XIX IMEKO Wold Congess Fundamental and Applied Metology Septembe 6 11, 29, Lisbon, Potugal UNCERTAINTY ESTIMATION OF SIZE-OF-SOURCE EFFECT MEASUREMENT FOR 65 NM RADIATION THERMOMETERS Fumihio Sakuma, Laina Ma National Institute of Advanced Industial Science and Technology, Tsukuba, Japan, f-sakuma@aist.go.jp Abstact This pape descibes the uncetainty estimation of the size-of-souce effect () measuement fo the standad adiation themometes in the indiect method using an integating sphee with a black spot as the souce. We checked the ageement between two pocesses of changing the black spot size and changing the apetue size. The contibutions of each uncetainty factos wee analyzed. Keywods: size-of-souce effect, adiation themomete, uncetainty 1. INTRODUCTION The size of souce effect () is impotant in measuing by a adiation themomete the tempeatue of a souce with a diffeent size fom the calibation souce. Thee methods ae available fo the measuement. They ae a diect method, an indiect method [1] and a scanning method [2]. The diect method uses a lage apetue blackbody whose apetue size can be changed. The indiect method uses an integating sphee with a black spot in cente and with an apetue. The scanning method moves the souce o the themomete sideway so that no lage taget is necessay in the measuement. It needs some calculation to obtain the value. The indiect method has a meit that a small diffeence of two lage signals is measued diectly. This inceases the signal to noise atio. Theefoe we employed the indiect method [3]. The eview of the thee methods ae epoted ecently [4]. Many papes epoted about measuements using the indiect method [5, 6], howeve only one pape epoted about the uncetainty of the indiect method [7]. It epoted the case of lage nonunifomity in adiance distibution. Hee we epot the uncetainty factos and thei contibution. 2.1. definition 2. INDIRECT METHOD is defined as the output incease of a adiation themomete when the souce size inceases. Hee we define between two diametes d 1 and d 2 as follows. 2 1 =, (1) 2 o 2 = 1 /( 1 ). (2) Hee the output signals 1 and 2 efe to the diametes d 1 and d 2, espectively. If we conside anothe diamete d 3, we obtain = 13 13 + + 32 32 13 32. (3) This appoximation of the addition ule applies well because the values ae usually much smalle than 1. The subtaction law also applies. 13 23 2.2. Integating sphee and black spot. (4) A lage integating sphee of 4 mm inne diamete with an exit pot of 14 mm in diamete was used. The inside was coated with BaSO 4 paint. The sphee had six halogen lamps of 24 15 W aound the pot inside the sphee. The specifications of the sphee ae given in Table 1. The sphee was on a compute-contolled stage of a 17 mm ange in the hoizontal diection and a 5 mm ange in the vetical diection with a esolution of 1 µm. Table 1 Specifications of lage integating sphee Name Inne diamete Exit pot diamete Inne wall Lamps bulb cooling powe souce opeation Apetue Black spot Stage movement X ange Z ange esolution Lage Integating Sphee φ4 mm φ14 mm BaSO 4 coating Quatz-halogen lamp 24 15W 6 Fan Stabilized diect cuent souce fo each lamp Constant voltage mode φ96, 72, 48, 36, 25, 18,, 9 o 6 mm φ1, 2, 3, 4, 5, 6, 9,, 16, 24 o 48 mm silk pinted on quatz disk Compute contol ±85 mm ±25 mm 1 µm
Nine apetues fom 6 mm to 96 mm in diamete and eleven quatz disks with silk-pinted black spots of 1 mm to 48 mm in diamete wee used. One apetue and one disk could be inseted at once in font of the exit pot. A gaphite blackbody cavity of a cone type with 6 mm in diamete and 11.2 mm in length was also used in the hole of a quatz disk to incease the eliability. 