OPTIMIZATION OF WAVELENGTHS FOR QUADRI-SPECTRAL PYROMETER IN VISIBLE AND NEAR INFRARED RADIATION RANGE USED FOR HEAT TREATMENTS OF STEELS

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1 Vol- Issu-5 08 IJARIIE-ISS(O) OPIMIZAIO OF WAVELEGHS FOR QUADRI-SPERAL PYROMEER I VISIBLE AD EAR IFRARED RADIAIO RAGE USED FOR HEA REAMES OF SEELS RAIAARIVO Paul Ezkl, RASEFAO Elisé, RAKOOMIRAHO Soloniaina PhD studnt, SE-I-MSDE, ED-SII, Antananarivo, Madagasar Profssor, SE-I-MSDE, ED-SII, Antananarivo, Madagasar hsis dirtor and Laboratory Managr, SE-I-MSDE, ED-SII, Antananarivo, Madagasar ABSRA Optimum wavlngths for a pyromtr that an b usd during th hat tratmnt of stls will b sltd at th nd of this artil. hanks to on of th physial proprtis of hot stls whih has th possibility to radiat, it is possibl to rmotly masur its tmpratur on th surfa. his tmpratur is proportional to th infrard or visibl radiation mittd. h systm is quippd with optial filtrs to ontrol ltromagnti radiation and onvrg thm to th appropriat dttor. hs optial filtrs ar haratrizd aording to th wavlngths usd. h pyromtr w talkd about will b a quadri-sptral pyromtr. Stl is on of th nonlinar missivity mtals, so th masurmnt of tmpratur rquirs a thni whih is abl to ovrom this nonlinarity. A modl alld L.ab that mans mpratur by on Linar modl with, a, b, and th paramtrs to stimat will b usd to slt th optimal wavlngths. It will fous on minimizing a ost funtion by th ordinary last squars mthod. With this modl w will squntially hoos th optimal wavlngths on aftr th othr by invrs mthod. his mthod onsists in fixing th tmpratur and finding th wavlngth orrsponding to th tmpratur st. h first wavlngth obtaind will b usd to alulat th sond. And this prinipl will b applid to find th third as wll as th fourth. Optimum wavlngths will b obtaind from fiv (5) sltd tmpraturs in th tmpratur rang of hat tratmnt of stls. Eah of thos wavlngths must pass th tst of th various ritria to minimiz th rrors of masurmnts on th tmpratur. h wavlngth groups that will mt ths ritria will b th optimum wavlngths for a pyromtr for th hat tratmnt of stls. Kyword: Quadri-sptral pyromtr, optimal wavlngth, ltromagnti radiation, mpratur, and Hat tratmnt of Stl. IRODUIO h tmpratur is th physial quantity vry ssntial in th filds of produtions. And most of th tim, to know it, w us thrmomtrs that ar in dirt ontat with th objt whos tmpratur is masurd. But this thniqu is not appliabl at all for moving objts, loatd in a hazardous ara, for objts with poor thrmal ondutivity, dformabl surfa and spially for vry high tmpratur. h mtallurgial industris ar th

