The Henryk Niewodniczański INSTITUTE OF NUCLEAR PHYSICS Polish Academy of Sciences ul. Radzikowskiego 152, Kraków

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1 The Henryk Niewodniczański INSTITUT OF NUCLAR PHYSICS Polish Acadey of Sciences ul. Radzikowskiego 152, Kraków Kraków, October 2005 Report No. 1968/D The theroluinescence glow-curve analysis using GlowFit - the new powerful tool for deconvolution M. Puchalska and P. Bilski Abstract A new coputer progra, GlowFit, for deconvoluting first-order kinetics theroluinescence (TL) glow-curves has been developed. A non-linear function describing a single glow-peak is fitted to experiental points using the least squares Levenberg- Marquardt ethod. The ain advantage of GlowFit is in its ability to resolve coplex TL glow-curves consisting of strongly overlapping peaks, such as those observed in heavilydoped LiF:Mg,Ti (MTT) detectors. This resolution is achieved ainly by setting constraints or by fixing selected paraeters. The initial values of the fitted paraeters are placed in the so-called pattern files. GlowFit is a Microsoft Windows-operated user-friendly progra. Its graphic interface enables easy intuitive anipulation of glow-peaks, at the initial stage (paraeter initialization) and at the final stage (anual adjustent) of fitting peak paraeters to the glow-curves. The progra is freely downloadable fro the web site

2 Introduction Over the last two decades coputerized deconvolution of theroluinescence glowcurves has becae the ethod of choice for TL glow-curve analysis. This ethod is used to evaluate TL kinetics paraeters for a given peak in the glow-curve, but it is also applied nowadays in routine radiation dosietry. Several odels, approxiations and iniisation procedures have been investigated and a nuber of coputer progras have been developed for TL glow-curve analysis (1-5). An iportant step in establishing deconvolution as a reliable research tool was the GLOCANIN project (6) an intercoparison of glow-curve analysis progras. Participants in this project had to analyse TL peak paraeters in siulated and experiental glow-curves easured in LiF:Mg,Ti, the ost coon TL aterial. Probably the best deconvolution software currently available is the GCA progra developed by CIMAT (4). This progra (version 2.0) has been successfully used in our laboratory over a nuber of years (7). For well-separated peaks the quality of deconvolution is quite satisfactory. However, the GCA progra also has its liitations. A ajor one is the inability to set constraints on selected paraeters. In the case of the newly-developed MTTtype detector featuring enhanced high-lt response (8), constraining soe paraeters is the only ethod to obtain eaningful results. Another shortcoing of the GCA progra is its anual introduction of initial paraeter values, which is tie-consuing if large aount of data need to be analysed. Mainly for these reasons, we decided to develop our own deconvolution software, better suited to our particular needs. Within the MS Windows environent, we wished to create a progra which could address soe of the disadvantages of its predecessors, be ore efficient in coplex glow-curve analysis, and ore user-friendly. We report here a description of the GlowFit progra developed by us, and deonstrate results of its perforance tests. Model and ethod The developed glow-curve analysis software is based on the first-order kinetics odel of Randall and Wilkins. The TL intensity of a glow-peak in the TL glow-curve is given by the equation (1) : I( T ) = I exp where I is the glow peak intensity, [ ev ] constant, [ K ] T exp exp 2 T the activation energy, [ ev ] k K the Boltzann T the absolute teperature and T and I are the teperature and the intensity of the axiu, respectively. Because the exponential integral in quation 1 is not solvable analytically, several different approxiations and functions describing a single glow peak, extensively discussed by Bos et al (2,3) and Horowitz and Yossian (1), have been proposed. In our case the exponential integral is approxiated by the expression (6,9) : ' ' dt (1) T 0 ' ' 1 ( x ) dx ( x) ' ' 2 exp dt x exp = ' k k x x 2 (2) where ' x = x 2 is the second exponential integral function which can 2 ( x) = α x exp x, where α (x) is a quotient of 4 th order polynoials (9) : x, and ( ) = ' be evaluated by ( ) ( ) 2

