exploited for thermometry.There are many different types of materials that can be used as phosphors,e.g., Cr3+-doped insulating crystals, Nd:YAG, GaAs, and so forth. Theexact choice of phosphor depends on the range, sensitivity, and even thestability required by the particular thermometer. These are described indetail in Ref. [69].
The phosphor itself is often incorporated into the tip of a fiber, thestimulation light is conveyed to the phosphor material by the fiber and theresultant fluorescence is then conveyed by the same fiber to the detectionsystem. This type of device is often used in environments unsuitable formetal sensors such as microwave ovens or magnetic resonance imagingdevices [79]. Alternatively, the object whose temperature needs to bedetermined can be coated with a phosphor, which is then stimulated by anexternal light source and the luminescence detected by an optical system.This method has been used to investigate turbine engines, internalcombustion engines, and in the metal-processing industry such as thegalvanneal process [80,81].
Understanding the temporal and temperature responses of the phosphorsis essential to their performance as temperature measurement devices.A carefully thermostatted environment is required if this response is to beaccurately determined [82]. This type of thermometry is still an activeresearch field, e.g., identifying new phosphors [83] and pushing theboundaries of applications such as nanoscale thermometry using fluores-cence [84] and in microfluidics [85].
3.3.2.2. Temperature-sensitive elements intrinsic to the fiber. Thistype of sensor depends on the change of a particular property of thetemperature-sensitive element with temperature. There are several differenttypes of thermometers based on different properties; the two describedbelow are both based on changes in dimension of the sensitive element, inboth cases the sensor is incorporated within the fiber.
(1) A Fabry2Perot interferometer employs the interference effect inside adielectric film whose surface is coated by highly reflecting mirrors. Thethickness of the dielectric is a function of temperature. In aFabry2Perot thermometer, a Fabry2Perot etalon is essentially fixed
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to the end of the fiber. Light is sent down the fiber and partially reflectsoff the fiber2dielectric interface and partially off the dielectric2airinterface. These two reflected beams interfere with each other and aninterference pattern is detected, this can be related to the gap betweenthe two surfaces. As the temperature of the etalon changes this gap andalso the refractive index changes, the interference pattern shifts and thisshift can be calibrated in terms of temperature [67,86].
(2) A Bragg grating when incorporated within the matrix of an optical fibercan also be used as a temperature sensor. In this type of sensor thetemperature-sensitive element is a periodic change in the index ofrefraction in the core of the optical fiber. When a broadband source oflight is sent down the fiber and the region containing the grating isexposed to a change in temperature the period of grating changes andthe wavelength of light reflected from the grating changes [2,67,87].Interpretation of the output of such devices can be difficult as theoutput is sensitive to strain as well as temperature [87]. A number of thistype of sensor can be distributed along a long fiber (length ofkilometers) and interrogated using a broadband light source. The timetaken for the reflected light to return to the detector indicates how far aparticular sensor is from the detector. This type of device is particularlyuseful for monitoring large industrial plants.
4. Terms Commonly Used in Radiation
Thermometry
This section provides a glossary of radiation terms in layman language.More details can be found from, e.g., Meyer-Arendt [88], InternationalCommission of Illumination (CIE) publication [89], American Society ofTesting and Materials (ASTM) documentation [90,91].
Absorption: The process of converting photon energy tosome other types of energy throughradiation2matter interaction.
Absorptance: See absorptivity; usually used for a semi-infinitemedium.
Absorptivity: Fraction of the incident radiation that is absorbedby matter. Modifiers: directional, hemispherical,spectral, or total.
Bidirectional reflectancedistribution function(BRDF):
Ratio of the reflected spectral radiance to thespectral irradiance from a given direction.
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(Continued )
Blackbody: The ideal emitter and absorber. The exitance isdiffuse and depends on the temperature andwavelength only. See blackbody cavity. Modifierfor blackbody behavior or properties.
Blackbody cavity: An isothermal cavity that emits, through itsopening, thermal radiation that closely followsthe blackbody distribution.
Diffuse: Modifier referring to the directionalindependence of the emitted, reflected, orincident radiance.