2 Vol- Issu-5 08 IJARIIE-ISS(O) most afftd by ths problms, suh as th hat tratmnt of mtals. It is for this rason that th radiativ proprty of matrials is xploitd so that its tmpratur an b masurd rmotly []. hr ar svral thniqus usd for th ralization of a pyromtr. On of ths thniqus is th quad sptral mthod that uss svral wavlngths. A major problm in th dsign of suh a multi-sptral pyromtr is th hoi of wavlngths to b usd baus it is ssntial and kps a vry important rol in th tmpratur alulation. In addition, mtals ar haratrizd by thir nonlinar missivity, low in th rang of visibl and nar infrard wavs. his non-linarity of th missivity maks it diffiult to masur th tmpratur and auss srious rrors. h hoi of wavlngths is vry important in minimizing tmpratur rrors and rlativ rrors du to th sptral missivity of mtals. In this artil, w will try to find th optimal wavlngths usd for a four-band multi sptral pyromtr in visibl and nat infrard rang for th hat tratmnt of stls. h goal is to hav th four wavlngths whos rror on th tmpratur of th fluxs obtaind and th rror rlating to th sptral missivity of th stls ar minimal.. LAW OF ELEROMAGEI RADIAIO.. Law of Plank Lt a blak body at th tmpratur, th nrgy dnsity of th radiation of this body an b alulatd. h alulations ar basd on th assumption that th ltromagnti fild in th limitd avity of th blak body is quivalnt to a st of indpndnt harmoni osillators in thrmodynami quilibrium at tmpratur and obying th Boltzmann statisti. It is shown that th luminan L 0 ( ) of th blak body is qual to th nrgy dnsity of th radiation multiplid by, whr th luminan is th ratio of th luminous intnsity or nrgy dnsity of th radiation to th mission surfa []. L 0 ( ) 5 h xp h k Whr h= 6.655x0 - Js Plank onstant, k =.8x0 - JK - Boltzmann onstant, =.996x0 8 ms - spd of ltromagnti wavs in vauum. his formula is also usd with th so-alld Plank onstants and : 5 0 i ( ) xp L i.. Dfinition of sptral missivity with h and h k h ratio btwn th monohromati luminan of th ral sour L ( ) and that of th blak body L 0 ( ), for th sam valus of th wavlngth λ and th tmpratur, dfins th monohromati missivity or sptral missivity of th sour []. L ( ) ( ) 0 L In th gnral as, dpnds on th sour, th wavlngth λ and th tmpratur and th dirtion of mission. Whras th total missivity is dfind in th sam way by th following rlation: t d 0 h luminan of th blak body dos not dpnd on th dirtion of mission, and if it is th sam for th ral sour (sour radiating aording to Lambrt's law), th sptral missivity dos not dpnd ithr on th dirtion of mission

3 Vol- Issu-5 08 IJARIIE-ISS(O) Sptral missivity of mtals h dpndn on wavlngth missivity an b xprssd in svral forms, but w will onsidr thos that an adjust xprimntal masurmnts or simplify th analysis. Most surfas hav missivity that varis with wavlngth and tmpratur. h missivity of mtal surfas in th wavlngths of th visibl and th nar infrard oftn hav a polynomial dpndn on th wavlngth []. n 0... n In our as, w us th polynomial modl of ordr : a b But in thory, th missivity dpnds on th matrial, th natur of its surfa, th tmpratur, th wavlngth and possibly th masurmnt onfiguration usd. Sin mtals oftn rflt radiation, thy ar gnrally haratrizd by a low, non-linar mission lvl, whih is highly dpndnt on th surfa strutur and tnds towards long wavlngths. his dpndn an lad to diffrnt and unrliabl masurmnt rsults []. Whn hoosing th appropriat thrmal masuring dvis, it should b nsurd that th infrard radiation is masurd with a rtain wavlngth and a tmpratur rang for whih th mtals hav a rlativly high dgr of mission.. MULI-SPERAL MEHOD BASED O PLAK LAW.. Prsntation of th L.ab modl h goal is to find th tmpratur of th stl during th hat tratmnt with its missivity simultanously. h modl "L.ab" mans mpratur by on-linar modl with, a, b and, th paramtrs to b stimatd. his modl is unbiasd and basd on th stimation of flux xprssd using Plank's law. It will also tak into aount th polynomial modling of th missivity up to th ordr of th global sptral transfr funtion of th masurmnt hain using offiints (a, b, ). h flux as a funtion of wavlngth and tmpratur is L, a, b, [5]. i,,, i i L a b a b i i i i 5 i xp With a b sptral missivity. h stimation of th paramtrs (, a, b, ) will thn b arrid out by minimizing th funtion xp,,, L dnots th sptral xprimntal flux masurd at th wavlngth i, and J a b, in whih L i, a, b, i is th thortial sptral flux at th wavlngth i. xp,,,,,, J a b L L a b i xp i i xp J, a, b, L L, a, b,... L L, a, b, ot: h indx dsignats th four (0) wavlngths for th stimation of th four paramtrs,,, So w hav four (0) quations for th thortial flows L, a, b,, L,,, a b, L, a, b, L, a, b,. a b. t