2.3. Radiation themomete Tests wee pefomed on Topcon, Chino and LP3.65 µm adiation themometes. Thee adiation themometes wee made fo a tansfe standad and thei qualities wee much bette than the commecial devices. Table 2 shows the specifications of thee adiation themometes. Table 2: Radiation themomete specifications. Manufactue Topcon Chino KE Type OEP-PM- IR-RST 65H LP3 65NB Tempeatue 9~3 o C 1~3 78~35 o C ange o C Cente Wavelength Band width 65 nm 15 nm 65 nm 13 nm 65 nm 1.5 nm Measuing between objective lens and souce Objective focus Apetue stop position Taget size 2 mm ~ 4 mm ~ 5 mm (44 mm with an extende) ~ 15 mm 8 mm 14 mm Between field stop and objective.5 mm at 25 mm Resolution.1 K at 96 o C Between field stop and objective.6 mm at 4 mm.1 K at 1 o C Between field stop and detecto.5 mm at 4 mm.1 K at 923 o C.2 K at 1423 o C So is used instead of 2. Thee ae two pocesses to measue the between two diametes, d 1 and d 2. One is the changing apetue pocess. It uses a black spot of d 1 diamete and an apetue of d 2 diamete. The diamete of d 2 is changed. This is a common method. The othe is the changing black spot pocess to use two black spots d 1 and d 2 and an apetue d 3. The of the latte case was obtained by eq. (4). This pocess is not epoted anywhee. The pocess enables the measuement between two close diametes, 5 mm and 6 mm, fo example. Some combinations can be measued by both pocesses. Theefoe this pocess can check the eliability of the changing apetue pocess. 3. DATA Fig.1 shows the measued data of a Topcon.65 µm adiation themomete at a measuing of 49 mm. The efeence diamete was 6 mm. This value was selected because the apetue diamete of ou fixed-point blackbody was 6 mm. The changing apetue pocess is shown as a closed diamond and the changing black spot pocess is shown as an open diamond. Both pocesses ageed well with each othe. The cavity data with the changing apetue pocess is shown as an open squae. This also agees with the data of the black spot (closed diamond). (%).6.4.2 Measuing : 49 mm -.2 2 4 6 8 1 14 Souce Diamete (mm) 6 mm Black spot 14 mm Apetue 6 mm Cavity Fig. 1. of a Topcon.65 µm adiation themomete 2.4. Indiect method measuement In the indiect method a adiation themomete measues a black spot and a bight aea whose outputs ae b and, espectively. was measued in the half way between the black spot and the apetue. Data of a left halfway and a ight one wee measued and aveaged. Because the value was diffeent fo a diffeent apetue o a diffeent black spot, was measued at each combination. In this case and b = 2 1, (5) b =. (6) (%).2.15.1.5 6 mm Black spot 14 mm Apetue -.5 6 mm Cavity Measuing Distance : 49 mm -.1 -.15 2 4 6 8 1 14 Souce Diamete (mm) Fig. 2. of a Chino.65 µm adiation themomete
Fig. 2 shows the measued data of a Chino.65 µm adiation themomete at a measuing of 49 mm. Compaed to Fig. 1, the of the Chino themomete was about one thid of the Topcon. Fig. 3 shows the measued data of an LP3.65 µm adiation themomete at a measuing of 7 mm. The LP3 s was still bette and about one tenth of the Topcon and one thid of the Chino. The Objective lenses of the LP3 wee changed to Apochomat. This change impoved the to half the value epoted befoe [3]. Ageements between the changing black spot pocess and the changing apetue pocess wee good. Thee was a small diffeence between the pinted black spot data and the cavity data at apetues lage than the diamete of 96 mm. (%).5.4.3.2.1 Measuing Distance: 7 mm -.1 2 4 6 8 1 14 Souce Diamete (mm) 6 mm Black spot 14 mm Apetue 6 mm Cavity Fig. 3. of an LP3.65 µm adiation themomete 4. UNCERTAINTY FACTORS Following factos wee consideed fo the uncetainty of the measuement. efeence black spot size d 1 apetue o black spot size d 2 black spot output b bight aea output measuing l m epoducibility 4.1. Black spot size The black spots wee silk-pinted on a quatz glass. The specification of the size was ±.1 mm. The contibution was expessed as follows. d u ( d1 ) = u( d1). (7) dd 4.2. Apetue size The apetues wee made of aluminium disks and they wee mechanically cut with a good pecision. But it was painted with white baium sulphate in the back. The inne 1 diamete was smalle up to.3 mm due to the baium sulphate painting. d u ( d2 ) = u( d2). (8) dd The sensitivity factos in eqs. (7) and (8) wee obtained fom Figs. 1 to 3. 