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18 Temperature Measurement of Transparent Solid Bodies 18 .1  Pyrometric, Contactless Method All solid bodies which partially or totally transmit thermal radiation in the wavelength of visible and infrared radiation, are classified as transparent bodies . The notation used to consider pyrometric methods for measuring the surface temperature of solid bodies has already been introduced in Section 8 .2 . It will be recalled that solid bodies, which have a transmission factor limited to a = 0, are non-transparent bodies in the whole range of wavelengths used in optical pyrometry . The same notation will be used in this chapter . The general conditions to be considered in this chapter are illustrated in Figure 18 .1 . Behind and in the background of the transparent body, 1, whose temperature is to be measured, is another body 2, with a temperature, 62 . Simultaneously, the investigated surface may be irradiated by another body 3, with a temperature, 63 . Thus, the radiation incident upon the pyrometer, consists of the radiation from the investigated surface, the background radiation transmitted through the investigated body and the radiation from body 3, reflected from the investigated surface . Consequently, the pyrometer indication will be incorrect since errors are introduced by the radiation from both the background and the nearby influencing body . Errors caused by reflected radiation can be eliminated by either applying a shield to shadow the influencing body 3, in Figure 18 .1, or by applying a pyrometer with zero- sensitivity in the wavelength range emitted by this body 3, and reflected by 1 . The error caused by background radiation can be minimised, if not completely eliminated, by proper choice of a pyrometer whose operating wavelength is within the range where the spectral transmissivity of the body, 1, is as low as possible . To explain the mechanism of radiation of a semi-transparent body, consider Figure 18 .2 illustrating the conditions of a homogeneous body of uniform temperature having an optically smooth surface and a thickness, l . Neglect the background radiation and assume that the body has a transmissivity, r, corresponding to a logarithmic absorption coefficient, k= In (I/a) . Any layer of unity thickness at a depth, x, may send energy expressed by the heat-flux, 0X , towards the left-hand surface . Temperature Measurement Second Edition L. Michalski, K. Eckersdorf, J. Kucharski, J. McGhee Copyright © 2001 John Wiley & Sons Ltd ISBNs: 0-471-86779-9 (Hardback); 0-470-84613-5 (Electronic) 382  TEMPERATURE MEASUREMENT OF TRANSPARENT SOLID BODIES ,A SHIELD 1-TRANSPARENT 2-BACKGROUND 3 BODY 3 w PYROMETER 2 Figure 18 .1 Pyrometric temperature measurement of a transparent body 1, against a background 2 and irradiated by body 3 1 ~ze  ~z ~zs i L j X Figure 18 .2 Radiation notation for a transparent solid body The absorbed part, (Dxa of the total energy, Vx , in its leftward path, is given by : Vxa =Vx(I-e-/(X )  (18 .1) Eventually the energy from one layer of unity thickness at a distance, x, arriving at the left-hand surface is given by : Vxs `fix - VxQ =(Dxe-kx  (18 .2) Taking account of the surface reflectivity, p, the part of this energy, which is reflected from the surface, is : ( Dxr =`l'xSP  (18 .3) Now take account of the absorption in equations (18 .1) and (18 .2) . The energy coming from one layer of unity thickness, at the depth, x, that is emitted by the left-hand surface is finally given by : axe = V xs - (Dxr =(Pxe-"X(1-P)  (18 .4) The total energy, coming from all of the layers of the body of thickness l and emitted from its left-hand surface is given by the relation : PYROMETRIC, CONTACTLESS METHOD  383 1  1 ale - Iq)xe - Vx(I - p)Ye -kx x=1  x=1  (18 .5) It has been shown by Harrison (1960) that equation (18 .5) is equivalent to : (Dle =Vx(I- pI-e -k1)  (18 .6) A layer of unity thickness absorbs the proportion (1-e k) of the incident energy, which a black body would absorb . Hence, the equivalent emissivity, E el , of this layer is : Eel =(I-e-k)  (18 .7) Consequently, when the reflection is also considered, the equivalent emissivity of the investigated body of thickness, l, is given by : Ee =(I-e-kl)(I _ p)  (18 .8) where the logarithmic absorption coefficient, k, is a function of wavelength . The equivalent spectral emissivity, E, ,ti , can be defined in a similar way . For sufficiently large values of kl, which occurs for sufficiently large thickness, 1, the factor, e-k1 > 0 . Thus, the equivalent emissivity of a transparent thick body depends mainly on its reflectivity and consequently also on the surface state of the body . Energy, emitted at those wavelengths, where k is larger, is absorbed in a shorter distance, x . Thus, the emitted energy originates from layers nearer to the surface for larger k . This phenomenon does not influence the pyrometer readings, if no temperature differences occur inside the body . When the temperature distribution inside the body is non-uniform, the energy emitted from each layer has to be analysed separately for each wavelength . Pyrometer readings then depend on the superposition of the radiation emitted from particular layers . MacGraw and Mathias (1962) have shown that those layers situated nearer to the surface always exert a predominant influence . In industrial practice, it is often necessary to measure glass temperature . Figure 18 .3 shows relative spectral transmission and relative spectral reflectance of