PerkinElmer Optoelectronics GmbH ppl. note Wenzel-Jksch-Strße 31 65199 Wiesbden, Germny Phone: +9 (6 11 92-0 Fx: +9 (6 11 92-3 69 http://www.perkinelmer.com ppliction note thermopile sensors Remote temperture mesurement with PerkinElmer thermopile sensors (pyrometry: A prcticl guide to quntittive results Abstrct A thermopile sensor genertes voltge, which is proportionl to the incident infrred (IR rdition power. Becuse every ect emits IR rdition with power, which is strict function of its temperture, one cn deduct the ect s temperture from the thermopile signl. This method is clled pyrometry. PerkinElmer s thermopile sensors [1] re perfectly suited to be employed in precision devices, such s er thermometers nd pyrometers, s well s in pplictions like microwve ovens, ir conditioners, hir dryers, etc. Becuse of their cost effectiveness together with their excellent performnce, such s long term stbility nd very low temperture coefficient of sensitivity, millions of these devices hve found their wy into high volume pplictions, mking PerkinElmer the leding thermopile mnufcturer in the world. This brief ppliction note ims t better understnding of the use of PerkinElmer s thermopile sensors in temperture sensing nd mesurement. The focus here is on the quntittive nlysis of the signls nd the principle of the clibrtion procedures. The pper strts with review of the physicl picture of the het blnce equtions, continues with the introduction of n nlog temperture compenstion procedure, nd will finlly focus on the more precise method of employing numericl mens. Specil ttention is given to the discussion of mesurement errors nd chievble ccurcy. If there re ny questions you encountered, plese do not hesitte to contct the uthor by e-mil: juergen.schilz@perkinelmer.com. Contents 1 The het blnce eqution...2 2 Ambient temperture compenstion...3 3 Anlog solution... Digitl solution...5.1 The mesurement procedure...6.2 The clibrtion procedure...7 Version dted 12. July 2001; Jürgen Schilz, subject to chnge 2001 PerkinElmer Optoelectronics GmbH Pge 1 of 8
ppliction note thermopile sensors: quntittive pyrometry.2.1 Thermistor...7.2.2 Instrument fctor (thermopile...7 5 Conclusions...8 6 Literture...8 1 The het blnce eqution The totl rdition power P emitted by n ect of temperture T cn be expressed s P T = σ ε, (1 with σ being the Stefn-Boltzmnn constnt nd ε the so-clled emission fctor (or emissivity of the ect in question. In the idel cse ε hs the vlue 1 then we spek of blck-body. For most substnces the emission fctor lies in the rnge between 0.85 to 0.95. Equ. (1 is clled the Stefn-Boltzmnn lw. It sums up (integrtes the totl quntity of rdition over ll wvelength. If you re interested to gin deeper understnding of the IR rdition physics, I recommend you to look into suitble physics books under blck-body rdition. Here, we will not go deeper into it. We cn now use one of the PerkinElmer thermopile sensors, to mesure the het rdition ccording to Equ. (1. Well, this is not s stright forwrd s it might look t the beginning. First of ll, we needed to introduce into Equ. (1 something bout the sensing geometry; especilly the sensing ngle. Second, we need to tke into ccount the temperture of the thermopile itself (i.e. the instrument or the mbient temperture, becuse lso the thermopile itself emits het following Equ. (1. This leds us to the het-blnce eqution, which reltes the net power P rd received by the thermopile to the two tempertures T, in which we re ctully interested in, nd to the temperture of the instrument itself. Since in most cses the instrument s temperture equls (or is ner to the temperture of the mbient, we will refer this vlue to T, the mbient temperture. Therefore the totl het power P rd received from the ect t temperture T is given to P rd = K' ( ε T ε T. (2 sens In Equ. (2 we chnged from the physicl constnt σ to n empiricl fctor K which we cll the instrument fctor. K contins of cuse the constnt σ in some form, but it minly includes the view ngle or field-of-view (FOV of the thermopile instrument. The FOV is mrked by the Greek letter ϕ nd it is explined in Fig. 1. T T sens = T view ngle, ϕ het U Figure 1: The definition of the field of view (FOV or the view ngle, ϕ. ϕ is the ngulr mesure of the cone opening from which the sensor receives rdition. One cn now show tht the instrument fctor K cn be written s K ' = K sin( ϕ / 2 [2] nd thus the totl received rdition power mounts to 2001 PerkinElmer Optoelectronics GmbH Pge 2 of 8
