Real time processing with low cost uncooled plane array IR camera-application to flash nondestructive
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1 hp://dx.do.org/0.6/qr Real me processng wh low cos uncooled plane array IR camera-applcaon o flash nondesrucve evaluaon By Davd MOURAND, Jean-Chrsophe BATSALE L.E.P.T.-ENSAM, UMR 8508 CNRS, Esplanade des Ars and Meers Talence Cedex FRANCE - Phone : (33) Fax : (33) E-mal : mourand@lep-ensam.u-bordeaux.fr Absrac: A one-dmensonal ransen flash mehod based on nfrared hermography devce, allows o go back o hermal dffusvy map. However, each pxel of he emperaure mage presens a very nosy emporal sgnal. Moreover, n he case of an uncooled plane array camera, each plane array deecor presens ndependen calbraon coeffcens and ndependen offse levels. We presen, n hs framework, an denfcaon mehod based on he esmaon of hermal dffusvy varaons around a nomnal value by an asympoc graden expanson. Such mehod and real me processng and compung devces allow o oban he esmaon resul a he same me as he evoluon of he expermen..inroducon A ransen flash expermen based on nfrared hermography allows o oban a dffusvy varaon map, usng he asympoc graden mehod presened by Mourand and al, 998 []. The am of hs work s o realse a cheap and real me Non Desrucve Evaluaon devce (dryng process conrol, lne conrol, ec. ) on maerals of parallelpedc form and hckness abou one cenmeer. To do hs, we use an asympoc graden mehod wh a low-cos nfrared camera and hs o he dermen of he measuremen nose whch can be processed by usng a grea number of measuremen (see Mourand, 998 []). We have chosen an uncooled hermal magng camera wh a 40x30 ferromagnec plane array deecors: he PalmIR 50 of RAYTHEON. Frs, we wll call back he prncple of he denfcaon mehod based on he esmaon of hermal dffusvy varaons around a nomnal value by an asympoc graden expanson. Then, we wll show, ha he asympoc graden mehod can be used wh an uncooled hermal magng camera as he PalmIR 50. Then, an expermen wh he uncooled hermal magng camera s presened on a Poly Vnyl Chlorde sample of dfferen hckness generaed by machnng. A real me recordng and compung devce allows o oban a real me esmaon of he hermal dffusvy carography.. Esmaon mehod of a varaon of he hermal dffusvy around a nomnal value In he deal case, ha s o say wh an nsulaed sample, a nal me (=0), he emperaure s assumed o be unform (T(x,=0)=0), and s submed o a hermal
2 hp://dx.do.org/0.6/qr excaon. If he hea ransfer s supposed -D, hen, he emperaure response on he rear face (x=l), o an nsananeous and unform hermal pulse on he fron face (x=0), s gven by (See Parker and al,96 [3]): n n² ² a T Tlm exp Tlm f a, n L From expresson (), he esmaon problem of he parameer a (dffusvy) s he same as he esmaon of he parameer a / L (characersc frequency) when L s known. Boh parameers ( a or a / L ) wll hen be consdered ndfferenly. In he case where he average dffusvy a 0 of he maeral s known, and where he am s only o esmae s local varaon a=a- a 0, he emperaure a he me : T( ) can be wren wh a frs order developmen: f T( ) Tlm f ( a0, ) atlm (-a) a Tha s o say wh marx noaon, consderng he vecors: T T T, f ( a, ) f ( a, ), N ( a 0, ) f 0 0 f f f and a a a a a N ( 0, ) ( 0, ) and parameers: T lm and atlm, The relaon (-a) yelds: f T f X (-b) a Ths resul leads o an excellen approxmaon (beer han one percen) n a neghborhood of 0 % around a 0 (see fgure ). If he measuremen nose on each componen of he expermenal emperaure vecor T s assumed wh a consan sandard devaon and no correlaed, n he doman of valdy of he developmen (-a), hen, he opmal esmaor of he parameers vecor s obaned by (see Beck and Arnold, 97 [4]): ˆ X X X Tˆ ˆ As a /, he varaon of dffusvy can be wren: f f f f Tˆ f f Tˆ a a aˆ f f f f f Tˆ f Tˆ a a a a The lnearsaon gven by he expresson () allows no only he esmaon of he parameer a, bu also allows he confdence nerval of hs esmaon o be suded. N () (3) (4)
3 hp://dx.do.org/0.6/qr An nermedae sage s he covarance marx of he esmaon on he vecor, gven dependng on he sandard devaon of he emperaure measuremen nose T : ˆ cov X X T (5) ˆ The random varable relave o he esmaon error on he parameer a can be expressed as e a. Ths varable s lnked wh random varables relave o he esmaon errors on he parameers and expressed by e and e. Snce a / an asympoc expanson gves: e e e a Y (6) e e The varance characerzng he confdence nerval of he esmaon of a s hen gven n Beck and Arnold, 97 [4]: ˆ var e a Y cov Y T Y X X Y ˆ (7) The expressons (3) and (5) show ha he mehod can be used whaever he lengh of he vecor T f. Thus, he scalar producs T a and f T can be ncremened as and when he camera records mages. Ths sequenal mehod consderably eases he problems of sorage and mages manpulaon. Bu hs allows above all a real me sgnal processng, whch s necessary for a Non Desrucf Evaluaon devce. Moreover, he asympoc graden mehod s opmzed (n he leas squares sense) n he valdy doman of he lnear approxmaon. Therefore, consues a smple reamen of dscrmnaon even ou of he valdy doman of he model descrbed by (- a). A las, s no lmed o he rear face ransen mehod, whou hea losses. We can model wh he vecors f and f more complex responses (measured on he fron a face, wh hea losses, ec see Mourand, 998) provded ha he sole varably s he hermal dffusvy a. 3. Applcaon of he asympoc graden mehod o a hermal magng camera We have chosen a hermal magng camera: he PalmIR 50 of RAYTHEON. I uses a 40x30 ferromagnec uncooled plane array deecors. The camera whch only have one sgh and one vdeo oupu, has been conneced o an acquson board n order o record and process a blas of 8 bes coded mages n real me. Thus, he daa comng from he camera are 40x30 marx wh 56 emperaure level. We should specfy ha he hermal magng measuremen nose s very mporan, praccally as he same order as he sgnal amplude. Bu as we have ever shown (see [] and []), he asympoc graden mehod s suable o process very nosy hermograms. One can conclude ha for hese requred condons, he graden mehod s he mos convenen and accurae. 3
