PYROMETRIC METHOD OF TEMPERATURE MEASUREMENT WITH COMPENSATION FOR SOLAR RADIATION

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1 Metrl. Meas. Syst., Vl. XVII (010), N. 1, pp METROLOGY AND MEASUREMENT SYSTEMS Index , ISSN PYROMETRIC METHOD OF TEMPERATURE MEASUREMENT WITH COMPENSATION FOR SOLAR RADIATION Henryk Madura, Mariusz Kastek, Tmasz Ssnwski, Tmasz Orżanwski Military University f Technlgy, Institute f Optelectrnics, S. Kaliskieg, Warsaw, Pland ( hmadura@wat.edu.pl, , mkastek@wat.edu.pl, tssnwski@wat.edu.pl, trzanwski@wat.edu.pl) Abstract Outdr remte temperature measurements in the infrared range can be very inaccurate because f the influence f slar radiatin reflected frm a measured bject. In case f strng directinal reflectin twards a measuring device, the errr rate can easily reach hundreds per cent as the reflected signal adds t the thermal emissin f an bject. As a result, the measured temperature is much higher than the real ne. Errr rate depends mainly n the emissivity f an bject and intensity f slar radiatin. The psitin f the measuring device with reference t an bject and the Sun is als imprtant. The methd f cmpensatin f such undesirable influence f slar radiatin will be presented. It is based n simultaneus measurements in tw different spectral bands, shrtwavelength and lng-wavelength nes. The temperature f an bject is derived frm lng-wavelength data nly, whereas the shrt-wavelength band, the crrective ne, is used t estimate the slar radiatin level. Bth bands were selected t achieve prprtinal changes f the utput signal due t slar radiatin. Knwing the relatin between emissivity and slar radiatin levels in bth spectral bands, it is pssible t reduce the measurement errr several times. Keywrds: intensity f slar radiatin, emissivity, pyrmetry, radimetric temperature measurements. 010 Plish Academy f Sciences. All rights reserved 1. Intrductin Results f remte temperature measurements f lw-emissivity bjects can be very inaccurate when the bjects are under strng islatin. Especially, such a measuring situatin shuld be avided when slar radiatin reflects directinally frm a surface the temperature f which is measured. In sme cases, varius curtains can be used limiting the slar radiatin effect. The prblem f slar radiatin disturbing autmatic temperature measurements is still unslved. IR Ca mera SC 3000 Hea ter Thermmeter (10 10)cm S1 e = 0,91 S e = 0,65 S3 e = 0,40 S4 e = 0,31 S5 e = 0,0 Fig. 1. Measuring set-up fr investigatins f sun radiatin influence n bject temperature measurements. Article histry: received n Nv. 1, 009; accepted n Jan. 10, 010; available nline n Feb. 6, 010; DOI: /v

2 H. MADURA et al.: PYROMETRIC METHOD OF TEMPERATURE MEASUREMENT WITH COMPENSATION FOR SOLAR RADIATION A measuring set-up has been built fr investigatins f sun radiatin influence n the errr f temperature measurement in field cnditins (Fig. 1). The temperature f metal plates S1 S5 having varius emissivities was measured. The plates were subsequently situated inside a husing t have them in the field f view f a thermvisin camera. The distance between the camera s bjective and the plate was 10 cm. Sun radiatin reaches the examined plate thrugh a rectangular hle cut in the frnt wall f the husing t illuminate nly a part f the investigated plate. Due t this, simultaneus measurement f the temperature f the plate s part reached by sun radiatin (in Fig. 1 dented with lighter clur) and the part nt reached by sun radiatin (darker clur) is made. Sun rays, after reflectin frm the investigated plate prpagate alng an ptical axis f a thermvisin camera (Fig. ). IR Camera Temperature cntrller Testing plate Heater Aperture Termmeter Fig.. The verall view f the test stand. In rder t eliminate the heating effect in the investigated plates caused by incident sun radiatin, a rectangular hle was pened nly fr the measurement duratin, i.e., fr abut s. The temperature f the investigated plates was stated with a heater and mnitred with a thermmeter. Emissi vity 1,0 0,9 0,8 0,7 0,6 S4 S1 S 0,5 S3 0,4 0,3 0, S5 0, Wavelenght [ µ m] Fig. 3. Spectral emissivity f S1 S5 plates. The spectral emissivity f the plates was determined using a Specrd 71 IR spectrphtmeter (Fig. 3). The emissivity averaged fr a given range f camera peratin was intrduced int a thermvisin camera. Fig. 4 shws a thermgram f a plane, painted aluminium plate illustrating the influence f the reflected slar radiatin n the measurement result. The real temperature f the plate was 85 K. The rectangular area that can be seen in the figure was illuminated with sun light (intensity f 4 µw cm ) nly fr the time f the thermgram perfrmance.