4 Vol- Issu-5 08 IJARIIE-ISS(O) Modl with th mthod of squntial sltion of wavlngths h mthod usd to stimat th tmpratur is basd on th minimization of a ost funtion using ordinary last squars mthod. With this mthod w will dfin optimal wavlngths with th invrs mthod. his mthod onsists of fixing th tmpratur and finding th wavlngth orrsponding to this tmpratur. hs wavlngths minimiz th standard dviation on th stimatd tmpratur. h dtrmination of th diffrnt optimal wavlngths will b arrid out using th ost funtion assoiatd with th modl "L.ab" baus this dos not rquir th approximation of Win, dos not prsnt any systmati bias in th prsn of J, a, b, additiv nois to th flux and zro avrag [][5][6]. h statistial proprtis of th paramtr stimator assoiatd with th L.ab modl and th paramtrs providd by th last squars mthod ar givn by th Varian-ovarian matrix. h matrix from whih on an dtrmin th standard dviations of th diffrnt paramtrs, and in partiular, that of th tmpratur i. h L.ab modl is a nonlinar modl, w will thn us th approximat xprssion of th Ordinary Last Squars varian- ovarian matrix, whih is givn for a paramtr vtor, a, b, nois, indpndnt, idntially distributd (varian ov ov, a ov, b ov, a a a b a b a b b b a b ov, ov, ov, ov, ov, ov, ov, ov, ov, nois is onstant, and zro man), by: t XX, undr assumptions of an additiv nois With X th snsitivity matrix assoiatd with th varian-ovarian matrix, dfind by: X,,,,,,,,,,,, L a b L a b L a b L a b a b L, a, b, L,,,,,,,,, a b L a b L a b a b L, a, b, L, a, b, L, a, b, L, a, b, a b L, a, b, L, a, b, L, a, b, L, a, b, a b And th standard dviation on th tmpratur is givn aording to th standard dviation on th nois nois, by: XX t nois W will tak as valu th standard dviation of th nois, whih w hav xprimntally with th infrard amra, and having for valu law [5]. nois 8,97.0 Wm.. Psudo-optimal mthod for th sltion of wavlngths, hat is to say % of th maximum of Plank's h psudo-optimal mthod onsists in squntially slting th wavlngths whil rspting all th diffrnt ritria. hs wavlngths ar thos that minimiz th standard dviations on th tmpratur at a

5 Vol- Issu-5 08 IJARIIE-ISS(O) fixd tmpratur finding th tmpratur rang of th hat tratmnt of th stls. In our as, w will us a tmpratur st ( S ) for th alulation at 07.5 K, 7.5 K,.5 K, 7.5 K and 7.5 K. Sltion of th first optimal wavlngth h mthod of squntial sltion of "psudo-optimal" wavlngths onsists of hoosing for th first wavlngth filtr OP, th on whih minimizs th standard dviation on th tmpratur, assuming that th masurmnt is mono sptral. h ost funtion J onsists of only on paramtr: th tmpratur. xp,,, J L L a b h tmpratur is thn th only paramtr to stimat. h snsitivity matrix X is omposd only of th first olumn and first row. X L, a, b, Exprssion of th standard dviation of tmpratur: nois h minimization of th ost funtion J, involvs th snsitivity matrix X of th flux at th various paramtrs to b stimatd. h first optimal wavlngth OP will minimiz this standard dviation. Sltion of th sond optimal wavlngths h sltion of th sond filtr is prformd by stting a =, b =, and OP. And looking for sond wavlngth, th shortst that minimizs th loal standard dviation of tmpratur in th L.a modl. h funtion ost, J a and th snsitivity matrix X ar rsptivly omposd as follows: xp xp xp i i i J, a L L, a, b, L L, a, b, L L, a, b, X,,,,,, L a b L a b a L, a, b, L, a, b, a t Aftr th sltion of th first raw and olumn of th matrix X X, th xprssion of th standard dviation of tmpratur will b shown in th nxt rlation