( ε T ε T sin 2 ( ϕ / 2. ppliction note thermopile sensors: quntittive pyrometry P rd = K sens (2 The thermopile sensor is n instrument, which genertes voltge U, which is proportionl to the incident net rdition, P rd. The proportionlity constnt is the so-clled sensitivity S. Therefore, one rrives t the following eqution ( ε T ε T sin 2 ( ϕ / 2. U = S Prd = S K sens (3 Equ. (3 is the fundmentl nd correct reltionship tht tells us the output voltge s function of the ect (nd mbient temperture. For fixed mbient, the output voltge of the thermopile is proportionl to T. This is however only vlid, if the sensor senses the whole electromgnetic spectrum with the sme sensitivity! (Remember tht Equ. (1 is lredy n integrl. Since in ll prcticl situtions one never senses over ll wvelengths for exmple most PerkinElmer thermopiles hve built-in 5.5 µm infrred longpss the pure T dependence will rrely be seen, or it will only be n pproximtion for restricted temperture rnges. Wht the exct curve is, depends on severl fctors, such s the ect temperture rnge in question nd the spectrl chrcteristics of the instrument response. The thermopile itself senses rdition from bout 1 to over 20 µm with constnt sensitivity, but ny lens, mirror, or filter in the opticl pth chnges the response chrcteristics. To show the devition from the physicl T lw, we will here introduce devition constnt δ to mke the temperture dependence T -δ lw. Additionlly, to fcilitte the further nlysis, we will melt the two emission fctors ε nd ε sens into one effective constnt ε. Thus Equ. (3 will red: ( δ δ T T sin 2 ( ϕ / 2. U = S K ε (3 Equ. (3 is indeed bsed on physicl nlyticl pproch, but it lredy contins empiricl fctors, which re needed to be determined in order to ttribute to the prcticl relity. Wht the exct temperture dependence is, whether it relly cn be described by T -δ or whether it needs more complicted formul, needs in fct to be individully determined for every ppliction. The direct pproch to this is experimentlly by performing precise mesurements nd looking for n empiricl fit to derive reltionship of thermopile output voltge nd ect temperture. If micro controller is used, the vlues will then mostly be listed in the form of look-up tble. In this cse no explicit nlyticl formul is needed. 2 Ambient temperture compenstion For fixed mbient temperture, ny empiricl fit of U versus T or ny look-up tble will give the correct result. From device to device single proportionlity constnt is then sufficient s clibrtion fctor. However, s seen from Equ. (3, the output signl will vry, when the mbient temperture chnges. Any IR temperte mesurement system needs therefore to compenste this effect i.e. so-clled mbient temperture compenstion needs to be implemented to mke sure tht the instrument determines n ect temperture vlue, tht is independent from the sensor temperture itself. In mny industril pplictions the mbient temperture compenstion of the output signl is chieved by employing n nlog circuit. The circuit is designed in wy, tht voltge is generted, which mtches exctly the loss or gin in output voltge due to ny mbient temperture chnge. This method, which is lso employed in the PerkinElmer thermopile module M is explined in prgrph 3. For high ccurcy pplictions, s needed for er thermometers or precision pyrometers, digitl (numericl clcultion method is needed. The principle how to perform this, is explined in section. 2001 PerkinElmer Optoelectronics GmbH Pge 3 of 8