3 Metrl. Meas. Syst., Vl. XVII (010), N. 1, pp Fig. 4. Thermgram f a plate, with an emissivity ε = 0.9 and temperature T = 85 K, illuminated by slar radiatin, made with a thermal imaging camera Therma CAM SC3000 wrking in the 8 9 µm infrared range. Belw, the prfile f temperature distributin alng the straight line. The values f temperature at the illuminated and nn-illuminated areas f the same element can differ even frm several t hundred degrees [1]. In such a case, the measurement shuld be repeated several times at varius bservatin pints. When an bject s surface is nt plane, an effect f reflected sun radiatin can be bserved even after the change f a camera psitin with reference t an bject. Fr IR pyrmeters, in which the result is nt presented as a thermgram but as a single value, interpretatin f the result is much mre difficult. The trials are undertaken t reduce the influence f slar radiatin n remte temperature measurements []. At present, there are n available pyrmeters having a crrectin system r a system fr slar radiatin eliminatin. Sme special multispectral pyrmeters are knwn which deliver the infrmatin abut the measurement errr caused by slar radiatin [3] and the necessity f measurement repetitin.. Mdel fr determinatin f bject temperature.1. Taken symbls Energetic exitance f an abslute blackbdy f temperature T, fr a given spectral range λ 1 λ, results frm the Planck M(T) relatin. Optics D pt Object S A d S 1 IFOV f Detectr R r Fig. 5. Gemetrical relatins in an ptical unit with the bject fcused n a detectr (S wrking aperture f ptics, S 1 field f view, R distance between bject and ptics, r distance between ptics and detectr, D pt diameter f ptics, f ptics fcal length). The pwer f radiatin reaching the detectr s surface is (Fig. 5):

4 H. MADURA et al.: PYROMETRIC METHOD OF TEMPERATURE MEASUREMENT WITH COMPENSATION FOR SOLAR RADIATION P( T ) = qm ( T ), (1) where q is the cnstructin cnstant resulting frm the pyrmeter design (Fig. 5): IFOV q = Dpttg A design cefficient can be written in an equivalent frm [4, 5]:. () q = A d 4F 1 r + R where A d is the detectr area r a single pixel in a detectr array and F number (rati f fcal length t wrking aperture)... The Sun radiatin In real measuring cnditins, the pwer f radiatin reaching the input aperture f an ptical system f a measuring device depends n many factrs. The mst imprtant are radiant prperties f the bject itself which are determined by its temperature and emissivity. In measuring practice, mst frequently the emissivity value is nt knwn and even the use f tables des nt ensure assumptin f its prper value. It is because the emissivity depends n such factrs as, e.g., structure and xidatin degree f a surface, its temperature, bservatin directin, and spectral range fr which it will be determined r smetimes will be eliminated by sme, specially designed, ptical system fr emissivity cmpensatin [8, 9]. The Sun radiatin temperature is apprximately 5900 K. A spectral distributin f slar radiatin is best apprximated by the spectral distributin f an abslute blackbdy with a temperature f 5770 K, the size f which crrespnds t Sun s size [4]. This bdy emits the same radiatin in all directins. Befre it reaches the Earth, it is absrbed r scattered in the atmsphere. The rati f slar radiatin intensity, measured utside the Earth atmsphere E e (λ) t the intensity f slar radiatin reaching the Earth surface E S (λ), determined fr particular wavelengths is called the spectral permeability