4.3. Black spot output This measuement is vey impotant because the output b is small and the sensitivity facto is lage. d d b b 2 = 1 =. (9) The output eo fo the black spot came fom the tansmittance and eflectance of the black spot. In the visible ange the tansmittance was usually negligibly small. The adiation fom the souce apetue was eflected by the objective lens to each patly the black spot and then eflected back to the objective lens. If the measuing happened to be close to the diamete of the lens cuvatue and if the black spot suface is specula, this contibution can be significant. The initial black spot was specula and had some lage eflectance in some cases, so we made an additional diffuse silk pint on the black spot. Using a blackbody cavity fo the black spot, we estimated this contibution by the diffeence between the black spot and the cavity. 4.4. Bight aea output The sensitivity facto is calculated as follows. d d b = = 2 (1) Because is lage, the contibution is small. We conside following thee cases. adial non-unifomity of adiance diffeence between left and ight Radiance diffeence between 2 and A. Radial non-unifomity of adiance Fig. 4 shows the adiance distibution at the 14 mm apetue of the integating sphee measued in a 2-mm step by the Topcon.65 µm adiation themomete. The cente is the efeence point and the diffeence is shown in %. The unifomity was good nea the cente but the spectal adiance deceased as it appoached nea the edge. Fig. 5 shows the adiance dependence on the fom the cente. The fou o eight data with the same wee aveaged and in the figue the diamond and the ba show the aveage and the standad deviation, espectively. The dependence was appoximated by a quadatic equation shown by the solid line. The fitting was good. The decease was about.3% at the edge. Because the themomete used fo the unifomity measuement had an, the distibution diffeence was coected fo the in Fig. 1. The boken line shows the coected diffeence. The
-.25 -.51 -.27 -.17 -. -. -.4 -.15 -.5..4 -.21 -.8 -.22 -.3 -.32 -.2.5 -.11.2 -.4 -.4 -. -.9 -.8 -.6 -.5 -.27 Fig. 4. Radiance non-unifomity of the sphee in %. coection at the edge was about.1 %. By using the boken line, the output decease of 2 due to the distibution was estimated by using the following equation. u d 2 d = DW ( s ds. (11) d 1 ds Nu ) Hee DW is the elative diffeence of adiance fom the cente. The contibution was calculated as.2% at the edge fo the Topcon themomete. Diffeence fom cent (%).5 -.5 -.1 -.15 -.2 -.25 -.3 -.35 -.4 -.45 Diffeence Coected diffeence Fitting Fitting coected 2 4 6 8 1 14 Diamete (mm) Fig. 5. Radiance dependence on the fom cente B. Diffeence between left and ight Radiance In the measuement we measued the left and ight side halfway of the bight aea and use the aveage of the outputs as. The adiance diffeence between left and ight was usually within.1 % and at most.2 %. A ectangula distibution was assumed. C. Diffeence between 2 and The diffeence using instead of 2 was calculated by the following equation. d. () b b 2 = = 2 If the adiance distibution is unifom, following equation applies, Fom this we obtain < <. (13) 1 2 1 2 < <. (14) If we include the adiance distibution, we obtain following esult of hoizontal distibution fom Fig. 4. Note that we used only halfway to the apetue and the aveage of the ight and left sides was taken. < 4.5. Measuing < 1 2 +.1%. (15) Fig. 6 shows the measuing dependence of the of the.65 µm adiation themomete. The data wee measued at s 25 cm, 49 cm, 7 cm and 1 cm. When the measuing was fathe, the taget aea became lage and the solid angle of the souce fom the objective lens was smalle. These effects wee small fo the Topcon.65 µm adiation themomete. We assumed an uncetainty of 1 mm in focus adjustment and alignment fo Topcon and 15 mm fo Chino and LP3. (%).8.6.4.2 -.2 -.4 2 4 6 8 1 Measuing (cm) 2 3 4 5 6 9 16 18 25 36 48 72 96 14 Fig. 6. Measuing dependence of of the Topcon.65 µm adiation themomete 4.6. Repoducibility The epoducibility was obtained by five measuement of the with changing the alignment. The epoducibility was.6 % between 6 mm and 25 mm fo Topcon. The focusing was vey clea fo the Topcon and LP3 themometes but not clea fo the Chino.
