Radiance Calibration of Target Projectors for Infrared Testing

Transcription

1 Radiance Calibratin f Target Prjectrs fr Infrared Testing Greg Matis 1, Jack Grigr 1, Jay James 1, Steve McHugh 1, Paul Bryant 2 1 Santa Barbara Infrared, Inc., 30 S. Calle Cesar Chavez, Suite D, Santa Barbara, CA eft Cast Cnsulting, 1222 Manitu ane, Santa Barbara, CA ABSTRACT This paper prvides a prcedure fr radimetric calibratin f infrared target prjectrs using the RAD-9000 MWIR/WIR spectral radimeter a high-perfrmance instrument supprting extremely accurate abslute and relative radimetric calibratin f EO test systems. We describe the ratinale fr radimetric calibratin, an analysis f errr surces typically encuntered by investigatrs during calibratin f infrared imaging cameras when using target prjectrs, and a strategy fr perfrming an abslute system end-t-end radimetric calibratin with emphasis n high accuracy and ease f use. Keywrds: Abslute radimetry, detectr, calibratin, blackbdy, reference surce, RAD9000, spectral radimeter. 1. INTRODUCTION Target Prjectrs are key instruments used in the test, evaluatin, and calibratin f infrared imaging sensrs and cameras. In its mst basic frm, a target prjectr prduces a radiance cntrast between an infrared blackbdy surce and a backgrund, via a target prjected at infinity, ref. Fig. 1. Targets can be emissive and/r reflective which affects the cnfiguratin f the prjectr and defines required assets such as blackbdies r ptics. OPTICA COIMATOR TARGET WHEE BACKBODY TEMPERATURE SENSORS Figure 1 Generic Infrared Target Prjectr Radiance calibratin f an infrared target prjectr is essential t prperly determine the prjectr s radiance utput as a functin f temperature set pint. An accurate radiance calibratin curve is required t set target cntrast and perfrm high-reslutin infrared imaging system tests such as Minimum Reslvable Temperature Difference MRTD), Signal Transfer Functin SiTF), and Nise Equivalent Temperature Difference NETD). As infrared sensrs inherently measure radiance rather than temperature, it makes sense t calibrate the test system radimetrically, prvided an apprpriate instrument is available. Given a well-behaved SiTF characteristics fr a given UUT, the thermal imager s utput signal is linear as a functin f scene radiance. Hwever, as radiance is inherently nnlinear as a functin f temperature, sensr utput is als nnlinear as a functin f temperature.

2 Object radiance may be cnverted t apparent temperature using the fllwing relatinship [, λ λ, λ λ amb )] T ) ε W T ) + 1 ε ) W T dλ = [1] Where T ) is the integrated bject radiance, W λ T ) is the spectral bject radiance determined using the Planck equatin, W λ T amb ) is the spectral backgrund radiance, and ε,λ is the spectral emissivity f the bject. Equatin [1] prduces a nn-linear radiance vs. temperature curve as wuld be measured by a high quality spectral radimeter such as the RAD9000, bserving a reference blackbdy. 4.5E-04 RADIANCE T) 4.0E E-04 RADIANCE [W/cm2-sr] 3.0E E E E E E E TEMPERATURE [K] Figure 2 Radiance t Temperature Calibratin Curve T amb = 293 K, ε = 0.998, λ CW = µm) The differential radiance seen by a UUT lking at an ideal target prjectr system may be expressed as the difference between target blackbdy surce and target backgrund radiance: [2] = bkg Fr real-wrld blackbdy and target surfaces with nn-unity emissivity i.e., ε < 1.0), the reflected ambient cmpnents f the radiance must be included. The differential radiance can then be expressed as a sum f the Planck terms fr each emitted and reflected radiance surce: [ ] [ ε W T ) + 1 ε W T )] ] dλ [ ε W T ) + 1 ε ) W T ) = [3], λ λ, λ λ amb bkg, λ λ bkg bkg, λ ) The nn-linearity f the Planck functin gives rise t a variatin in differential radiance with ambient temperature change - even when thermmetric T is maintained. This variatin is knwn as a radimetric T errr. Table 1 illustrates the magnitude f the radiance difference as a functin f ambient temperature change when bserving a target blackbdy surce at a T f 1 K. T amb [K] T [K] Delta Radiance, [µw/cm 2 ] MWIR 3-5 µm) WIR 8-12 µm) Table 1 MWIR and WIR Delta Radiance, vs. T -amb = 1 [K], change λ amb

