Metrl. Meas. Syst., Vl. XVII (010), N. 1, pp. 77 86 METROLOGY AND MEASUREMENT SYSTEMS Index 330930, ISSN 0860-89 www.metrlgy.pg.gda.pl 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, 00 908 Warsaw, Pland ( hmadura@wat.edu.pl, +48 683 9383, 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: 10.478/v10178-010-0008-6.
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 0,1 3 4 5 6 7 8 9 10 11 1 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.
Metrl. Meas. Syst., Vl. XVII (010), N. 1, pp. 77 86 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):
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:
Metrl. Meas. Syst., Vl. XVII (010), N. 1, pp. 77 86 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 7.5 13 µm (Fig. 6). a
H. MADURA et al.: PYROMETRIC METHOD OF TEMPERATURE MEASUREMENT WITH COMPENSATION FOR SOLAR RADIATION 70 60 - E S [ µ W cm ]. 50 40 30 0 8 9 µ m 8 1 µ m 7.5 13 µ m 10 0 0 10 0 30 40 50 60 70 80 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=43 363 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.4 3.4 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
Metrl. Meas. Syst., Vl. XVII (010), N. 1, pp. 77 86 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 1 + + 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.4 3.4 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.4 3.4 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.4 3.4 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.4 3.4 µm and in selected lngwavelength detectin ranges 8 9 µm, 8 1 µm, and 7.5 13 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.4 3.4 µm, E S, LW is the intensity f slar radiatin in the selected detectin ranges 8 9 µm, 8 1 µm, r 7.5 13 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
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.4 3.4 µm are shwn in Fig. 9 and fr the band 7.5 13 µm in Fig. 10. - E S,LW [ µ W cm ]. 100 90 80 70 60 50 40 30 0 8 1 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 = 70 0 00 400 600 800 - E S,SW [ µ W cm. ] Fig. 9. Slar irradiance in 8 9 µm and 8 1 µm ranges vs. slar irradiance in the.4 3.4 µm band. - E S,LW [ µ W cm ]. 110 100 90 80 70 60 50 40 30 0 7,5 13 µ m Summer, Rural, Vis = 3 km, θ z = 10 10 Trpical, Urban, Vis = 5 km, θ 0 z = 70 0 00 400 600 800 - E S,SW [ µ W cm. ] Winter, Rural, Vis = 3 km, θ z = 30 Fig. 10. Slar irradiance in 7.5 13 µm range vs. slar irradiance in the.4 3.4 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
Metrl. Meas. Syst., Vl. XVII (010), N. 1, pp. 77 86, 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 7.5 13 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 11 13. 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.4 3.4 µm and the measuring band 7.5 13 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.
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 7.5 13 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, 53 57. [] 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. 69 73. [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, 185 189.