3 a + a x + a x + a x + x α ( x) = 1 (3) b0 + b1 x + b2 x + b3x + x Then, finally, the following expression is used to describe a single glow peak (1) : I( T ) = I exp exp α T T exp α (4) As is shown above, the glow-curve is a non- linear function of T, I and paraeters. To find the best-fitted values of peak paraeters an iterative procedure ust be used. GlowFit is capable of siultaneously deconvoluting as any as ten glow peaks fro the TL glow-curve. For ten glow peaks the nuber of unknown paraeters is thirty three - the additional three paraeters are used in the background expression, such as a + b exp( T ) c, where a, b and c are the unknown background paraeters. A χ 2 function ust be defined and the best fit paraeters are deterined by its iniization. The iniization process starts with trial values. In this progra the Levenberg-Marquardt ethod for non-linear function iniization was chosen. In order to enable the user to control the fitting peak paraeters, the original algorith (10) was odified to exclude or constrain any given paraeter of the peak. Progra description GlowFit is a MS Windows-based progra and can operate on ost PCs. It was written in C++ language. The progra is equipped with a user-friendly graphical interface. Typical coputer fitting ties for an entire TL glow-curve are 1-10 s. Starting paraeters Generally, non-linear fitting is strongly dependent on the choice of the initial values of the paraeters. The χ 2 function is uch ore dependent on the position of the peaks (T ) than on other paraeters (1,11), so the first estiation of T is quite critical for reaching convergence. The GCA progra uses an autoatic algorith for searching peak positions (4). In principle this ay sees to be the best approach, but for soe peaks the initially-guessed paraeters often require anual adjustent before starting the fitting procedure, which is tieconsuing. In the GlowFit another approach was therefore developed. We introduced a socalled pattern file which defines the relation between peak paraeters and the global axiu of the glow-curve. Soe pattern files for LiF glow-curves are available together with the progra file but if no predefined file is appropriate, the user ay create his own pattern file. In this case the starting paraeters can be easily defined by clicking with a ouse on a plot at positions where peak axia should be located (energy of 1.7 ev is assued by default). There is also the option of anual adjustent, which allows the user to easily anipulate each initial value. The typical tie necessary for setting up the starting paraeters for a new experiental glow-curve consisting of several peaks is usually no ore than 1-3 inutes. Once a successful deconvolution is perfored a pattern file can be autoatically generated. Then each next glow-curve of a siilar shape can be processed in a few seconds. If the predefined pattern file is opened the algorith starts by finding the global axiu of the glow-curve. Then the teperature distance between position of each peak and the global 3

4 axiu are read fro the file. The second inforation read fro this file is the ratio between the peak height and the easured TL signal in the teperature channel corresponding to the peak position. Finally, starting values of energy are read fro the pattern file. Constraints and fixing The fitting procedure searches for a iniu value of χ 2 but, unfortunately, this does not iply obtaining true peak paraeter values. Soeties the best nuerical solution corresponds to unacceptable paraeter values. In such cases we should exploit our previously gathered knowledge about peak positions, proportions and energies in order to force the progra to aintain the fitted values within preset liits. Such a constraint option was ipleented in the GlowFit. The user ay set nuerical liits or a percentage range around the initial value. Soeties it is necesarry to fix soe of the paraeters, e.g. in the cases of very coplex curves or of very low statistics. The fixed paraeters reain unchanged during the fitting procedure. The graphical interface also enables the operator to anipulate the glow peaks after the fitting, as a anual fit adjustent. This ay be helpful if the iniization ethod fails. Results output Results are presented on the screen and stored in the defined report file. The report contains all the iportant inforation: nae of the analysed file, a coent (detector type, heating rate etc.), peak height, energy, the teperature position at the peak axiu and the integrals of each fitted peak. In the report a paraeter describing the quality of fitting, called Figure Of Merit (FOM) is also stored: where: y i - content of the channel i y(x i ) value of fitting function in the centre of channel i Additionally, a plot of residuals, i.e. of the relative differences between easured and fitted values in each channel is also presented on the screen. The user ay also save to the disk a file containing data for plotting all fitted glow-curves and peaks. ( x ) yi y i i FOM[%] = y 100% i i Progra perforance Reference glow-curves As a test, the GlowFit was used to analyze the reference glow-curves fro the GLOCANIN intercoparison project (6). In Table 1 the FOM values obtained using GlowFit are copared with the FOM values obtained by a participant of the GLOCANIN, who used the sae function to describe a single glow peak and also had one of the best results in the GLOCANIN project (progra B in Reference 6). Our results are better in all cases except RefGlow.003 and RefGlow