cefficient f the earth atmsphere τ E (λ). A detailed determinatin f τ E (λ) requires cnsideratin f a lt f factrs and parameters describing the atmsphere. The mst imprtant are: cntent and cndensatin degree f steam, temperature, atmspheric pressure, thickness f Earth s atmsphere and cncentratin f gas and aersls cntained in it. The intensity f the ttal slar radiatin E S, in the chsen spectral range λ 1 λ, can be determined as: λ, ( ) ( λ) S E e λ1 (3) E = τ λ E dλ. (4) The spatial distributin f a slar radiatin beam, after its reflectin frm the bject s surface, depends n the type f radiatin reflectin [5, 6]. It can be a specular reflectin (regular reflectin), ccurring fr the reflectin frm a plane plished surface, diffuse reflectin ccurring fr the reflectin frm a rugh surface, directinal diffuse reflectin (mixed reflectin, hybrid reflectin) shwing the features f bth specular reflectin and diffuse nes. Thus, spatial distributin f slar reflectin reaching a detectr depends n a surface s structure and its rughness [7]. The cases f specular reflectin and diffuse reflectin are extreme nes and rarely ccur in reality. The slar radiant exitance P S fr directinal diffuse reflectin can be expressed as:

5 Metrl. Meas. Syst., Vl. XVII (010), N. 1, pp P S R f A d E = f q E, S S = R IFOV tg E, α = β S α β (5) where α is an angle incidence f slar radiatin and β is an angle reflectin f slar radiatin. Amng ther factrs affecting the pwer f radiatin reaching the input aperture f an ptical system f a measuring device, the fllwing factrs shuld be mentined: the radiatin reflected frm an bject s surface, absrptin, as well as dissipative and radiant prperties f the atmsphere. The ttal pwer f radiatin reaching the input aperture f an ptical system can be expressed fr typical measuring cnditins as [6]: ( ) ( ) P = ε τ P( T) + 1 τ P ( T ) + 1 ε τ P ( T ), (6) c a a a a a t t where ε is the bject s emissivity, τ a is the atmsphere transmissin cefficient between the bject and the ptical system, P(T) is the radiant exitance f a blackbdy f the temperature T, exitance P a (T a ) is the radiant exitance f atmsphere f temperature T a, and P t (T t ) is the radiant f the ambient f temperature T t. If we assume that each f the cmpnents f the radiant exitance, i.e., P(T), P a (T a ), and P t (T t ), generates at the detectr utput, a signal vltage prprtinal t this pwer, U(T), U a (T a ), U t (T t ), respectively, the expressin fr the ttal value f a vltage signal is as fllws: ( ) ( ) U = ε τ U( T) + 1 τ U ( T ) + 1 ε τ U ( T ). (7) c a a a a a t t In devices in which the abve relatin is used fr the determinatin f the bject s temperature, the user shuld estimate and intrduce the crrectins fr such parameters as: the bject emissivity ε ', the cefficient f atmsphere transmissin τ a ', the atmsphere temperature Ta ', and the ambient temperature T t '. By slving Eq. (6), with respect t U(T), and cnsidering the intrduced crrectins we have: 1 1 τ a ' 1 ε ' U ( T ) = Uc Ua ( Ta ') Ut ( Tt '). (8) ε ' τ ' ε ' τ ' ε ' a Knwing the value f the vltage U(T ), the bject s temperature T can be determined n the basis f a calibratin characteristic f the device. The subscript is intrduced t distinguish a calculated value frm a real ne. The relative errr f the bject temperature determinatin: T ' T δt = 100%, (9) T depends mainly n the difference between the real values f the parameters f Eq. (7) and the intrduced nes. It shuld be nticed that using this methd, the assumptin