6 Vol- Issu-5 08 IJARIIE-ISS(O) D D nois With 0 0 a a D a a D 0 0 Sltion of th third optimal wavlngths For th third wavlngth, it is obtaind by minimizing th ost funtion J, a, b with th snsitivity matrix X assoiatd with th modl L.ab by fixing OP and OP. xp xp xp i i i J, a, b L L, a, b, L L, a, b,... L L, a, b, X,,,,,,,,, L a b L a b L a b a b L, a, b, L,,,,,, a b L a b a b L, a, b, L, a, b, L, a, b, a b t Aftr slting th first raw and olumn of th matrix X X, th xprssion of th standard dviation of tmpratur will b shown in th nxt rlation. D D D D D D D D D D D D D D nois

7 Vol- Issu-5 08 IJARIIE-ISS(O) With a b a b a b D D D D a b a b a b a b a b a b D

8 Vol- Issu-5 08 IJARIIE-ISS(O) D D a b a b a b Sltion of th fourth and last optimal wavlngths h fourth optimal wavlngth will b obtaind on th sam prinipl as how to obtain th sond and th third optimal wavlngth by fixing a =, b =, =, OP, OP and OP. h ost funtion J, a, b, and th snsitivity matrix X assoiatd with th modl L.ab ar rsptivly rprsntd as follows: xp xp xp i i i J, a, b, L L, a, b, L L, a, b,... L L, a, b, X,,,,,,,,,,,, L a b L a b L a b L a b a b L, a, b, L,,,,,,,,, a b L a b L a b a b L, a, b, L, a, b, L, a, b, L, a, b, a b L, a, b, L, a, b, L, a, b, L, a, b, a b t Aftr slting th first raw and olumn of th matrix X X, th xprssion of th standard dviation of tmpratur will b shown in th nxt rlation. D nois

9 Vol- Issu-5 08 IJARIIE-ISS(O) D D D D5 D6 D7 D7 D D5 D D D D D D7 D 6 D6 D D D5 D6 D7 D D5 D9 D 8 D D D D6 D D9 D6 D7 D D5 D D D D5 D 9 D D D D D7 D9 D 6 D7 D6 D D D D D6 D D 9 D 7 D7 D D D7 D9 Av a b a b a b a b D D

10 Vol- Issu-5 08 IJARIIE-ISS(O) D a b a b a b a b D D a b a b a b a b D6 D D a b a b a b a b D9. RIERIA FOR HE SELEIO OF OBAIED OPIMUM WAVELEGHS Our pyromtr must b vry snsitiv to th tmpratur btwn K and 7.5 K. his rang bordrs th tmpratur rang of th hat tratmnt of stls whih is btwn K and.5 K [8]. So that w an hav bttr optimal wavlngths, w will try to find optimal wavlngths from th tmpratur st ( S ) at 07.5 K, 7.5 K,.5 K, 7.5 K and 7.5 K... ritria on th sptral rang of th pyromtr Our first ritrion for th sltion of optimal wavlngths is th sptral rang of our pyromtr whih oprats in th band btwn 0. μm to μm. h missivity of th stls is vry low from th sptrum of lngth μm. But to hav many hois on th wavlngths obtaind, w will us th sptral band of 0. µm to.5 µm (abl-). Masuring th tmpratur of a mtal rquirs th us of short wavlngth to avoid th rlativ rror du to missivity. h multi sptral masurmnt minimizs th rror so th hoi of short wavlngth givs a bttr prision on th tmpratur. It is obsrvd that ah tim a wavlngth is addd, th standard dviation dtriorats

