Journal of Engineering Science and Technology Review 7 (1) (2014) Research Article

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1 Jestr Journal of Engineering Science an Technology Review 7 () (04) 8 Research Article JOURNA OF Engineering Science an Technology Review Research on the Measurement Error of MWIR Average Atmospheric Transmittance Yuanyuan Ji, Wenhai Xu *, Ying i, Qilei Cao, Yukun Sun, Debin Ma an Ming Zhao College of Information Science Technology of Dalian Maritime University, Dalian, iaoning province, 606, China Receive 6 August 03; Accepte 7 January 04 Abstract The atmospheric transmittance in mi-wavelength infrare (MWIR) ban reflects the characteristics of atmospheric particles, which is typically use in MWIR imaging system correction an ata extraction. MWIR imager is wie spectral ban instrument an its measuring output is usually affecte by broaban atmospheric transmittance which is usually consiere as average influence, therefore it is exactly of great importance to stuy the measurement of MWIR average atmospheric transmittance, which is valuable for MWIR images correction an application. A measurement error moel of MWIR atmospheric transmittance was propose accoring to the measuring metho of the broaban average atmospheric transmittance. Because the transmittance measurement principle mentione in this paper is inirect measurement, some irect input ata are neee to be acquire through infrare imager, blackboy, etc. Finally, combining the measurement error theory with ata of the experiments, the MWIR atmospheric transmittance an its measurement error are extracte. The results show that the MWIR atmospheric transmittance measure value is reasonable accoring to the empirical value in sunny ay. An the measurement error objectively reflects most aspects of the test, exactly proving the valiity of the measurement experiment. Keywors: MWIR average atmospheric transmittance, MWIR imaging system, Measurement error. Introuction MWIR average atmospheric transmittance refer to the effects cause by atmospheric molecular an aerosol particles on the raiation transfer of the groun objects, which is an important research content in the fiel of infrare imaging, roa monitoring an city security etc. MWIR broaban average atmospheric transmittance is generally use for correcting the raiation or temperature measurement of infrare scene [], [], so that the groun can be observe even in the smog-weary city. Besies, they coul be use for infrare imaging generation, simulation [3] an so on, which are of significant value in infrare evelopments an applications. There are many measurement methos to get the atmospheric transmission characteristic in the whole worl. For instance, Jun Zhu [4], eli Wei [5] from China presente the measurement methos by using interferometric infrare spectral raiometer to obtain the atmospheric spectral transmittance ata. An D. Saot [6] from Israel suggeste using CO laser system to measure 0.6µm wavelength atmospheric transmission. Moreover, Michael Engel [7] presente a remote measurement by using a thermal imager to stuy the transmittance in the intereste spectral ban. Compare with the spectral transmittance measurement * aress: whxu@lmu.eu.cn ISSN: Kavala Institute of Technology. All rights reserve. mentione above, the research of MWIR wavelength, generally consiere as 3~5µm, average atmospheric transmittance has rarely been reporte. owever, the MWIR average atmospheric transmittance plays an important role in infrare fiel for they coul be use as correction ata for MWIR infrare imager, which makes them attractive to the researchers graually. Ciyin Yang once i some research on the MWIR atmospheric transmittance measure [8], while the measurement error was unerstate which neee to be pai enough attention in fact to ensure the valiity of measurement metho an results. Moreover, the affection of spectral response i not been taken into account for the measurement as well as the error source of uncertainty of spectral responsivity, etc. This paper aims at eveloping a thorough measurement error theory for the MWIR average atmospheric transmittance. A measurement error moel of average transmittance is presente base on the error analysis theory [9]. The error sources from most measure aspects are consiere in etail, which are usually neglecte by the preecessors. Finally, the MWIR average atmospheric transmittance measurement metho an the error are analyze through the experiment in sunny ay, so that the correctness of the measurement metho an error evaluation theory is teste accoring to the experimental ata.