ppliction note thermopile sensors: quntittive pyrometry 3 Anlog solution The Figure 2 shows the principle s it is employed the PerkinElmer thermopile module M, which is lredy in use in millions of microwve ovens, ir conditioners, nd numerous other consumer pplictions. The thermopile output follows the lredy known lw ccording Equ. (3. Becuse thermopile signls re usully in the rnge of millivolts, they need mplifiction by very low noise nd low offset opertionl mplifier (OpAmp. The output signl simply multiplies by the mplifiction fctor A. U ( ' δ δ ε sin 2 = S K T T ( ϕ / 2 ( δ δ U = A S K ε T T sin 2( ϕ / 2 ϑ A U Comp out = A U U = 2 ( A S K ε ( T T sin ( ϕ / 2 ( U αt th 0 I A Th U ( = α δ th T U T 0 Figure 2: Schemtic of the pyrometer circuit with nlog mbient temperture compenstion s employed in the PerkinElmer thermopile module M. The inset shows photo of the module ML1 which opertes s temperture controller in e.g. microwve ovens. For the mbient temperture compenstion, the internl thermistor is used, which sits in the thermopile housing nd therefore records exctly the sensor s temperture. The thermistor hs n NTC behvior with non-liner resistnce vs. temperture chrcteristics. It is well known tht the best fit to the resistnce-temperture function R(T is chieved by using n exponentil eqution, but for limited temperture rnge one cn pproximte the thermistor s R(T behvior by T (or of course lso by T -δ lw of the form ( T = R ςt R, ( 0 with ζ being proportionlity fctor nd R 0 constnt. A constnt (but smll electricl current through the thermistor genertes concomitntly voltge, which is subsequently mplified by fctor A Th to mount to U th. This voltge is proportionl to R: = α δ th ( T U0 T U. ( This voltge is dded to the thermopile signl by mens of second opertionl mplifier s seen in the Figure 2. This mplifier is clled the compenstion stge. The resulting voltge t the output of tht stge is then U out = A U U th = A S K ε 2 ( T T sin ( ϕ / 2 ( U αt 0. (5 The desired mbient temperture compenstion is chieved, if the output, i.e. Equ. (5 is independent of the mbient temperture T. This mens tht the two terms contining T, must cncel out, i.e. the following reltion must be fulfilled: ( ϕ / 2 0 α ASK ε sin 2 =. (6 2001 PerkinElmer Optoelectronics GmbH Pge of 8
ppliction note thermopile sensors: quntittive pyrometry The djustment of the compenstion of the module is performed by regulting the mplifiction of the first stge. According to Equ. (6 this mplifiction fctor mounts to α A =. (7 SKε sin 2 ϕ / ( 2 Equ. (7 is worth closer look. The djustment of the mplifiction of the thermopile stge is not only due to the thermopile sensitivity S s one would of course imgine, but lso on both the fieldof-view of the sensor nd the emission fctor of the ect to be sensed! This mens tht, if you get clibrted PerkinElmer thermopile module M, you re not llowed to bring ny dditionl filter or perture into the opticl pth, since then not only the output curve will chnge its vlue, but lso the mbient temperture compenstion will be gone. The module is usully clibrted nd the mbient temperture compenstion is set for certin optics nd n emission coefficient of 0.95, which covers most pplictions. Two remrks here, before we continue with the digitl version: Of course it is possible to djust the mplifiction stge to your specil ppliction, where you need to sense n ect with different emission fctor, or hve the requirement to put ny dditionl filter or perture into the opticl pth. The thermopile ppliction tem of PerkinElmer in Wiesbden, Germny, is hppy to perform the necessry mesurements nd clcultions for you nd deliver device tht perfectly suits your ppliction. These ctions need, however, to be reimbursed if your ppliction runs only in low volumes!. Plese do not employ the nlog temperture compenstion for ny ppliction tht requires high ccurcy, nmely er thermometers or precision pyrometers. Becuse the two functions, thermopile output nd thermistor curve, tht hve to be dded, do not hve exctly the sme functionl behvior, the devitions re too lrge to meet interntionl stndrds for e.g. medicl devices. The nlog version cn hrdly deliver n bsolute ccurcy better thn ± C. This is indeed sufficient for the mjority of consumer pplictions nd industril regulting devices, but not for n instrument, where n bsolute vlue hs to be deducted in rnge better thn 0.1 C. Digitl solution In the lst section it becme cler tht one of the