11 Vol- Issu-5 08 IJARIIE-ISS(O) abl-: Optimum wav lngths prsltd aording to th sptral rang of th pyromtr HAEL HAEL HAEL HAEL S [ K] OP [ K] OP [ K] OP [K] OP [µm] [ K] [µm] [µm] [µm] ritria on th minimum dviation of th two sussiv wavlngths o avoid amplifying th masurmnt rror, whil rmaining as los as possibl in ordr to minimiz th masurmnt rror du to th sptral variation of th missivity, th minimum diffrn of th two sussiv wavlngths must b rsptd. M in M in ji j i j j i h minimum diffrn btwn th first and th sond wavlngth will thrfor b. So th sond maximum wavlngth will b sltd aording to this rlation OP OP M in OP Max OP M in. h diffrn btwn th sond and th third wavlngth will b OP OP M in. h maximum valu of th third wavlngth is thn OP Max OP M in. Sam prinipl for th last and fourth optimal wavlngth, OP OP M in thn OP Max OP M in. h four sltd optimal wavlngths rspting th ritrion of th minimum standard dviation on th tmpratur and th minimum diffrn btwn two sussiv wavlngths, for a tmpratur of 07.5 K, 7.5 K,.5 K, 7.5 K and 7.5 K will b rprsntd in tabl

12 Vol- Issu-5 08 IJARIIE-ISS(O) In th infrard, th standard dviation an not b xdd by 5%. h highst valus wr ahivd for th shortst wavlngth and wavlngths disturbd by atmosphri absorption. In th othr infrard sptral rangs, th standard dviation btwn th first and th last sptrum was lss than % []. abl-: Optimum wavlngths obtaind from 07.5 K, 7.5 K,.5 K, 7.5 K and 7.5 K aording to th ritrion of minimum dviation of th two sussiv wavlngths S [ K] OP [µm] [ K] [%] [µm] min λ OP =.6 λ OP =.55 λ OP = λ OP - λ OP = 0.7 λ OP - λ OP = 0.9 λ OP - λ OP = 0.9 λ OP = λ OP = λ OP - λ OP = 0.65 λ OP = λ OP - λ OP = 0.8 λ OP = λ OP - λ OP = 0.0 λ OP = λ OP = λ OP - λ OP = 0.6 λ OP = λ OP - λ OP = 0.05 λ OP = λ OP - λ OP = 0.9 λ OP = λ OP = λ OP - λ OP = λ OP = λ OP - λ OP = 0.9 λ OP = λ OP - λ OP = 0.85 λ OP = λ OP = λ OP - λ OP = λ OP - λ OP = 0.7 λ OP - λ OP = 0.7 λ OP = λ OP = λ OP = [µm] λ OP - λ OP = 0. λ OP - λ OP = 0.9 λ OP - λ OP = 0. λ OP - λ OP = 0. λ OP - λ OP = 0.60 λ OP - λ OP = λ OP - λ OP = 0.9 λ OP - λ OP = 0.5 λ OP - λ OP = 0.09 λ OP - λ OP = 0.7 λ OP - λ OP = 0.8 λ OP - λ OP = λ OP - λ OP = 0.9 λ OP - λ OP = 0.9 λ OP - λ OP = 0.08 Obsrvation of abl-: First, it is obsrvd that only on group of optimal wavlngth whih is obtaind from ah tmpratur st rspts th ritrion of minimum distan btwn two sussiv optimal wavlngths. Sond, in addition, th minimum distan rquird btwn two wavlngths is proportionally with th largst wavlngth among th two sussiv ons. hird, w also not that all groups of optimal wavlngths that hav th lowst standard dviation do not mt th ritrion of minimum distan btwn two sussiv wavlngths... Standard dviation on th tmpratur at th tmpratur rang of th fluxs obtaind from th optimal wavlngths Vrifiation of th standard dviation of th optimal wavlngths is almost nssary to know th rrors on th tmpratur throughout th tmpratur rang from K to 7.5 K of th hat tratmnt of th stls (abl-). Obsrvation of abl-: First, w hav four (0) optimal lngths that rspt th minimum diffrn btwn two () sussiv wavlngths for a tmpratur st. Mor th tmpraturs sts inrass to 7.5 K, th wavlngths dras to at last 0.0 μm. Sond, w also not that th standard dviation on tmpratur improvs as wll as th tmpratur to b masurd inrass. hird, mor th wavlngth drass, th standard dviation dtriorats, that is to say inrass ( S =.5 K: λ OP =.970 μm, λ OP =.6 μm, λ OP =.0 μm, λ OP = 0.88 μm If w apply ths wavlngths at = 07.5 K, w hav rsptivly a standard dviation of tmpratur: K, K, K, K)