2 . MWIR average atmospheric transmittance Measurement The transmittance shoul be carrie out uner a proper metho with a special system. Through the error theory, the error can be obtaine to prove the valiity of the measurement.. MWIR average atmospheric transmittance measurement system For getting the MWIR average atmospheric transmittance, a measure system is neee. The measurement system inclues three parts: the MWIR imaging system, big area blackboy source an a portable computer. MWIR imaging system is an important evice for stuying the infrare fiel, which objectively reflects the infrare material (incluing solis an gases, etc.) characteristics. In this paper, the infrare camera, with the wie spectral of 3~5 µm, is selecte as measurement instrument. Besies, blackboy source is another significant component tool for measuring the MWIR average atmospheric transmission characteristic. The atmospheric transmittance is measure by ajusting the temperature of the stanar blackboy. An the wearable computer is use for recor the measure ata. An the schematic iagram of the system test scenario is liste in Fig., which illustrates the measure instrument an their setting position when the system works. Blackboy Yuanyuan Ji, Wenhai Xu, Ying i, Qilei Cao, Yukun Sun, Debin Ma an Ming Zhao/ Journal of Engineering Science an Technology Review 7 () (04) 8 MWIR imaging system Fig.. Atmospheric transmittance measurement scene Computer the pupil raiance from the low temperature blackboy an K is the thermal imager raiometric calibration coefficient. an can be erive from the blackboy parameters an infrare camera s characteristics. Accoring to infrare response rule [0], the following formula can be erive. ε (4) = ( ) R( ) ( ) B where spectral wavelength, =3µm. =5µm. ε() is emissivity of blackboy, R() is spectral responsivity of infrare camera an B () is the spectral raiance of ieal high temperature blackboy, which can be expresse by the following formula accoring to Planck s blackboy law []. B ( ) = 5 π c e c T where c an c are the raiation constants, c = W. cm -. µm 4, c = µm. K. T is the surface temperature of the high temperature blackboy. π is constant. Similar to, can be calculate by the following formula. = π c ε( ) R( ) c 5 T e Combining Eqs.()~(5) an consiering the spectral characteristics of responsivity an raiation, the broaban average transmittance τ can be represente by the equation liste below. (5) (6) The MWIR average atmospheric transmittance of the transmission path between the blackboy target an the infrare imager, inicate by the ashe line, can be measure by the system. Then the experimental output woul be store by the computer.. MWIR average atmospheric transmittance measurement principle Accoring to theory of the infrare imaging link, the high temperature an low temperature blackboy gray values are expresse by the following formulas: g = K( τ + ) + B () path g = K( τ + ) + B () path MWIR average atmospheric transmittance can be obtaine by simultaneous equations () an (). g g τ = K( ) where τ is the MWIR average atmospheric transmittance, g is high temperature blackboy gray value, g is cryogenic blackboy gray value, is infrare camera pupil raiance in zero istance range from the high temperature blackboy, is (3) g g τ = c ε( ) R( ) c ε( ) R( ) K (7) ( ) c c π π 5 T 5 T e e where the parameters are exactly of the same meaning to the nomenclature appear before..3 MWIR average atmospheric transmittance measurement error From the measurement principle, atmospheric transmittance is an inirect measure value, i.e. the value is a function of some irect measurements. Therefore, the atmospheric transmittance error is a function of each irectly measurements error. The relative stanar eviation may well reflect the impact of the error. In this paper, the relative stanar eviation is unifie to represent the synthesis of systematic errors an ranom errors. After the system errors are correcte, the measurement process can be consiere as only ranom errors left: σ r (x ), σ r (x i ),..., σ r (x s ). An then the system error σ r (y) is erive, shown as follows: σ s y ( y) = ( ) r σ x (8) r i i= xi