natrium-silicon glass, as a function of the layer thickness . Measurement of glass temperature depends on the effective wavelength, A . e , of the pyrometer used . The spectral transmission, aX , of the glass is a function of the effective wavelength, A e , and of the thickness of the glass layer as shown in Figure 18 .3 (Ircon Inc ., 1997) . Thus, when the Ircon Inc . Modline Plus 7000 pyrometer, operating at A e = 4 .5 pm, is used, the glass transmission, r ;L , and the spectral reflectance . p,I , are both near zero . Using equation (8 .4) it can be seen that the equivalent glass emissivity, E,L , approaches unity so giving : s~ =1- za -Pa  (18 .9) ~1 100  7 384  TEMPERATURE MEASUREMENT OF TRANSPARENT SOLID BODIES 100 0,22mm == \~  11 80 Z ;) 60  1,55mm  60 - Z V) 40 ,' 0-  0 WAVELENGTH IL jim  in  . , influence function of wavelength, A . (Courtesy of Ircon Inc, USA) ,  ,-  , . The pyrometer readings are those of a glass surface, as also indicated in Table 11 . 3 . The -,  ,-  . n of the glass layer thickness is given in Figure 18 .4 for three different Ircon Inc . photoelectric pyrometers . From this it follows : ,-  , in contact with the surface, requires pyrometers with A, , &7 .9 ~tm . " temperature measurement of a I mm thick glass layer requires the use of pyrometers with A, in the range 4 .8 pm to 5 .3 pm . ,- rature measurement of layers with thickness more than about 10mm needs -  :, ) advises the use of pyrometers with . . 0,9 - PYROMETER  ., METER  PYROMETER gjjm , : 0,7 0,025 QOS 0,1  0,25 0,5  1  2,5 5  10  25 THICKNESS OF GLASSLAYER  I  mm ,-  , ,  , pyrometers with three different effective wavelengths, /1, PYROMETRIC, CONTACTLESS METHOD  385 When measuring the temperature of deeper glass layers it is essential to judge the degree to which the glass has been through-heated, while the temperature measurement of the glass surface is relevant in glass cooling processes . Simultaneous temperature measurement of a glass surface and of internal glass layers permits the determination of the temperature gradients in the glass, which is a deciding factor in glass hardening processes . Two simultaneously used, but different, pyrometers enable the formation of a differential signal . Surface temperature measurement of plastics, commonly in the temperature range of 50 °C to 300 °C, is more difficult for two reasons . In the first place the wavelength ranges of low transmissivity are very narrowand secondly, thin plastic films enhance the errors due to background radiation . Figure 18 .5 gives the relative spectral transmission of some plastics of given thickness as a function of wavelength Orcon Inc ., 1997) . The recommended wavelengths for temperature measurement of different plastics is given by Land Infrared (1998) . For example, for polyester, polycarbonate and polyamide films of thickness even as low as 0 .025 mm, it is, A e = 7 .95 pm . A value of /1 e = 3 .43 pm is advised for polyethylene, polypropylene and PVC films of similar thickness . A detailed survey of recommended wavelengths, for measuring the surface temperature of plastics is given in Table 11 .3 . The thickness of transparent bodies exerts a vital influence on their equivalent, spectral emissivity e e ; L . In the case of some plastics, this influence is shown in Figure 18 .6 . The wavelength ranges which are used should coincide with the so-called atmospheric windows . This also enables measurements in the presence of gases and flames which is considered in Section 10 .4 .1 . ACRYLIC 0,3mm  POLYETHYLENE0,25mm  POLYURETHANE 0,25mm  POLYAMIDE(NYLON) 0,25mm 1  100 J  . V Q 50 w a  1  I  . . '  \ 0- Ix O  Y  . ./ 2,5  3  4  5  6  7  8  9  10 11 12 13141516 WAVELENGTH  9 . , ym POLYCARBONATE 0,5mm  POLYESTER 0,25mm POLYPROPYLENE Q25 mm ~~100 -  I ~ 50  PCV0,3mm V1 . ti a  \ 1 N .  v  i / 1  :v 1  a wr 0 2,5  3  4  5  6  1 , 8  9  10 11 12 13141516 WAVELENGTH  ' , ym Figure 18 .5 Relative spectral transmission, rA , of some plastics as a function of wavelength, .1, (Courtesy of Ircon Inc, USA) 386  TEMPERATURE MEASUREMENT OF TRANSPARENT SOLID BODIES POLYESTER, POLYCARBONATE,TEFLON POLYAMIDE J 10 a ~ _  I d 0,8 PCV  a =8,07±0,15Nm z> 0,6/ w ~-  POLYETHYLENE, POLYPROPYLENE J N 0,4 .N o W  0,2 0  20 40 60 80 100 120 140 160 180 200 220 THICKNESS I , ym Figure 18 .6 Equivalent spectral emissivity c A versus thickness, 1, of some plastic films . 18 .2  Contact Methods Contact methods, which are also applied for surface temperature measurement, are discussed in Chapter 16 . In some cases, the energy influencing the sensor is not solely due to conduction from the surface itself . Some radiation from the interior of the body may also be detected by the sensor . This phenomenon, which can cause some measuring errors, typically occurs in measuring the surface temperatures of thick material layers exhibiting large internal temperature differences . 18 .3 References Harrison, T .R . (1960) Radiation Pyrometrv and its Underlying Principles of Radiant Heat Transfer, John Wiley and Sons, New York . Ircon Inc ., USA ( 1997) Plastic Film Measurement, Technical Note . Land Infrared (1998) System 4, Advance Product Information MacGraw, D .A . and Mathias, R .G . (1962) Radiation pyrometry in glass-forming process . Temperature : Its Measurement and Control in Science and Industry, 9(2), Reinhold Publ . Co ., New York, 381-390 . Tenney, A .S . (1986) An Introductory Review of Radiation Thermometry, Product Information Bulletin No . 9, Leeds & Northrup Co ., North Wales, PA, USA .