Table 3. Uncetainty budget fo measuement of a Topcon adiation themomete using a pinted black spot between 6 mm and 25 mm Facto u i Distibution facto Sensitivity u Black spot size.1 mm.58.23 %/mm.13 % Apetue size.3 mm 1.64 %/mm.19 % Output of black spot.38 % 1 1.38 % Radial non-unifomity.2 % 1 1. % Diffeence between left and ight.2 %.58.2.2 % Diffeence between and 1.3 % 1.2.5 % Measing 1 mm.58.13 %/mm.8 % Repoducibility.6 % 1 1.6 % Combined standad uncetainty.46 % 5. UNCERTAINTY RESULT Table 3 shows the uncetainty budget fo the measuement of the Topcon.65 µm adiation themomete between 6 mm and 25 mm diametes. The main facto was the measuement fo the black spot output. This eo was estimated fom the output diffeence between the black spot and the blackbody cavity. Next main facto was the apetue size. Fig. 7 shows the uncetainty in measuement of the Topcon.65 µm adiation themomete fo vaious souce diametes. Fo the souce diamete lage than 1 mm the changing apetue pocess was used and othewise the changing black spot pocess was used. Note that the abscissa was scaled in logaithm. Main uncetainty factos wee the output of the black spot, the black spot size and the measuing. The black spot size contibuted moe fo a smalle souce diamete. In contast, the measuing contibuted moe fo a lage souce diamete. Standad uncetainty (%).1.9.8.7.6.5.4.3.2.1. 1 1 1 1 Souce diamete (mm) Black spot size (6 mm) Apetue o black spot size Output of black spot Radial Unifomity Diffeence betwen ight and left Diffeence between and 1 Measuing Repeatability Combined standad uncetainty Fig. 7. Uncetainty in measuement of the Topcon.65 µm adiation themomete (k=1) Fig. 8 shows the uncetainty in measuement of the Chino.65 µm adiation themomete. The main uncetainty facto was the black spot size and its contibution was lage at a smalle souce diamete. Fig. 9 shows the uncetainty in measuement of the LP3.65 µm adiation themomete. The main uncetainty facto was the output of the black spot. It contibuted moe at a lage souce diamete. Fo the small souce diamete the uncetainty was dominated by the epeatability. If we use a black body cavity fo the black spot, we can neglect this facto and the standad uncetainty would be smalle than.1 %. Standad uncetainty (%).7.6.5.4.3.2.1. 1 1 1 1 Souce diamete (mm) Black spot size (6 mm) Apetue o black spot size Output of black spot Radial Unifomity Diffeence betwen ight and left Diffeence between and 1 Measuing Repeatability Combined standad uncetainty Fig. 8. Uncetainty in measuement of the Chino.65 µm adiation themomete (k=1) Standad uncetainty (%).4.35.3.25.2.15.1.5. 1 1 1 1 Souce diamete (mm) Black spot size (6 mm) Apetue o black spot size Output of black spot Radial Unifomity Diffeence betwen ight and left Diffeence between and 1 Measuing Repeatability Combined standad uncetainty Fig. 9. Uncetainty in measuement of the LP3.65 µm adiation themomete (k=1)
6. CONCLUSIONS The indiect method techniques fo the measuement at AIST wee descibed, data of thee.65 µm adiation themometes wee shown and thei uncetainty factos wee analyzed. The addition law fo was confimed by changing both the apetue size and black spot size. The uncetainty of the measuement depended on the themomete. The standad uncetainties in the measuement of the Topcon, Chino and LP3 themometes wee estimated as bette than.1 %,.6 % and.4 %, espectively. If we use the blackbody cavity fo the black spot, the standad uncetainty will become.1 % fo the LP3. ACKNOWLEDGMENTS The autho would like to thank Ms. Yunfen Ou fo he assistance in the additional measuements. REFERENCES [1] G. Machin, R. Segienko, A Compaative Study of Size-ofsouce-effect () Detemination Techniques Poc. of TEMPMEKO 1, ol. 8, pp.155-16, 21. [2] M. Bat, E. W. M. van de Ham and P. Saundes A New Method to Detemine the Size-of-Souce Effect Int. J. Themophys. ol.28 2111 2117, 27. [3] F. Sakuma, L. Ma, Z. Yuan Distance Effect and Size-ofsouce effect of Radiation Themometes Poc. of TEMPMEKO 1, ol. 8, pp161-166, 21. [4] P. Saundes and H. Edga On the chaacteization and coection of the size-of-souce effect in adiation themometes Metologia ol. 46 62 74, 29. [5] T. Ricolfi, L. Wang Expeiments and emaks on the sizeof-souce effect in pecision adiation themomety Poc. of TEMPMEKO 93, ol. 5, pp.161-165, 1993. [6] H. W. Yoon, D. W. Allen, R. D. Saundes Methods to educe the size-of-souce effect in adiation themometes Poc. of TEMPMEKO 4, ol. 9, pp521-526, 24. [7] M. J. Matin, J. P. Peez,. Chimenti, An Altenative Calculation of the Size-of-souce effect Uncetainty fo Nonunifom Souces Int. J. Themophys. ol. 29 1131-114, 28.