3 Yuanyuan Ji, Wenhai Xu, Ying i, Qilei Cao, Yukun Sun, Debin Ma an Ming Zhao/ Journal of Engineering Science an Technology Review 7 () (04) 8 The atmospheric transmittance measurement principle [ R( ) ] [ R( ) ] shows that the error sources from most of the measuring link: M = c c the infrare image value acquisition, the blackboy 5 ( T 73.5) 5 ( T 73.5) temperature an infrare imager calibration, et al. Accoring e + e + to measurement error synthesis theoretic Eq.(8), atmospheric c transmittance measurement error σ r (τ) can be euce to the ( T ) mathematical Eq. (9). e M = 3 c 6 ( T ) τ τ τ e σ ( g ) + σ ( g ) + σ ( K) r r r ( g ) ( g ) ( K) τ τ τ σ τ σ σ σ ( T ) ( T ) ( R) ( ) = + ( T ) + ( T ) + ( R) r r r r τ + σ ( ε) r ( ε ) where σ r (g ), σ r (g ), σ r (T ), σ r (T ), σ r (K),σ r (R) an σ r (ε) are respectively the relative stanar eviation of g, g, T, T, K, R an ε. Substituting the Eq.(7), the formula for calculating the MWIR average atmospheric transmittance, to the Greek letter τ referre by Eq.(9), the average atmospheric transmittance error moel can be obtaine as the Eq.(0). σ ( τ) = r π σ ( g ) c π σ ( T )( g g ) M r r 4 + M c K R ε ( T ) M 4 4 π σ ( g ) c π σ ( T )( g g ) M r r 3 + a + M c K R ε ( T ) M 4 4 π σ ( K)( g g ) π σ ( R)( g g ) r r c K ε M c K ε M π σ ( ε)( g g ) r + 4 c K ε M (9) ( 0) where M, M, M, M, M 3 M 4 is represente by the following integral formulas: R( ) R( ) ε e e M = c K c c 5 ( T ) 5 ( T ) R( ) R( ) M = c c 5 ( T ) 5 ( T ) e e R( ) R( ) M = c c 5 ( T ) 5 ( T ) e e M 4 = e 6 e c ( T ) c ( T ) where all of symbols have the same meaning to that mentione before. The euce Eq.(0) is exactly the average atmospheric transmittance measurement error moel. From formula (0), it can be known that, in orer to obtain atmospheric transmittance measurement error, g, g, σ r (g ), σ r (g ), T, T, σ r (T ), σ r (T ), K, σ r (K), R, σ r (R), ε an σ r (ε) are neee to be acquire, which are name as input ata for getting the measurement value an error of MWIR average atmospheric transmittance. The acquiring metho of these input parameters an their corresponing errors, requires specific measurement trials to support the analysis an calculation. The metho, gaining the average atmospheric transmittance by actual measurement with proper measure error, objectively reflects the atmospheric transmittance characteristic of the mi-infrare ban, with important value of research an application. 3. Input ata acquisition To measure the atmospheric transmittance in terms of Eq.(7), some input parameters, incluing blackboy temperature, infrare imager gray value an the calibration coefficient, nee to be known. This section will introuce the ways of acquiring these input ata an the consieration of relative stanar eviation. 3. Blackboy temperature acquisition Blackboy temperature can be easily collecte from the inicating panel. owever, it is noteworthy that the blackboy nees aroun half of an hour to stabilize in a setting temperature. Thus, the temperature acquisition shoul wait until the blackboy temperature stop floating. Because the relative stanar eviation may well reflect the conition of errors, so the relative stanar eviation σ r is chosen as unifie physical quantity to express the error analyze in the paper. The errors of blackboy temperature, T an T, may come from three aspects: Firstly, the inherent error, the ifference between the showing value an the actual temperature of the blackboy. Seconly, blackboy surface temperature instability (also calle unrepeatability), introucing the testing process with unrepeatability error. Thirly, the non-uniformity of blackboy, cause the slight 3

4 Yuanyuan Ji, Wenhai Xu, Ying i, Qilei Cao, Yukun Sun, Debin Ma an Ming Zhao/ Journal of Engineering Science an Technology Review 7 () (04) 8 ifference in the temperature blackboy surface area. Thus the error of blackboy temperature can be expresse by Eq.() σ ( T ) = σ ( T ) + σ ( T ) + σ ( T ) (3) r in rep un an (). σ = σ + σ + σ () ( T ) ( T ) ( T ) ( T ) r in rep un σ = σ + σ + σ () ( T ) ( T ) ( T ) ( T ) r in rep un where σ r (T ) is the total error of T, σ in (T ) is the inherent error, σ rep (g ) is the unrepeatable error an σ un (g ) is the nonuniformity error. An the metho of getting the error of g is the same with g. 3. Infrare images acquisition where σ r (T ) is relative error of high temperature blackboy, σ in (T ) is inherent error, σ rep (T ) is unrepeatable error, σ un (T ) is the non-uniform error. The meaning of symbols of T is similar to T. To test the eviation, the verification experiment is carrie out. Due to the blackboy is circular with iameter of 500 mm rather than a point, five positions in the area are chosen for test, incluing the mile, up, own, left an right (see Fig. ). Blackboy can