was taken that particular cmpnents f radiatin are described by Lambert s law, what in the case f specular reflectin and directinal diffuse reflectin is nt fulfilled..3. Calculatin results It was taken fr the abve presented mathematical descriptin f phenmena that fr shrt distances τ a =1. Exemplary calculatins were carried ut fr a slar radiatin spectrum determined with the PcMdWin 3.0 prgram fr a summer atmsphere, cuntry cnditins, visibility f 3 km, and a deviatin angle f the Sun frm the zenith θ z =30º. Ttal intensity f slar radiatin (E S ) was calculated fr typical peratin ranges f lng-wavelength IR pyrmeters and thermal cameras, i.e., 8 9 µm, 8 1 µm, and µm (Fig. 6). a

6 H. MADURA et al.: PYROMETRIC METHOD OF TEMPERATURE MEASUREMENT WITH COMPENSATION FOR SOLAR RADIATION E S [ µ W cm ] µ m 8 1 µ m µ m θ z [ ] Fig. 6. Ttal slar irradiance vs. zenith slar angle fr selected infrared ranges. Fig. 7. Calculated relative errr f temperature reading fr an bject with emissivity: ε = 0.6 and ε = 0.9; fr three infrared ranges. Summer mdel atmsphere and rural prfile f aersl; Vis = 3 km; θ Z = 50º. Fr calculatins f the relative errr f a temperature reading, the fllwing values f input parameters were assumed: R=10 cm, f=3.5 cm, D pt =5 cm, IFOV=1.1 mrad, and T= K. The values f the relative temperature errr f bjects with emissivity ε=0.9 and ε =0.6 are presented in Fig. 7. It results frm the btained results that the relative errr f temperature measurement is caused by slar radiatin and depends bth n the bject s emissivity and its temperature. Als, it depends n the width f the detectin band. In general, a narrwer bandwidth fr a cnstant initial wavelength gives a larger errr than bradband. It results frm the fact that the pwer f bject radiatin decreases in relatin t the pwer f slar radiatin reflected frm it. Mrever, the errr increases with increasing intensity f slar radiatin. 3. Measurement methd The methd f temperature measurement f an bject under slar radiatin cnsists in simultaneus measurements f a radiant exitance in the shrt-wavelength band µm and in the lng-wavelength band. The bservatin area f an ptical system is identical fr bth bands (Fig. 8). The shrt-wavelength band is significantly far frm the lng- wavelength band. Thus, n signal changes at the detectr utput, caused by bject radiatin in this band are bserved. The actual temperature measurement is made in the lng-wavelength band but

7 Metrl. Meas. Syst., Vl. XVII (010), N. 1, pp the shrt-wavelength band is used nly fr detectin f slar radiatin reflected frm an bject. 1 U(T,F ) ε 4 3 T F Filters - U 5 ε F U( T,F 1 ) 1 T T Fig. 8. Scheme f a pyrmeter with the unit fr slar radiatin cmpensatin: 1) measurement field; ) ptics; 3) signal prcessing; 4) crrectin set f slar radiatin; 5) signal analysis set. When an bject is illuminated with slar radiatin, the signal value increases at the utputs f bth detectrs. Knwing the signal value at the utput f a shrt-wavelength detectr, the signal value at the utput f the lng-wavelength detectr shuld be crrected, the same the errr f temperature readut caused by adding the reflected slar radiatin shuld be reduced r ttally eliminated. The crrectin is made by substituting the value f the signal measured in the shrt-wavelength band int the crrectin functin and thus, the btained signal value is subtracted frm the signal measured at the lng-wavelength detectr utput. It shuld be mentined that the bject s emissivity in the shrt-wavelength