3 2. CAIBRATION ACCURACY 2.1 Errr Surces Surces f errr during calibratin include uncertainties in emissivity f the target surce and backgrund, emittance and/r reflectance f the prjectin ptics and baffling, thermmetric t radimetric temperature difference, tempral instability f the target r backgrund surce radiance, temperature drift, view angle f the sensr r prjectr, and radiance unifrmity f the surces. Typical target prjectrs can maintain differential temperatures f ± C, but as ambient temperature varies, the target temperature can drift, resulting in an unstable image thus affecting cnsistency f the test results 3. The magnitude f these errrs is dependent n the rate f change f the ambient temperature, and afrementined system-specific factrs such as target and backgrund emissivity, ptical emittance and baffling, and target edge characteristics. The measurement mst sensitive t radimetric calibratin errr is that f MRTD. The fllwing analysis assesses the degree f MRTD accuracy achievable with the current state-f-the-art in radimetric calibratin instrumentatin and measurement techniques Radimetric Errr Analysis The radimetric utput f a target prjectin system during MRTD testing is affected primarily by the errr terms; radimetric calibratin uncertainty and ambient temperature drift effects. State-f-the-art IR calibratin transfer standards such as SBIR s RAD9000 prvide thermal sensitivity f apprximately C and abslute radimetric accuracy f ± 0.25% per single-ended radiance measurement. Thermal sensitivity is limited by detectr nise, and abslute accuracy limited by NIST radimetric calibratin f the transfer standard s thermal references. Ambient temperature drift is a factr t be cnsidered in the accurate measurement f MRTD fr high-perfrmance sensrs. We cnsider the implicatins f ambient drift n prjected MWIR and WIR differential radiance, assuming a cntrlled ambient temperature f 25 ± 1 C and ± 3 C, prjected T set pints f 5.0 and 0.1 C, and a reflected backgrund target prjectr cnfiguratin utilizing a cntrlled surce and passive backgrund. OPTICA COIMATOR BACKBODY BKG TARGET WHEE BACKBODY OBJ Figure 3 Generic Reflective Backgrund Target Prjectr System Target and backgrund radiance at the cllimatr aperture are given by: t arg et = bb2 + f + p [4] backgrund = bb1 R t + t + f + p [5]

4 Where and R dente radiance and reflectance, and the subscripts bb, t, f, and p indicate blackbdy, target, fld, and primary surfaces. Differential radiance ) is cmputed as in equatin [2] by subtracting equatin [5] frm [4]: = t arg et backgrund [6] [ ] = bb 2 + f + p bb1 R t + t + f + p [ ] = bb2 R t bb1 t Expanding the target and backgrund blackbdy radiance terms t include reflected ambient cntributins yields: = R R f p ε bb2w Rt λ, Tbb 2 ) + 1 ε bb2 ) W λ, Tamb ) Rtε bb1w λ, Tbb 1 ) 1 ε ) W λ, T ) 1 R ) W λ, T ) bb1 amb t amb [7] Where ε is the surface emissivity and Wλ,T) is the Planck functin. Evaluating this expressin fr 0.98 target and mirrr reflectance, blackbdy emissivity, and different cmbinatins f ambient temperature, T set pint, and spectral band yields the fllwing tables fr MWIR and WIR testing: MWIR 3-5 µm) WIR 8-12 µm) T bb K) T amb K) T app K) W/cm2/sr) T app K) W/cm2/sr) K) K) = err = 0.4% = err = 1.1% = 1.23E-7 err = 0.4% = 3.82E-7 err = 1.2% = err = 0.4% = err = 1.1% = 1.2E-6 err = 0.4% = 3.56E-6 err = 1.2% K) K) = err = 18% = err = 63% = 1.23E-7 err = 19% = 3.80E-7 err = 57% = err = 20% = err = 60% = 1.17E-6 err = 20% = 3.56E-06 err = 61% Table 2. Ambient Drift-Related T Errr MRTD errrs can becme significant fr large ambient temperature deviatins Tamb). This illustrates the ptential fr cmpensatin r crrectin methdlgies fr minimizing the influence f ambient temperature drift during IR testing. Fr small thermal cntrast settings i.e. lw angular frequency MRTD testing), RDT accuracy is limited by the transfer standard s thermal sensitivity and ambient drift effects. Calibratin accuracy near zer T is twice the transfer standard s thermal sensitivity, r ± C. Ambient drift-related errr due primarily t the target emittance; and less s the passive backgrund surce, is apprximately ± C fr a T f 1 C. The wrst-case errr is an RSS f these terms, r ± C fr a T f 1 C. Fr ambient temperature drift > 3 C the errr increases significantly.