13 Vol- Issu-5 08 IJARIIE-ISS(O) Fourth, th standard dviation dtriorats rapidly if th wavlngth xds th lowr limit of th nar-infrard rang (λ OP = μm alulatd from th tmpratur st at S = 7.5 K, th standard dviations on th tmpratur of this wavlngth for th tmpratur rang of our pyromtr ar, at = K givs = K and at = 7.5 K givs = K). Fifth, th tmpratur rang of our pyromtr is K up to 7.5 K, w s that th optimal lngths obtaind at S = 07.5 K hav a bttr standard dviation ompard to thos obtaind at S = 7.5 K. h worst standard dviation is K at = K for S = 07.5 K, against K at = K for S = 7.5 K. abl-: Standard dviation on th tmpratur [ K] at th sptral rang of th pyromtr of th optimal wavlngths obtaind S [ K] λ OP Pyromtr tmpratur rang [ K] [µm] λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = Snsitivity of th flux at tmpratur and wavlngth h modl alld L.ab onsists in making tmpratur masurmnts without mastring all th influning fators. Howvr, it is nssary to tak rtain prautions to minimiz th masurmnt rror on th tmpratur. Howvr, our fild of work is on th inrasing part of th Plank urv baus th rdud snsitivitis of th flux at th tmpratur and at th wavlngth ar all th bttr that w work at short wavlngths. h wavlngths obtaind should giv bttr snsitivity to tmpratur (abl-) and wavlngth (abl-5). dl and L d Obsrvations of tabl-: dl L d First, th snsitivity of th flux to th tmpratur inrass as th wavlngth drass. Sond, in th sptral band of our pyromtr, th snsitivity of th flux to th tmpratur applid to a wavlngth drass if th tmpratur inrass. hird, in th sptral band btwn 0. μm and.5 μm, th snsitivity of th flux to th tmpratur is mor and bttr at K than at 7.5 K uppr limit of our tmpratur to b masurd. abl-: Snsitivity of th flux obtaind from th optimal wavlngths at th tmpratur

14 Vol- Issu-5 08 IJARIIE-ISS(O) S [ K] λ OP Pyromtr tmpratur rang [ K] [µm] λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = abl-5: Flux snsitivity at th wavlngth in th tmpratur rang of th pyromtr S [ K] λ OP Pyromtr tmpratur rang [ K] [µm] λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = λ OP = Obsrvations of tabl-5: First, th snsitivity of th flux to th wavlngth inrass whn th wavlngth drass. Sond, th snsitivity of th flux at th wavlngth of th wavlngths obtaind from th highr tmpratur is mor and bttr than that obtaind at th lowr limit in th tmpratur rang to b masurd. hird, th xistn of ngativ valus justifis that th us of ths wavlngths obtaind at S btwn 07.5 K and.5 K an giv srious rrors if th tmpratur to b masurd is gratr than 7.5 K. hrfor ths wavlngths do not ovr, in trms of snsitivity on flow, th tmpraturs nssary for th hat tratmnt of stls