5 Table 1. Coparison of FOM [%] values obtained using GlowFit with FOM values obtained within the GLOCANIN intercoparison project [taken fro Reference 6]. File nae GlowFit FOM GLOCANIN Progra B (6) FOM RefGlow RefGlow RefGlow RefGlow RefGlow RefGlow RefGlow RefGlow RefGlow RefGlow Table 2 shows a coparison between the activation energy obtained by GlowFit analysis with the actual activation energies of the GLOCANIN project for synthetic and average for experiental glow-curves. Agreeent for the synthetic glow-curves is within 0.09% or less. These results are rather natural because the data were siulated using the Randall-Wilkins odel, the sae that was used to develop the GlowFit software. Analysis was perfored without any pattern file and without setting any constraints. The percentage deviation between the ean activation energies of the GLOCANIN project and activation energies obtained using the GlowFit is below 6%. Table 2. Percentage deviation between the activation energies of the GLOCANIN project and activation energies obtained using the GlowFit for synthetic and the experiental reference glow-curves. Percentage deviation File nae Peak 1 Peak 2 Peak 3 Peak 4 Peak 5 Synthetic reference glow-curves RefGlow RefGlow RefGlow.003 RefGlow.004 RefGlow.005 RefGlow.006 RefGlow.007 RefGlow.008 RefGlow.009 RefGlow.010 xperiental reference glow-curves The ost coplicated glow-curve was RefGlow.009, easured for LiF:Mg,Ti irradiated with a dose of 600Gy, which shows a coplex structure over high-teperature peak region. These overlapping peaks ake the fitting procedure quite difficult. The GLOCANIN participants results differed not only in the position and shape of resolved peaks but also in their nuber (9 or 10). Because there are several possibilities of obtaining a good fit, it is not surprising that a great spread, up to 60%, in peak areas and activation energies was found. This coplex glow-curve presented in Figure 1 shows how iportant it is to be able occasionally to introduce paraeter constraints to the fit. If peaks strongly overlap, the fitting procedure is evidently not so unequivocal, so inforation about the peak s position and about other 5

6 paraeters ust be taken fro additional experiental sources, e.g. the T -T stop ethod (12). As shown in Figure 1 (a) and (b), the results are copletely different if we analyse this curve with or without constraining the peak paraeters. The constrained paraeters were T and for high-teperature peaks. It should be noted that in both cases the FOM value is very good, and in case of unconstrained fit it is even better, but the physical eaning of soe paraeters is wrong. Other reference glow-curves were analysed without any paraeter constraints. Figure 1. Results of fitting of RefGlow.009 of the GLOCANIN project by GlowFit (a) Fitted with constraining paraeters T and for high-teperature peaks and (b) fitted without paraeter constraints TL signal [counts] (a) FOM=1.35% Teperature [K] 5 5a TL signal [counts] (b) FOM=1.1% Teperature [K] 4 5 5a Application of GlowFit for analysis of different LiF glow-curves The GlowFit progra s ain advantage is the ability to analyse coplex glow-curves with overlapping peaks. A good exaple is the analysis of a set of curves easured for an experiental version of LiF:Mg,Cu,P aterial doped with decreased aount of agnesiu (0.05%) exposed to doses up to 1kGy (Fig. 2) (13,14). It was found that at doses higher than 200Gy on the low-teperature side of the ain peak a sall bulge appears, suggesting the presence of a new peak. At still higher doses this new peak becoes ore pronounced. While for the highest doses the deconvolution is quite siple, below 50Gy, when the newly eerging peak is hardly visible or even copletely hidden under the ain peak, it is ipossible to distinguish between the overlapping peaks. Fro the analysis of curves easured after higher exposures one ay deterine the position (T ) of this sall peak on the low-teperature side of the ain peak. According to this knowledge we can liit the peak paraeters, especially the teperature of the peak axiu. In Figure 2b we present an exaple of a deconvoluted glow-curve in this aterial irradiated by a dose of 49.6Gy, with a sall peak appearing at 467K. 6