5 T amb = 1 C T amb = 3 C System Calibratin Accuracy ± C ± C Ambient Drift Errr ± C > C MRTD Accuracy T O-BKG = C) ± C > C Table 3. Tlerance Allcatin fr MRTD T = C) Fr large thermal cntrast settings, RDT accuracy is limited by the transfer standard s abslute radimetric accuracy at bth the high and lw set pints, and ambient drift fr large DT settings. Tw times the wrst-case transfer standard accuracy is ± 0.5%. Ambient drift effects at r abve the specified crssver pint f ± 5 C are 0.4% fr a T f 1 C. The wrst-case errr is the sum f these tw terms, r ± 0.9% and ± 1.7% fr a T f 1 C and 3 C respectively. T amb = 1 C T amb = 3 C Radimetric Accuracy ± 0.5% ± 0.5% Ambient Drift Errr ± 0.4% ± 1.2% MRTD Accuracy T O-BKG = 5.0 C) ± 0.9% ± 1.7% Table 4. Tlerance Allcatin fr MRTD T = 5.0 C) It shuld be nted that the standardized MRTD prcedure actually prduces a result mre accurate than the hardwarerelated T errrs listed abve. Averaging the psitive and negative cntrast settings at the tw reslutin limits cancels the systematic calibratin errr assciated with each measurement, and thus imprves accuracy f the MRTD test result. As such, these errr analyses are intended t be cnservative. A straightfrward, end-t-end radimetric target prjectr calibratin prcedure utilizing SBIR s RAD9000 spectral radimeter system is discussed in the next sectin. Once calibrated, the target prjectr serves as a measurement standard fr full characterizatin f IR sensr perfrmance. 3. CAIBRATION METHODOOGY In rder t characterize spectral radiance as a functin f wavelength, a spectral radimeter is emplyed. SBIR has develped and currently utilizes an extremely accurate abslute spectral radimeter system called the RAD9000 1,2. The RAD9000 prvides spectral reslutin f 1.8% in the 3-5 micrn and 8-12 micrn bands, thermal sensitivity better than K in each IR channel, and abslute radimetric accuracy f ± 0.25% ver an perating temperature range f C. Figure 4 RAD9000 Spectral Radimeter System Frnt and Side Views