15 Vol- Issu-5 08 IJARIIE-ISS(O) Synthsis of th ritria rsult In our as, aording to th pyromtr sptral rang, th high irradiation rang of stls in visibl and nar infrard rgion, and all th ritria to slt optimal wavlngths for hat tratmnt of stls, two groups of four wavlngths hav bn sltd. h first group is obtaind from S =7.5 K. hos wavlngths ar λ OP =.89 μm, λ OP =.9 μm, λ OP =.000 μm, λ OP =0.85 μm. hy found in th nar infrard rgion. So thos optimal wavlngths do not rovr totally our sptral rang whih is in th visibl and nar infrard. h sond group of optimal wavlngths was obtaind by using S =7.5 K. hy ar λ OP =.755 μm, λ OP =.99 μm, λ OP =0.97 μm, and λ OP =0.756 μm. In omparison of th first group, thy hav bttr standard dviation and ovr in th visibl and nar infrard rang that stls hav bst irradiation with missivity is highr than Graphial vrifiation of th four optimal wavlngths in th visibl and nar infrard rang 5.. First optimal wavlngth λ OP =.755 μm A singl wavlngth is obtaind for th first sltion, it is λ OP =.755 μm. It minimizs th standard dviation on th tmpratur or th rror on th tmpratur. It is in th sptral rang of our dttor. It is far from th ara whr th nois quivalnt powr and th snsitivity of th flux to th tmpratur ar low. his wavlngth fully rspts all th sltion ritria (hart-). hart-: First optimal wavlngth minimizing standard dviation of tmpratur 5.. Sond optimal wavlngth λ OP =.99 μm wo () optimal wavlngths ar availabl for th sond filtr. hy minimiz th tmpratur rror. On is λ OP =.99 μm whih has a standard dviation on th tmpratur of K and th othr is λ OP =.8 μm whih givs a standard dviation on th tmpratur of K. h optimum wavlngth λ OP gratly xds th sptral band of our dttor. It is also in th ara whr th snsitivity of th flux of th tmpratur is low. W know that th mission of stls is vry low for sptra longr than μm. Howvr, th optimal wavlngth λ OP =.99 μm lis in th sptral rang of our dttor whih is from 0. μm to.5 μm. It is loatd nithr in th ara whr th snsitivity of th flux to th tmpratur is wak, nor in th ara of low nois quivalnt powr. h sond optimal wavlngth will thrfor b λ OP =.99 μm with (hart-)

16 Vol- Issu-5 08 IJARIIE-ISS(O) hart-: Sond optimal wavlngth minimizing standard dviation of tmpratur 5.. Fird optimal wavlngth λ OP =0.97 μm In th sltion of th third wavlngth, thr wavlngths wr sltd and minimizd th standard dviation on th tmpratur. wo wavlngths λ OP = 0.97 μm, λ OP =.5 μm ar in th sptral rang of our dttor whih ar btwn 0. μm and.5 μm. hs two wavlngths ar nithr th zon whr nois quivalnt powr is low, nor th ara of low snsitivity of th flux to tmpratur. hir tmpratur rrors do not xd 5%. h third lngth λ OP =.8 μm far xds th uppr limit of th sptral rang of th pyromtr. It is in th part of th sptrum whr th stls mit wakly so it an giv an unrliabl masurmnt for th tmpratur. By alulating th minimum diffrn btwn λ OP =.99 μm and λ OP, only λ OP = 0.97 μm whih may b th third optimal wavlngth for th third filtr baus it rspts th minimum distan rquird by th sond optimal wavlngth. his wavlngth has a standard dviation on th tmpratur of K (hart-). hart-: hird optimal wavlngth minimizing standard dviation of tmpratur