7 Figure 2. xaples of glow-curves in LiF:Mg,Cu,P aterial doped with decreased aount of Mg (0.05%) irradiated by a dose 467.8Gy (a), 49.6Gy (b), and deconvoluted by GlowFit ( a ) 3000 ( b ) T L s ignal [ c ounts ] T L s ig n a l [ c o u n t s ] Te p e ra t u re [ K ] Te p e ra t u re [ K ] Another good exaple of the advantages offered by the GlowFit progra are MTT-7 detectors irradiated by high doses. MTT-7 is a newly developed version of LiF:Mg,Ti with a changed activator concentration and increased high-lt response (8). Figure 3a presents results of deconvolution using the GCA software (i.e. without constraints), which produced apparently incorrect paraeters (peak 6 has oved to the position of peak 5 and an enorously wide peak 10 is observed). When we use GlowFit with constraints set only on the starting paraeters of peak 6, which is the ost overlapped and difficult to distinguish, the result is such, as shown in Figure 3b. Figure 3. xaple of a glow-curve of MTT-7 aterial irradiated by a dose of 100Gy; deconvoluted by the GCA progra (4) (a) and by GlowFit with a constraint regarding peak 6 (b) (a) (b) TL signal [counts] Teperature [K] 9 10 TL signal [counts] Teperature [K] 7

8 Conclusions Basing on the successful analysis of GLOCANIN reference glow-curves, we believe that the GlowFit software developed by us is able to accurately and correctly analyse first order TL glow-curves. Unlike siilar deconvolution progras, GlowFit is able to resolve coplex glow-curves consisting of strongly overlapping peaks, which is achieved ainly through the possibility of setting constraints or fixing any of fitted paraeters. Another iportant feature of the progra is the very effective ethod of setting initial values of the fitted paraeters, by using the so-called pattern files. GlowFit features a well-developed graphical user interface, which enables easy, intuitive anipulation of glow-peaks in the easured TL glow-curve, prior to the coenceent of fitting and after the fit has converged. The GlowFit ay be a useful research tool for theroluinescence studies and for practical dosietry. It is freely downloadable fro the web side Further work is in progress to also include the possibility of fitting the second- and general-order kinetics glowcurves. Acknowledgents This work was partly supported by a research project fro the Polish State Coittee of Scientific Research (KBN) over the years (No. 4T10C03824). References 1. Horowitz, Y. S. and Yossian, D., Coputerised Glow Curve Deconvolution: Application to Theroluinescence Dosietry. Radiat. Prot. Dosi Bos, A. J. J., Piters, T. M., Gŏez Ros, J. M. and Delgado, A., An Intercoparison of Glow Curve Analysis Coputer Progras: I. Synthetic Glow Curves. Radiat. Prot. Dosi. 47, Bos, A. J. J., Piters, T. M., Gŏez Ros, J. M. and Delgado, A., An Intercoparison of Glow Curve Analysis Coputer Progras: II. Measured Glow Curves. Radiat. Prot. Dosi. 51, Delgado, A. and Gŏez Ros, J. M., Coputerised Glow Curve Analysis: A Tool for Routine Theroluinescence Dosietry. Radiat. Prot. Dosi. 96, Horowitz, Y. S. and Moscowitch, M., LiF-TLD In The Microgray Dose Range via Coputerised Glow curve Deconvolution and Background Soothing. Radiat. Prot. Dosi. 17, Bos, A. J. J., Piters, T. M., Gŏez Ros, J. M. and Delgado, A., An Intercoparison of Glow Curve Analysis Coputer Progras. IRI-CIMAT Report Olko, P., Bilski, P., Budzanowski, M., Molokanov, A., Ochab,. and Waligórski, M. P. R., Supralinearity of peak 4 and 5 in theroluinescent lithiu fluoride MTS-N (LiF:Mg,Ti) detectors and different Mg and Ti concentration. Radiat. Meas. 33, Bilski, P., Budzanowski, M., Olko, P. and Mandowska,., LiF:Mg,Ti(MTT) detectors optiised for High-LT radiation dosietry. Radiat. Meas. 38, Abraowitz, M. and Stegun, I. A. Handbook of Matheatical Functions. (New York: Dover). 10. Brandt, S., Analiza Danych. Wydawnictwo Naukowe PWN. 11. Gŏez Ros, J. M. And Kitis, G., Coputerised Glow Curve Deconvolution Using General and Mixed Order Kinetics. Radiat. Prot. Dosi. 101, Horowitz, Y. S., Satinger, D., Yossian, D., Brandan, M.., Buenfil, A.., GaboadeBuen, I., Rodriguez-Villafuerte, M. and Ruiz, C. G., Ionisation Density ffects in the Theroluinescence of TLD-100: Coputerised T -T stop Glow Curve Analysis. Radiat. Prot. Dosi. 84,