6 Radimetric calibratin f the instrument invlves characterizatin f the relatinship between the signal respnse f each channel and incident radiatin per spectral interval. The key t accurate calibratin is the use f high-perfrmance reference radiatin surces with accuracy and stability cmparable t r better than) the RAD9000 system itself. T address this need, the RAD9000 radimetric reference mdule RRM) was develped fr use as an integral part f the RAD9000 system. The RRM includes tw adjustable reference blackbdies t verfill the RAD9000 aperture. Each blackbdy is calibrated radimetrically at NIST, and thus represents the mst accurate extended thermal reference surce currently available. When integrated with the RAD9000, the RRM prvides autmated bracketing f bject radiance via autmatic translatin f the tw RRM surces int and ut f) the RAD9000 aperture. This allws the user t accurately determine radimetric qualities such as emissivity, spectral radiance, apparent temperature, and ther parameters. The dual-extended surce blackbdies have an 8 diameter, with variable temperature cntrl frm 5 C t 100 C, exhibit high effective emissivity > frm 2-14 µm), and perate under autmated PID cntrl. Due t their lcatin external t the RAD9000 ptical path, the RRM reference blackbdies prvide better than 1% abslute radimetric calibratin accuracy f the entire signal path, frm the entrance aperture t the detectr. As the RRM is designed t serve as an integral part f the RAD9000, calibratin may be perfrmed prir t each data cllectin, thereby delivering the mst accurate MWIR and WIR spectral radiance measurement capability available. 3.1 Spectral Radimeter Calibratin The RAD9000 detectrs and electrnics are designed t prduce a linear utput as a functin f input irradiance, fr all wavelengths in the MWIR/WIR channels. First, the tw NIST traceable extended surce blackbdy reference surces are presented t the radimeter t determine slpe and ffset cefficients that fully characterize the instrument s spectral respnse functin. The radimeter alternately views the tw RRM reference blackbdies and cllects signals frm the high and lw thermal reference pintsthe RAD9000 averages measured data ver a number f measurements selected fr the calibratin perid. et the radiance levels frm reference surce 1 and 2 be defined as 1 and 2, respectively, and the crrespnding signal cunts measured by the radimeter as S 1 and S 2. Gain G λ ) and radiance ffset O ffset,λ ) may be determined using the fllwing relatinships: 1/ Gλ = 2 1 ) / S2 S1) [8] and 0 ffset, λ = 1S 2 2S1) / S 2 S1) [9] Rearranging terms, bject radiance may be expressed as a linear relatinship t the cllected signal: T A S T + = where A λ = 1/G λ [10] λ ) λ λ ) Offset, λ Radimeter respnse signal, in mv) may alternately be expressed in terms f respnsivity and irradiance: S λ T ) R λ) T ) [11] Where Rλ) is the abslute instrument respnse [typically expressed in V/W/cm 2 /sr] and λ T) in the integrated in-band radiance [in W/cm 2 /sr]. λ

7 Calibratin f the MWIR and WIR infrared channels is initially perfrmed using data cllected at any tw pints within the range f ptential bject radiance using the RRM s reference blackbdies. Calculating gain and ffset fr each spectral band and string the results in cnvenient sftware-based lk-up tables UTs) allws easy cnversin frm radiance t apparent temperature using equatins [1] and [11]. 3.2 Infrared Target Prjectr Calibratin The basic apprach fr determining abslute radiance frm a target prjectr is the same as that used fr calibrating the spectral radimeter, as described abve. Bth target prjectr and the RRM reference blackbdy surces are placed clse t the same plane when viewed by the RAD9000. In this arrangement, the difference in ptical path length between the target and backgrund surces and the RRM reference surces is kept small < 2 m) t limit atmspheric attenuatin at the shrter wavelengths. The RAD9000 is psitined n-axis with respect t the target prjectr, t limit the angular rtatin in azimuth r elevatin needed t view the backgrund radiance. The angular reslutin IFOV) f the RAD9000 is 1.7 mrad in its basic cnfiguratin, thereby prviding adequate sampling capability fr high-reslutin IR targets. A typical target used fr bth prjectr calibratin and UUT evaluatin is the half-mn target shwn in Fig. 5. The RRM reference blackbdy surces verfill the IFOV f the RAD9000 detectrs, and are used as fld surces. In rder t accurately determine the radiance f an unknwn bject target r backgrund) the RAD9000 autmatically brackets the bject radiance at multiple apparent temperature set pints within the linear respnse range f the IR sensr r camera UUT. Similar t calibratin f the RAD9000, this is achieved via the use f tw calibrated, variable temperature reference blackbdies, typically set t bracket the expected bject temperature by ± 5-10 K. This tw-pint calibratin apprach is mst precise ver the nrmal range f bserved temperatures, and the effect f target prjectr nn-linearity is minimized by the small differential temperature range bserved. Each RRM reference surce radiance and emissivity characteristic is knwn as a functin f temperature. Abslute radiance accuracy has been characterized well belw 0.5%, as discussed previusly. Figure 5 - Half-Mn Calibratin Target A plt f measured vs. ideal radiance may be cnstructed ver the bject temperature range f C. inear regressin is used t determine crrectin cefficients a,b) fr target radiance. A secnd-rder plynmial is used with the fllwing frm t determine the radiance difference. Crrectin cefficients may be stred in sftware t prvide a dynamic crrectin f radiance as a functin f temperature set pint. [ T ) T )] + b[ T ) T ] 2 [12] T ) = a amb amb )