17 Vol- Issu-5 08 IJARIIE-ISS(O) Fourth optimal wavlngth λ OP =0.756 μm Four optimal wavlngths wr obtaind for th sltion of th fourth lngth. hr λ OP = μm, λ OP =.088 μm, λ OP =.6 μm ar in th visibl and nar-infrard sptra ara. hy ar also in th sptral rang of our dttor. hs thr wavlngths ar sparatd by aras whr th signal-to-nois ratio is low. hir standard dviations ar all lss than 5%. h wavlngth λ OP = μm whih is largly far from th sptral rang of our pyromtr. his wavlngth is obviously not optimal for our as. Stls hav a vry low sptral mission in th far infrard rgion. h minimum diffrn rquird by th third optimum wavlngth λ OP = 0.97 μm is 0.7 μm. So only λ OP = μm whih ould b th fourth optimal wavlngth. It has an rror on th tmpratur of 0.7 K. hart-: Forth optimal wavlngth minimizing standard dviation of tmpratur 6. OLUSIOS h L.ab modl basd on Plank's law givs th possibility of finding tmpratur and sptral missivity at th sam tim. his modl allowd us to squntially slt optimal wavlngths for a multi sptral pyromtr for th hat tratmnt of stls. Among th optimal wavlngths obtaind from 07.5 K, 7.5 K,.5 K, 7.5 K and 7.5 K, only a group of four wavlngths rspts th ritrion of minimum distan btwn two sussiv wavlngths. h hoi of ths wavlngths starting from th minimum standard dviation is thn an insuffiint ritrion. All optimal wavlngths hav good tmpratur snsitivity btwn K and 7.5 K. But th fluxs at ths optimal wavlngths ar not at all snsitiv if th tmpratur is btwn 7.5 K and 7.5 K. In addition, thir standard dviation is vry far from xding th 5% rror limit. o onlud, only th optimal wavlngths obtaind from th tmpratur st at 7.5 K mt all th ritria for slting th four optimal wavlngths for a quadri-sptral pyromtr in th visibl and nar infrard rang for th hat tratmnt of stls. hrfor, with th mthod of squntial sltion of th optimal wavlngths of th modl L.ab by th ordinary last squar mthod, it is bttr to us th tmpratur towards th uppr limit of th tmpratur rang (975.5 K and 7.5 K) to b masurd than th tmpratur towards th lowr limit. And th losr you gt to th highr limit, th longr th wavlngths rah th visibl part. In th visibl and nar infrard rang, just on group of four optimal wavlngth mt all ritria. hos wavlngths ar λ OP =.755 μm, λ OP =.99 μm, λ OP =0.97 μm, and λ OP =0.756 μm

18 Vol- Issu-5 08 IJARIIE-ISS(O) REFEREES [] François ABAES, Pyrométri optiqu (R60), Edition hniqus d l Ingéniur, traité Msurs t ontrôl [] J.P. BARDO, mpératurs d surfa, otions fondamntals (R70) Edition hniqus d l'ingéniur [] Magdlin HUEZ-AUBER, Rayonnmnt thrmiqu ds matériaux opaqus (A50), Edition hniqus d l'ingéniur [] h.duvaut, omparison btwn multiwavlngth infrard and visibl pyromtry: Appliation to mtals, [5] hristoph RODIE, Msur d mpératur par Méthods Multi-Sptrals t aratérisation hrmiqu d Matériaux Anisotrops par ransformations Intégrals : «Aspts héoriqus t Expérimntaux» hsis prsntd on July 7, 0 [6] hristoph Rodit, Bnjamin Rémy, Alain Dgiovanni, Frank Dmuri, Optimisation of wavlngths sltion usd for th multi-sptral tmpratur masurmnt by ordinary last squars mthod of surfas xhibiting non-uniform missivity, [7] hristoph Rodit, Bnjamin Rmy, Alain Dgiovanni, Optimal wavlngths obtaind from laws analogous to th Win s law for monosptral and bisptral mthods, and gnral mthodology for multisptral tmpratur masurmnts taking into aount global transfr funtion inluding nonuniform missivity of surfas, [8] Philipp POUPEAU, raitmnts thrmiqus ds métaux t alliags (M05), Edition hniqus d l Ingéniur, traité Matériaux métalliqus [9] airan Fu, Jiangfan Liu, Minghao Duan, Anzhou Zong, mpratur masurmnts using multiolor pyromtry in thrmal radiation hating nvironmnts,