Directional: Modifier referring to the particular direction.Emission: The process in which radiation or photon energy
is released from matter due to radiativetransitions.
Emissivity: Also emittance: ratio of the radiation emittedfrom a surface to that emitted by a blackbody atthe same temperature. Modifiers: directional,hemispherical, spectral, or total.
Exitance: Rate of radiant energy leaving a surface per unitarea as a result of emission, reflection, ortransmission (W/m2). Sometimes it is calledradiosity. Modifiers: radiant, photon, self,spectral, total, or blackbody.
Exitent: Modifier referring flux leaving a surface.Flux: Time rate of propagation of radiant energy (often
called radiant power instead, W), photons(photon flux, s1), or lumens (luminous flux,lm/s).
Gray surface: A surface whose spectral absorptivity and theemissivity are independent of wavelength overthe spectral region of significance.
Heat flux: Rate of energy transfer across a surface per unitarea (W/m2).
Hemispherical: Modifier referring to all directions in the spaceabove a surface.
Incident: Modifier referring to radiation striking a surface.Intensity: Radiant power (flux) per unit solid angle (W/sr).
Modifiers: spectral, total.Irradiance: Rate at which radiant energy is incident on a
surface from all directions above the surface perunit area (W/m2). Modifiers: spectral, total.
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(Continued )
Kirchhoff ’s law: Relation between emissivity and absorptivity of amaterial. At thermal equilibrium, the emissivityof a body (or surface) equals its absorptivity.
Lambertian surface: A surface with equal exitent radiance in alldirections.
Planck’s law: Spectral distribution of blackbody exitance orradiance.
Radiance: Radiant power or flux (W) from a surface perunit solid angle per unit area. Modifiers: spectral,total, incident, exitent, emitted, reflected, orblackbody.
Radiant flux or radiantpower:
Time rate of propagation of radiant energy (W).
Radiance temperature: Temperature of a blackbody radiator havingthe same radiance, over a certain spectralband, as that from a surface. Modifiers: spectral,total.
Ratio temperature: Temperature of a blackbody radiator having thesame ratio of spectral radiance, at two fixedwavelengths, as that from a surface.
Reflectance: Fraction of the incident radiation reflected bymatter. Modifiers: bidirectional, directional-hemispherical, hemispherical2hemispherical,hemispherical2directional, specular, diffuse,spectral, or total.
Reflectivity: See reflectance; used for reflection between twosemi-infinite media with a perfectly smoothinterface.
Self-exitance: Exitance due to thermal emission from thesurface; also emitted exitance.
Semitransparent: Refer to a medium that absorbs radiationvolumetrically and a portion of the incidentradiation can penetrate through the medium.
Solid angle: Region subtended by an area element on thesurface of a unit sphere with respect to the centerof the sphere. Unit: steradian (sr).
Spectral: Modifier referring to a monochromatic quantity.Specular: Refer to a perfectly smooth surface for which the
angle of reflection is equal to the angle ofincidence. Modifier for the reflected componentin the specular direction.
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(Continued )
Stefan2Boltzmann law: Emissivity power of the blackbody isproportional to the absolute temperature to thefourth power.
Thermal radiation: Electromagnetic energy emitted by matter at afinite temperature.
Total: Modifier referring to the integration over allwavelengths.
Transmittance: Fraction of the incident radiative energytransmitted through a medium.
Wien’s displacement law: Locus of the wavelength corresponding to peakemission by a blackbody.
Wien’s formula: Approximate blackbody distribution functionthat is good at relatively short wavelengths.
5. Summary
This chapter gives a general introduction to radiation thermometry,from the basic operating principles according to the fundamental laws ofthermal radiation to the central problems with the practical applicationof the technique associated with the unknown emissivity of the surfaces andthe environment effect. The selection of wavelengths for a measurement isshown to be dependent on the temperature ranges. Some emissivitycorrection methods are summarized and typical radiation thermometers andtheir operating mechanisms are outlined, including traditional singledetector, thermographic imagers, and various optical fiber thermometers.Terms commonly used in the radiation thermometry are also described instraightforward language for the convenience of the reader.
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