band can be different than in the lng-wavelength band. The device user has t knw the emissivity values. Basing n calculatins with the PcMdWin 3.0 prgram and using the characteristics f slar radiatin intensity btained with the SR-5000 spectrradimeter, it can be shwn that the changes f slar radiatin in µm band are best crrelated with the changes f slar radiatin in the lng-wavelength range (LWIR). A decrease/increase in slar radiatin intensity in the µm range is accmpanied by a decrease/increase in the value f slar radiatin intensity in the lng-wavelength range. Thus, it is pssible t determine the slar radiatin intensity in the LWIR band as a functin f slar radiatin intensity in the µm range fr any type f earth atmsphere. T verify the abve statement: 180 spectral distributins f slar radiatin in the LWIR range were analyzed. These distributins were btained with the PcMdWin prgram fr the fllwing mdels f atmsphere: Trpical, MidLatitude Summer, MidLatitudeWinter, 1976 US Standard, fr varius aersl mdels Rural VIS=3 km, Rural VIS=5 km, Navy Maritime, Maritime VIS=3 km, Urban VIS=5 km, and sun deviatin angles frm the Zenith frm 0 t 80 with a step f 10 ; ttal intensity f slar radiatin in the crrectin band µm and in selected lngwavelength detectin ranges 8 9 µm, 8 1 µm, and µm was determined; the btained data were apprximated with a third-degree plynmial f the frm: 3 ( ) ( ) E = a E + a E + a E + a (10), S, LW 1 S, SW S, SW 3 S, SW 4 where E S, SW is the intensity f slar radiatin in the shrt-wavelength crrectin band f µm, E S, LW is the intensity f slar radiatin in the selected detectin ranges 8 9 µm, 8 1 µm, r µm, a 1 a 4 are the plynmial cefficients determined fr particular LWIR ranges. The changes f slar radiatin intensity in the ranges 8 9 µm and 8 1 µm, btained T

8 H. MADURA et al.: PYROMETRIC METHOD OF TEMPERATURE MEASUREMENT WITH COMPENSATION FOR SOLAR RADIATION frm the calculatins as a functin f slar radiatin intensity in the band µm are shwn in Fig. 9 and fr the band µm in Fig E S,LW [ µ W cm ] µ m Vis = 3 km, θ z = 30 Summer, Rural, Vis = 3 km, θ z = 10 Winter, Rural, 8 9 µ m 10 Trpical, Urban, Vis = 5 km, θ 0 z = E S,SW [ µ W cm. ] Fig. 9. Slar irradiance in 8 9 µm and 8 1 µm ranges vs. slar irradiance in the µm band. - E S,LW [ µ W cm ] ,5 13 µ m Summer, Rural, Vis = 3 km, θ z = Trpical, Urban, Vis = 5 km, θ 0 z = E S,SW [ µ W cm. ] Winter, Rural, Vis = 3 km, θ z = 30 Fig. 10. Slar irradiance in µm range vs. slar irradiance in the µm band. The efficiency f this methd can be estimated by cnsidering the decrease in the relative errr f temperature measurement when the value f slar radiatin is cmpensated accrding t Eq. (10). T d it, the difference E S between the apprximating curve and the real values f slar radiatin shuld be determined, i.e. the value f nn-cmpensated slar radiatin in the prcess f temperature measurement is equal t: E = E - E. (11) S S, LWIR S, LW When E S =0 µw cm, the measurement f an bject temperature will be errr-free (accurate) because the value f the cmpensated intensity f the slar radiatin E S, LW is the same as its real value E S, LWIR. Fr E S > 0 µw cm, the indicated bject s temperature will be higher than the bject temperature because nly a part f slar radiatin will be cmpensated. Fr E S < 0 µw cm, the indicated bject s temperature will be lwer than the bject temperature because the cmpensated value f slar radiatin intensity is higher than the real ne. It was taken fr