8 After Calibratin Befre Calibratin Figure 6 - Target Prjectr Surce Radiance Calibratin at 10 µm!" "!" "" "! "" "" """!!" "" "! "" "" "" " "" "" " Table 5 - Delta Temperature Errr: Target Prjectr Surce Radiance Calibratin at 10 µm A plt f backgrund radiance is typically cnstructed t mnitr drift as a functin f bth target radiance and ambient temperature fluctuatin. Typically, the time cnstant f envirnmental temperature instability is lnger than the time required t perfrm a radimetric measurement, s as nt t affect the end result. Hwever, drift due t radiant cupling f the backgrund t the target surce blackbdy r the lack f test facility temperature cntrl) can influence measurements if nt subtracted ut f the final radiance calculatin. This errr term is separate frm any emissivity mdels as emissivity is typically a cnstant radiance ffset ver the measurement cnditins. Drift ffset is typically nn-linear and is encuntered in MRTD testing as described in the abve errr analysis) where small differences in radiance between target and backgrund must be maintained in rder t prvide repeatable radiance cntrast t the bserver. If drift is repeatable, then UT r algrithmic-based crrectin such as the RDT crrectin may be emplyed as a functin f ambient cnditins and target radiance t maintain a cnstant difference in prjected differential radiance between surce and backgrund. If drift effects are nt well-behaved, the best ptin is t emply a cntrllable backgrund surce with reflective targets. 3.3 Factrs Affecting Calibratin It shuld be nted that a spectral radimeter can ften deliver mre accurate target prjectr calibratin than a bradband transfer standard, since the spectral variability f prjectr and radimeter) respnse is inherently calibrateable using spectral techniques. In particular, the effects f CO, CO 2, and H 2 O in the ptical path are mre easily cmpensated with spectral measurement techniques. The RAD9000 allws the user t select filters t prvide mre accurate calibratin in the MWIR than culd be btained with a bradband instrument.

9 The RAD9000 RRM s reference blackbdy surces prvide virtually flat spectral emissivity in the infrared. In mst cases, RRM reference surce emissivity varies less than ver the spectral range f each IR channel MWIR and WIR). Therefre, a cnstant crrectin term may be applied t the calibratin accunting fr emissivity. In general, it is recmmended that befre applying bradband radimetric calibratin t any IR target prjectr, system utput shuld be characterized using a spectral radimeter such as the RAD9000, t validate the prjectr s spectral cntent and identify any ptential limitatins assciated with a bradband calibratin. 3.4 Determinatin f Prjectr/Surce Radimetric Prperties In sme cases, it may be desirable t use a spectral radimeter t measure the spectral emissivity f an IR surce in either a stand-alne r target prjectr cnfiguratin. The integrated radiance f an unknwn surce is determined frm equatin 1. Three unknwns must be determined; T, T amb, and ε,λ - Using a tw-pint measurement f references f knwn emissivity and radiance such as thse prvided in the RAD9000 RRM), ne may slve fr bject radiance, as fllws: Ht Ht, λ λ Ht Ht, λ λ amb ) = ε W T ) + 1 ε ) W T dλ [13] and Cld Cld, λ λ Cld Cld, λ λ amb ) = ε W T ) + 1 ε ) W T dλ[14] Measured bject integrated radiance can nw be btained frm the RAD9000 by using the frm f equatin [10] T = A S T ) + ) λ ffset[15] Befre bject temperature can be derived an accurate determinatin f bject emissivity and ambient temperature must made. - Ambient temperature shuld be mnitred via a NIST traceable high precisin thermmeter in the lcatin f the test measurement; apprpriately shielded frm stray radiatin surces, and recrded as a functin f time during calibratin. The RAD-9000 features an internal reference blackbdy that is mnitred via a calibrated smart thermmeter and is plled alternately with the measured surce t facilitate accurate determinatin f surce radiance. T amb is knwn t better than ±0.010 C. amb can be determined by integrating the Planck functin ver the spectral band at T amb. - If we assume that bject emissivity des nt vary significantly within the particular spectral band being measured, that the spectral band λ/λ is less than a few percent, bject emissivity may be estimated using the fllwing relatin: ε amb =ε T ) dλ = ε = ε bb bb amb bb amb bb amb [16]