be extracte from the images taken by the MWIR imaging system to get the gray values. To ensure the accuracy of the test, several pictures were taken rather than one, the average of which was consiere as the final acquisition result. owever, ue to the tiny ifference between each image, this process woul introuce errors. Accoring to the physical meaning of the relative error, the formula of the error of g is: σ ( g ) σ ( g ) = r (4) g U where σ r (g ) represents the relative stanar ifference of g, g represents an average of g, an σ(g ) is the stanar eviation that can be estimate from the Bessel formula []: M R D σ ( g ) = n vi (5) i= n where i is the number of multiple measurements, n is the measure times, v i is the resiual error which formula is shown by Eq.(6). Fig.. Test points of blackboy Consiering the far wavelength infrare thermometer as reference instrument, the blackboy temperature can compare with the reference value. Because the nominal value of the emissivity is 0.97 with the error of ±0.0, the emissivity input of FWIR thermometer will be set as 0.95, 0.97, 0.99 respectively. In view of the temperature of 5 an 35 will be use for measuring the average transmittance, these two temperature are taken as test values. In aition, there are two options for infrare etection, one is D, suitable for the range of 0~5, the other is D, suitable for the range of 0 ~ 500. An D is more accurate than D, so as to choose D grae for test. From the test of blackboy, three kins of errors can be erive, incluing the inherent error, unrepeatability an non-uniformity. Taking these error source into account, the total error of the temperature of blackboy can be euce by Eq.(3). v = g () i g (6) i where g (i) is multiple measure values (i =,,..., n). Beyon the unrepeatable error mentione above, there is another very important error along with the image acquisition, which is the spectral response error. The wie-ban infrare raiance is receive an converte to gray value by the MWIR imaging system. Due to the uncertainty of spectral response istribution influencing the output ata, it is necessary to take the infrare spectral responsivity error into account. To sum up, the total relative error of image acquisition is a combination of both the unrepeatable error an the spectral response error. In view of these two kins of error sources, the finalize error can be calculate by Eq.(7). σ = σ + σ (7) ( g ) ( g ) ( g ) r rep spec 4

5 where σ r (g ) is the total error of g, σ rep (g ) is the unrepeatable error an σ spec (g ) is the spectral responsivity error. An it is the same with the metho of getting the error of g. 3.3 Raiance calibration coefficients aqucisition Infrare raiation calibration of the MWIR imaging system is to etermine the relationship between the output image an the input raiation energy. Raiometric calibration metho is to use a stanar blackboy source to analyze the raiometric calibration response coefficient K of the MWIR imager by ajusting the surface temperature of the target. It is remarkable that infrare equipment often have a rift characteristic, which manifests that certain performance parameters of the instrument are alterable along with the time. Thus, shortly before the measure is to be carrie out, the infrare evice nee raiance calibration test to ensure the valiity for the measurement. To calculate the thermal imager raiometric calibration coefficients, the blackboy raiance reaching the entrance pupil of the infrare camera an receive by the infrare etector in wie wavelength range uner each surface temperature nees to be calculate. An then the ata shoul be fitte to get the raiance calibration coefficient. The fitting moel is the linear etermine by the linear region characteristic of the infrare imaging system an the application in the measurement. Moreover, the fitting metho is least square metho, an its meaning is to get the minimum of root mean square error (RMSE). In aition, ue to the uncertainty of the spectral response of infrare imager, the accuracy of the raiometric calibration coefficient can also be affecte. Infrare spectral responsivity is escribe as previously. In consieration of the linear fitting error an infrare spectral error, raiometric calibration coefficients integrate error can be gaine by the following expression: Yuanyuan Ji, Wenhai Xu, Ying i, Qilei Cao, Yukun Sun, Debin Ma an Ming Zhao/ Journal of Engineering Science an Technology Review 7 () (04) 8 ata are so