min fctors tht determine the ccurcy of thermopile bsed pyrometer device is the mbient temperture compenstion. The nlog solution presented is indeed t very low costs, but lcks of bsolute ccurcy. For precision devices it is therefore needed to employ numericl method which llows the ddition of compenstion vlue which fits exctly to the signl chnge. For this purpose, the two signls, thermopile voltge nd thermistor resistnce (voltge re derived seprtely nd fed into n nlog-digitl (A/D converter. The A/D trnsfers the vlues into micro controller system, where the necessry clcultions re mde. The clculted temperture output cn then either be presented in digitl form or it will be fed into digitl-nlog converter stge tht delivers linerized signl. The principle circuit is shown in Fig. 3. If you look t Equ. (3 gin, it seems tht it is necessry to feed two-dimensionl field of U versus T nd T into the micro controller to mke the computer ble to derive the ect s temperture t ny possible mbient condition. Fortuntely, by nlyzing the structure of the eqution, we cn come to much simpler solution. In fct, only two one-dimensionl look-up tbles re necessry: One for the thermopile voltge U versus T t fixed mbient temperture T ref, nd one tble for the thermistor resistnce (or thermistor voltge versus the mbient temperture T. To see this, we will chnge the nottion of the formuls from the physicl (nlyticl picture to more bstrct wy. In generl it is not necessry to know the exct functionl behvior of U versus T nd T, it is only importnt to know bout the following property of the functionl behvior. The het blnce eqution cn generlly be written s 2001 PerkinElmer Optoelectronics GmbH Pge 5 of 8
ppliction note thermopile sensors: quntittive pyrometry U = K f T, T. (8 ( The function f does not need to be known in n explicit wy. Importnt to know is the expnsion property of the het blnce eqution s follows: U = K f T, T K f ( T, T, (9 ( ref ref with T ref being n rbitrry fixed temperture, e.g. 0 C. Now we cn work with single look-up t- f T,. For mesurement, this tble is now used twice: first the correction ble, where we list ( T ref term ( f T, T ref is obtined, by using T s look-up prmeter nd then T is derived by looking into the sme tble in reverse direction. T T ref = 0 C A U = A K f ( T, T U ϑ A/D MCU Output signl I A Th T = g ( R th T Figure 3: Schemtic of micro controller bsed pyrometer circuit with numericl mbient temperture compenstion. R th.1 The mesurement procedure To be more specific, the mesurement procedure will be listed here step by step, where it is ssumed, tht the clibrtion fctors re lredy known. We will del with the clibrtion procedure in the next prgrph. Step 1: Mesure the thermistor resistnce R th vi the thermistor voltge U th. Then derive the mbient temperture from the thermistor vlue R th. The necessry function g ( R th is listed in look-up tble, from which T is derived by multiplying R th with the clibrtion fctor : Step 2: T ( = g. (10 R th With T now known, obtin the mbient temperture compenstion term f ( T, T ref. 2001 PerkinElmer Optoelectronics GmbH Pge 6 of 8
Step 3: ppliction note thermopile sensors: quntittive pyrometry Now you cn get the ect temperture by reverse looking in ( T f U ( T Tref = + f ( T, Tref T f, :,. (11 K This method cn be very ccurte if the clibrtion fctors nd K re known. How to obtin these is subject of the following section..2 The clibrtion procedure.2.1 Thermistor A thermistor is chrcterized by two prmeters: first the so-clled β-vlue nd second by n bsolute resistivity vlue t fixed temperture mostly t 25 C. For exmple, the two different thermistors which re employed in the vrious PerkinElmer thermopile sensors hve nominl vlues of 30 kω nd 100 kω t 25 C, respectively. Since the mterils of these two thermistors re identicl, their β-vlues re equl. In prctice, the nominl vlue t 25 C nd lso the β-vlue hve certin vrition from both their specified vlue nd from device to device. For exmple, the nominl vlue my vry ±5%, which is n error resulting minly from geometricl devitions. The β-vlue vries typiclly round 1% this error is result of structurl