4 hp://dx.do.org/0.6/qr As we can see n he expresson (4), hs mehod doesn need he absolue emperaure o deermne he hermal dffusvy varaons. We jus need a measuremen proporonal o he emperaure. Thus, s no necessary o calbrae he dfferen camera s deecor, or o know he maeral s emssvy. The man problem of he PalmIR 50 camera s ha modfes connously he mage s mean level, n order o opmze he mage dynamc. Thus, f hey had no measuremen nose, he rear face ransen pulse response would be obaned such as hese presened on he fgure. Therefore, we have numercally suded he nfluence of he mean level varaons of he hermal magng camera. In fac, only he look of he emperaure response o he excaon changes durng he expermen, hus, only akes o replace he seady sae emperaure sensvy n he process, by ha we wll call he magng emperaure sensvy (see fgure ). Therefore, we have performed a numercal smulaon of he parameer esmaon of he "hermal dffusvy varaon" a wh he magng camera emperaure response dependng on he sandard devaon of he measuremen emperaure. 4. Expermenal resuls To llusrae he heorecal resuls, an expermen was performed on a parallelppedc form Poly Vnyl Chlorde sample. Insead of varyng he dffusvy, we vared he hckness. Indeed, n all he prevous presenaon he varaons of he parameer a / L may be analyzed nsead of a. The esed hcknesses are respecvely : 4.95 mm, 4.9 mm, 4.8 mm, 4.6 mm. The expermenal resuls were obaned wh he nfrared camera ype PalmIR 50. The maxmal scannng speed s 30 mages/s, each mage s composed of 30 x 40 pxels. Each expermen s composed of more han 000 mages recorded a a regular me nerval. Durng he expermen, he daa are recorded and processed n real me wh a Marox recordng devce (Sony) on a PC penum II 33. Only he scalar producs f T a and f T are ncremened and no mage s defnely sored. Fgure 3 presens an expermenal hermogram correspondng o a pxel amed by he camera, afer a flash. Fgure 3 presens he mage obaned hanks o he expresson (4). One observes dfferen zones correspondng o he dfferen hckness of he plae. The maxmum dffusves of he mage are he darkes. Fgure 4 presens he average profle aken from he las mage. The good agreemen beween he esmaed hckness and he real hckness, may be noed. Such average hckness profles are compared wh resuls obaned n he same condons wh a mechancal scannng camera of ype AVIO TVS 000 and prevously publshed (see []). Some dscrepances (D effecs) can be abued o he specfces of elecronc sysem. Somes sudes o ake no accoun such D effecs are n sudy. Concluson Our esmaon mehod assocaed on an uncooled hermal magng lke he PalmIR 50 of RAYTHEON, consues a low-cos Non Desrucve Evaluaon devce by nfrared hermography.ths work shows ha he poor performances or he parculares of he nfrared camera can be compensed by adaped daa processng. 4
5 hp://dx.do.org/0.6/qr References [] Mourand D., Gouno J., Basale J.-C., New sequenal mehod o process nosy emperaure response from flash expermen measured by nfrared camera, Revew of scenfc nsrumens, Vol. 69, N 3, pp , (998). [] Mourand D., Conrbuon à he mse au pon de méhode de Conrôle Non Desrucf hermque Traemen de sgnaux foremen brués. Thèse de l ENSAM Cenre Bordeaux, (998). [3] Parker W. J., Jenkns W., Abo J., Flash mehod of deermnng hermal dffusvy, Hea capacy and hermal conducvy, Journal Appl. Phys., vol 3, No 9, pp , (96). [4] Beck J.V. and Arnold K. J., Parameer esmaon n engneerng and scence,john Wley and Sons, NY, (977). Temperaure level 40 Classcal emperaure Response PalmIR 50 emperaure Response T(a 0 ) T(a 0 +a) 5 0 T magng (a 0 ) 5 0 T magng (a 0 +a) Tme (s) Fgure : Comparson of emperaure response o a rear face ransen mehod n he classcal case and when he emperaure s measured wh he hermal magng PalmIR 50. Sensvy Seady sae emperaure 0.9 sensvy X Tlm Dffusvy sensvy X a 0.8 Imagng emperaure X sensvy X Tlm 0.7 Tmagng X Tmagng Tme (s) Fgure : Sensvy curves numercally calculaed for he seady sae emperaure, he hermal dffusvy, and he magng emperaure. 5
6 hp://dx.do.org/0.6/qr P x e l l n e p o s o n Pxel column poson Dffusvy (m². s - ) Fgure 3: Thermal dffusvy map correspondng o a sample machned wh dfferen hcknesses and obaned wh he PalmIR 50 and real me processng. Apparen hermal dffusvy (m²/s) x 0-7 Thckness (mm) Esmaed hckness wh he PalmIR 50 Esmaed hckness wh he AVIO TVS 000 Real hckness Pxels column poson Fgure 4 : Average hckness profles obaned wh he palmir 50 camera aken from fgure 3 and comparson of resuls obaned n he same condons wh a camera of ype AVIO TVS
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