long that only the primary parts are liste here. (see Table ~). Table. Test of blackboy on 5 emissivity point test test ( ) ( ) mile up own left right mile up own left right mile up own left right Table. Test of blackboy on 35 emissivity point test test ( ) ( ) mile up own left right mile up own left right mile up own left right analysis inherent error<0.6 unrepeatability<0.09 non-uniformity<0.06 inherent error <0.04 unrepeatability<0.5 non-uniformity <0.3 inherent error <0.5 unrepeatability<0.7 non-uniformity <0.3 analysis inherent error <0.7 unrepeatability<0. non-uniformity<0.08 inherent error <0.07 unrepeatability<0.07 non-uniformity <0.05 inherent error <0.5 unrepeatability<0.06 non-uniformity <0.05 σ = σ + σ (8) ( K) ( K) ( K) r fit spec In the above formula, σ r (K) is a comprehensive error of raiance calibration coefficient, σ fit (K) is the fitting error, σ spec (K) is the spectral response error. 4. Results an iscussion The measurement of MWIR average atmospheric transmittance was carrie out in accorance with the theory an metho introuce in section an 3. The experiment was eucte in Dalian when the season is winter. An the weather is nice, atmospheric visibility was 5375m, the air temperature was 4.6, relative humiity is 45.% an the air pressure is 00.7hPa. The teste istance is 97.m, of which the transmittance was measure. 4. Result of Blackboy temperature acquisition Accoring to the error test introuce in section 3., twice tests were carrie out, each of which inclue at least 0 sets of ata, to make sure the results objective an accurate. The From the experiment, it can be conclue three points. First, the measure temperature an the blackboy surface temperature are closest when the FWIR thermometer emissivity is set as 0.97, while the ifference increases with the temperature. An the maximum is about an Besies, the blackboy has a stable repeatability, less than an Moreover, the non-uniformity of blackboy source is goo, aroun an From Eq.(3) an the input value obtaine here, the final error of T is 0.87%. Similarly, the final error of T is.4%. Obviously, T is equal to 35 an T is equal to Result of Infrare images acquisition From section 3., the infrare images acquisition experiment was one to recor the thermal images of 5 an 35 blackboy, as well as the fluctuation of the grays. The results are shown in Fig.3 an Fig.4. 5

6 3.5 x Yuanyuan Ji, Wenhai Xu, Ying i, Qilei Cao, Yukun Sun, Debin Ma an Ming Zhao/ Journal of Engineering Science an Technology Review 7 () (04) 8 where, is the wavelength, i is the bounary value of each sub ban of the wie wavelength range, k i, k i, k i3, k i4 is the cubic spline fitting coefficients. Gray / time /h Fig. 3. Gray value of 5 blackboy Gray / 5.8 x time /h Fig. 4. Gray value of 35 blackboy Uner the ata shown by Fig.4 an Eqs.(4)~(6), σ r (g ), the error of 35 blackboy can be solve: σ(g )=6, g =507, σ r (g )=0.05%. Similarly, the error of 5 blackboy σ r (g ) can be obtaine: σ(g )=6, g =34889, σ r (g )=0.08%. Besies of the above error, the spectral response error is another error source. From the manual of infrare etectors, the actual spectral response istribution of MWIR optielectronic etector is more narrow than the nominal cutoff wavelength range of 3~5 µm. The relate literature Infrare spectral responsivity shows that the spectral response curve can be fitte by cubic spline fitting metho, which uses the following formula Eq.(9) an coefficients (see Table 3) for the spectral response characteristic characterization: R = k + k + k + k (9) 3 ( ) ( ) ( ) ( ) i i i i i3 i i4 Table 3. Three times polynomial coefficients Wavelength range (µm) three times polynomial coefficients k k k 3 k ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ Wavelength range (µm) three times polynomial coefficients k k k 3 k ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ Combining the thermal imager chip ata with cubic spline fitting metho an the fitting coefficients, the infrare spectral response curves can be rawn as Fig. 5. Infrare Spectral Responsivity / Wavelength /ɼ m Fig. 5. Infrare Spectral Responsivity Curve As illustrate in Fig. 5, the cutoff wavelength of the spectral response curve is approximately 3.5~4.8µm. The overall spectral response within the wavelength range is greater than 0.9, slightly unulating. The relevant materials [3], [4] show that the measurement error of spectral responsivity of infrare etector is generally less than.%. From Eq.(7) an the known input value, the final error of g is.%. Similarly, the final error of g is.%. 6