nd/or composition devitions, i.e. mteril properties. For the typicl mbient temperture which is of interest, e.g. 10 to 5 C, the β-vlue is often ssumed to be constnt nd will therefore not clibrted, i.e. djusted to fit the individul thermistor curve. The devition from the bsolute vlue, however, is mostly significnt nd hs to be clibrted. With the nominl thermistor curve R th versus T clled g ( R th, one cn djust this curve by multipliction fctor to fit the nominl (tbulted vlue. This is shown in Equ. (10. The prmeter is obtined by mesuring the thermistor resistnce t fixed nd stble, well known mbient temperture, e.g. within n extremely good thermosttized chmber or room nd then compring with the nominl vlue. The lookup tble then contins the nominl thermistor vlues in e.g. steps of 2.56 C or 1.28 C, dependent, wht bsolute ccurcy is needed. By liner interpoltion in tble with 2.56 C spcing, it should be possible to chieve n ccurcy better thn 0.3 C. This cn esily be seen by compring the linerized vlue with the nominl one. For the PerkinElmer thermistors, tbulted vlues re obtinble on request. One remrk t lst: Before being ble to clibrte for thermistor vlue devition, it is of course necessry to clibrte ech device with known resistor nd/or voltge to be sure to mesure the right thermistor resistnce..2.2 Instrument fctor (thermopile The instrument fctor K contins ll device vritions in thermopile sensitivity nd view ngle. If the overll response chrcteristics of the thermopile stys constnt nd tht is mostly the cse, since smll devitions in the filter properties do virtully not ffect the integrted signl one cn store n experimentlly derived lookup tble for the thermopile vlues, i.e. f ( T, T ref for the ect temperture rnge in question. The clibrtion will now be performed t fixed mbient temperture T. The thermopile will be shown two blck bodies t different tempertures T 1 nd T 2. This results in the two output voltges: ( f ( T T f ( T T U 1 = K 1, ref, ref nd (12 ( f ( T T f ( T T U =, (12b 2 K 2, ref ref T ref 2001 PerkinElmer Optoelectronics GmbH Pge 7 of 8
ppliction note thermopile sensors: quntittive pyrometry By subtrcting these two equtions, (12 nd (12b, one cn eliminte the constnt term f ( T, T ref nd thus clculte the instrument fctor K. After these two clibrtion steps, the device is redy for mesurement. For the finl test check of the right clibrtion should be performed with third blckbody t nother temperture. Remrk: This wy of clibrtion ssumes tht the sensitivity of the thermopile nd concomitntly the instrument fctor K is not function of the mbient temperture! For the PerkinElmer thermopiles mde by CMOS comptible Si-technology nd not contining Bi-Sb lloys, the sensitivity S vries only bout 0.02%/K, which is virtully constnt over the mbient rnge of interest. 5 Conclusions This short pper could of course not cover ll the detils regrding your specil ppliction of remote temperture mesurement (pyrometry by using PerkinElmer thermopiles. We hope, however, tht we could give you the necessry hints to bring your project to successful ending. If there re ny dt necessry for your ppliction, plese do not hesitte to contct us. Well, we re not ble to tke your development prt, but the ppliction tem t PerkinElmer Wiesbden is hppy to give you the necessry (nd hopeful useful dvice. For the nlog solution, the PerkinElmer thermopile modules come redily clibrted to be plugged in into the ppliction. For the digitl solution PerkinElmer cn offer n instrumenttion mplifier tht includes multiplexer, low-noise opertionl mplifier, 1 bit A/D converter, n 8 bit micro controller, digitl input/output ports, which my lredy come in module form combined with one of our thermopile sensors to form digitl pyrometer. 6 Literture [1] J. Schilz, thermophysic minim: thermoelectric infrred sensors (thermopiles for remote temperture mesurements; pyrometry, PerkinElmer Optoelectronics. [2] see e.g.: W.J. Smith; Modern Opticl Engineering, The design of Opticl Systems, Opticl nd Electro-Opticl Engineering Series, Eds: R.E. Fischer & W.J. Smith, Mc Grw Hill 1990. 2001 PerkinElmer Optoelectronics GmbH Pge 8 of 8