10 In this relatin apparent temperatures f either Cld r Ht reference blackbdies is increased r decreased t match the thermmetric temperature f the bject. The rati will uniquely estimate the bject emissivity at the mean apparent bject temperature. Fr the target prjectr case shwn in Figure 1 the bject apparent emissivity must be adjusted fr the reflectance and self emittance f each f the mirrrs. The bject radiance expressin given in equatin [1] is re-written t accunt fr the mirrrs in the ptical path T ) = R R [ ε W T ) + 1 ε ) W T )] + R [ ε W T )] [ ε W T )] dλ f p, λ amb p f f + p p [17] T simplify the derivatin f bject emissivity we make the assumptin that the temperatures f the mirrrs equal ambient. This assumptin may nt be accurate in all cases particularly fr measuring lw radiance levels in the WIR due t degraded reflectance ptics, r cupled surces s the test prfessinal is cautined t fully characterize the test cnditins and the target prjectr prir t applying an emissivity factr t the system. Having said this fr mst typical applicatins we apply equatin [17] t equatin [16] and slve fr bject emissivity - Therefre ε ε T ) = dλ = R ε f bb R p amb bb amb [18] - Nw that bject radiance, bject emissivity and ambient temperature have been accurately determined the bject apparent temperature, T, can nw be derived by rearranging terms in the Planck functin. This apprach is particularly useful fr stand-alne IR surces and target prjectin systems previusly calibrated thermmetrically but requiring an accurate radimetric temperature calibratin. 4.1 NIST Calibratin 4. TRACEABIITY Radimetric calibratin f the tw RAD9000 RRM reference surces was perfrmed at NIST, using the NIST Water Bath Blackbdy WBBB) as a reference surce, and the NIST TXR and FTXR radimeters as transfer standards. Details f RAD9000 RRM surce calibratin 2 have been published elsewhere and will thus nt be repeated here. The calibratin test setup is illustrated in Figure 7. Fixed Optical Table WBBB RAD9000 Ref 1 RAD9000 Ref 2 Mveable Bench TXR FTXR Figure 7 RAD9000 Blackbdy Calibratin Test Schematic

11 The data set frm this calibratin was fit t an idealized radimetric respnse t determine thermmetric crrectin terms fr the blackbdies 4. The thermmetric crrectin was fit using a 4 th rder plynmial. This crrectin curve was then laded int RAD9000 cntrller firmware as a UT, enabling the system t prvide autmatic cmpensatin during peratin. SUMMARY Accurate MWIR and WIR calibratin f IR target prjectrs represents a challenge t the test prfessinal seeking t maintain a Test Accuracy Rati TAR) greater than 4:1 fr test and evaluatin high-perfrmance thermal imagers. The RAD9000 spectral radimeter system prduced by SBIrvides the test and metrlgy cmmunity with the capability t perfrm radimetric calibratin accurate t better than ± 0.5%, with utstanding thermal sensitivity acrss bth the MWIR and WIR spectral regins. The system supprts a wide range f bject temperatures, prvides better than 2% relative spectral reslutin, and allws autmated and remte peratin thrugh an advanced user interface. A prcedure fr accurate radimetric calibratin f target prjectrs has been described, and a radimetric errr analysis fr crucial MRTD measurement presented.. ACKNOWEDGEMENTS The authrs wish t acknwledge the useful cntributins and supprt prvided by J. Rice f Natinal Institute fr Standards and Technlgy NIST) REFERENCES 1. G. Matis, P. Bryant, J. James, S. McHugh, Develpment f a high-perfrmance spectral radimeter fr EO calibratin applicatins, Infrared Imaging Systems: Design, Analysis, Mdeling, and Testing XV, SPIE Prceedings Vlume 5407, Orland, F, G. Matis, P. Bryant, B. unt, J. Grigr, C. Psch, S. McHugh, RAD-9000: A high-perfrmance spectral radimeter fr EO calibratin applicatins, Infrared Imaging Systems: Design, Analysis, Mdeling, and Testing XVI, SPIE Prceedings Vlume 5784, Orland, F, Bryant, P., Stable Targets Imprve Test Results, OE Magazine, March J.P. Rice, Final Reprt fr RAD9000 Reference Mdule Testing, Internal SBIR Dcument. May 2005.