7 4.3 Result of Raiance calibration coefficients aqucisition This article follows the principle, so as to ensure effective an reliable of the acquire ata. Raiometric calibration ata collecte are shown in Table 4. Table 4. Blackboy temperature an gray value T ( ) gray On the basis of Eq.(6), the pupil raiance can be gotten by substituting the blackboy temperature, emissivity an the spectral response of infrare instrument, as follows: Table 5. Pupil raiance an gray value 0-5 (W. cm -. sr - ) gray In accorance with Table 5, the infrare raiation calibration ata can be plotte as the blue line in Fig.6. Due to the linear region of the ata in the MWIR ban, the blue line can be linear fitte to the re line by using least square metho. 5.5 x 04 Yuanyuan Ji, Wenhai Xu, Ying i, Qilei Cao, Yukun Sun, Debin Ma an Ming Zhao/ Journal of Engineering Science an Technology Review 7 () (04) Result of MWIR average atmospheric transmittance Blackboy temperature T an T are known from section 3. respectively: T =35,T =5. An the gray values of high an low temperature blackboy were obtaine by extracting blackboy area from the images: g =507, g = Infrare raiance calibration coefficient was obtaine from section 3.3, an K= Thus the MWIR average atmospheric transmittance can be euce by replace the input ata referre by Eq.(7) with the values acquire in section 3. An the result is τ=0.835, which is in line with the empirical value of the sunny atmospheric transmittance. 4.5 Error of MWIR average atmospheric transmittance From the foregoing analysis, the errors of high an low temperature blackboy were: σ r (T )=0.87%, σ r (T )=.4%. An the errors of infrare gray values are as follows: σ r (g )=.% an σ r (g )=.%. Moreover, the raiance calibration coefficient error is σ r (K)=3.0%. Instituting the above ata into Eq.(0), the MWIR average atmospheric transmittance measurement error is calculate as.5%, which is the integrate error of the entire measurement system an measure metho, reflecting the effectiveness of the measurement of the MWIR average atmospheric transmittance. Gray value / Measurment Fitting Raiance /w. cm -. sr - x 0-4 Fig. 6 Raiance calibration of infrare imaging system By fitting, infrare camera raiometric calibration coefficient was gotten, K= Since the fitting ata i not completely overlap the measure ata, the fitting error is introuce to K. Uner the constraint of the linear fitting moel an least square fitting metho [5], the most appropriate an the optimize fitting result is uniquely etermine, RMSE=38 an mean gray value is g = Taking RMSE values into Eq.(4), we obtain the relative stanar eviation of raiance calibration coefficient K, σ r (K)=.8%. Take the ata into Eq.(8), the final error is 3.0%. 5. Conclusion This paper analyzes the mi-infrare atmospheric transmittance measurement principle, an acquires the various input ata of atmospheric transmittance measurements require. Then, accoring to the measurement principle, the MWIR average atmospheric transmittance error moel is theoretically erive an establishe to stuy the effects of each component of the error link to the entire error of atmospheric transmittance. In aition, through the specific ata processing an error analyzing to the test, the measurement component an corresponing sub-errors are obtaine. Ultimately, a comprehensive theoretical analysis an testing process are eucte to seek a mi-infrare atmospheric transmittance an the measuring error. The work of this paper shows that the measurement of atmospheric transmittance an error analysis reflect the primary factors of the measurement link. The results emonstrate that the measure values meet with the empirical atmospheric transmittance in sunny ay very well. Moreover, the measurement error is less than %, proving the valiity of the measurement ata from the perspective of the actual measurement. Acknowlegment The corresponing author of this paper is Wenhai Xu, professor of Dalian Maritime University. An this work is financially supporte by the Funamental Research Funs for the Central Universities (Grant No. 0763, an Grant No ). References. Dario Cabib, "Complete afforable system for simultaneous VISNIR an MWIR/WIR spectral atmospheric transmittance measurements (ATMS)", Proceeings of the SPIE - Atmospheric Propagation VII, 7685(76850), 00, pp.-0. 7

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