9 Metrl. Meas. Syst., Vl. XVII (010), N. 1, pp , calculatins that E = ± E S where E S is the average value f the intensity f nncmpensated slar radiatin: 1 E = ± E E. (1) 180 i i S S, LWIR S, LW 180 i= 1 The value E S fr the detectin bands 8 9 µm, 8 1 µm, and µm is 0.7 µw cm, 1.9 µw cm, and. µw cm, respectively. The calculatin results f the maximal errr f temperature measurement using a pyrmetric methd with cmpensatin f slar radiatin are given in Figs The btained calculatin results cnfirm the crrectness f the chsen crrectin band and the prpsed methd f temperature measurement. The smallest errrs f temperature measurements f bjects illuminated with slar radiatin are btained fr the crrectin band µm and the measuring band µm. The btained calculatin results shw that fr the bjects with an emissivity ε 0.6, i.e., fr the majrity f industrial bjects (e.g. zinc cated sheets r steel sheets), the measured temperature des nt differ frm the real value mre than 10%. Fig. 11. Relative errr f temperature readut f an bject with an emissivity ε = 0.6 and ε = 0.9 fr the measurement band 8 9 µm and E S = ±0.7 µw cm. Fig. 1. Relative errr f temperature readut f an bject with an emissivity ε = 0.6 and ε = 0.9 fr the measurement band 8 1 µm and E S = ±1.9 µw cm.

10 H. MADURA et al.: PYROMETRIC METHOD OF TEMPERATURE MEASUREMENT WITH COMPENSATION FOR SOLAR RADIATION Fig. 13. Relative errr f temperature readut f an bject with an emissivity ε = 0.6 and ε = 0.9 fr the measurement band µm and E S = ±. µw cm. 4. Cnclusins A new methd f cmpensatin f slar radiatin influence n measurement results btained with pyrmeters f thermal cameras perating in the IR lng-wavelength range was presented. Cmputer simulatin f this methd allws t predict that its applicatin in an algrithm f temperature determinatin in pyrmeters and thermal cameras will reduce measurement errrs, in sme cases even f ne rder f magnitude. Basing n the simulatins presented in the article, it is planned t make a pyrmeter mdel in which the effect f slar radiatin influencing the results f remte temperature measurements will be reduced. References [1] Madura, H., Kłdziejczyk, M., (005). Influence f sun radiatin n results f nn-cntact temperature measurements in far infrared range. Opt-Electrnics Review, 13, [] Bielecki, Z., Chrzanwski, K., Matyszkiel, R., Piątkwski, T., Szulim, M. (1999). Infrared pyrmeter fr tem-perature measurement f bjects f bth wavelength- and time-dependent emissivity. Optica Applicata, 9, 84 9,. [3] H. Madura, T. Piątkwski, E. Pwiada: Multispectral precise pyrmeter fr measurement f seawater surface temperature. Infrared Physics and Technlgy, n. 46, 004, pp [4] Riedl, M.J., (001). Optical Design, Fundamentals fr Infrared Systems. Bellingham, Washingtn: SPIE Press. [5] Hlst, G.C. (1998). Testing and Evaluatin f Infrared Imaging Systems. Bellingham, Washingtn: SPIE Press. [6] Zissis, J.G. (1993). The Infrared&Electr-Optical Systems Handbk. Surces f Radiatin, 1, Bellingham: SPIE Press. [7] Nayar, S.K., Ikeuchi, K., Kanade, T. (1989). Determining shape and reflectance f lambertian, specular, and hybrid surfaces using extended surces. Internatinal Wrkshp n Industrial Applicatin f Machine Intelligence and Visin. Tky. [8] Madura, H., Kastek, M., Piątkwski, T. (007). Autmatic cmpensatin f emissivity in three-wavelength pyrmeters. Infrared Physics and Technlgy, 51, 1 8. [9] Madura, H., Piątkwski, T. (004). Emissivity cmpensatin algrithms in duble-band pyrmetry. Infrared Physics and Technlgy, 46,