9 13. Bilski, P., Budzanowski, M. and Olko, P., A Systeatic valuation of The Dependence of Glow Curve Structure on the Concentration of Dopants in LiF:Mg,Cu,P. Radiat. Prot. Dosi. 65, Bilski, P., Lithiu Fluoride: Fro Lif:Mg,Ti to LiF:Mg,Cu,P. Radiat. Prot. Dosi. 100,

10 Appendix A GlowFit anual

11 1. Introduction This software was designed using C++Builder 6 and runs under Windows environent. The best resolution is 1024x768 or higher with sall fonts. Distribution disk contains executable file, GlowFit.exe, and two exaple pattern files. GlowFit analyses previously recorded easureents of TL glow-curves. Data files should be ASCII files of a axiu of 1000 lines, in the following coluns forat: two coluns: teperature (ºC) intensity The ain application window consists of two panels (Figure 1). Operational panel is used to open the data file, set the starting paraeters as well as to adjust the paraeters after fitting in case the fitting procedure failed. Fitted curve is presented on the screen in the results panel area. The area of each glow peak, FOM value, the residue and nuber of iterations needed to fit the glow-curve are also shown in this panel. Figure 1. The ain application window of the GlowFit software. A1

12 2. The data file opening The data file is opened by arking the file nae (Figure 2). The plot according to this data appears in the Results panel (Figure 1). Figure 2. The data file opening. 3. The report content Results are presented on the screen (Figure 1) and also stored in the defined report file. At start user should open a new report file (Figure 3) which, after pressing Save data button, will contain all iportant inforation: nae of the analyzed file, any coent (detector type, heating rate etc.), peak height, energy, the teperature position at the peak axiu and the integrals of each fitted peak. In the report a paraeter describing the quality of fitting, called Figure Of Merit (FOM) is also stored: where: y i - content of the channel i y(x i ) value of fitting function in the iddle of the channel i For plotting the fitted glow-curve and particular peaks, the file with.plo extension is saved autoatically after using Save data button (Figure 3). ( x ) yi y i i FOM [%] = y 100% i i Figure 3. The results storage. A2

13 The report and the plot files are the ASCII files, which could be opened by the Notepad or MS-xcel. 4. Fitting procedure 4.1. The starting peak paraeters There are two possibilities of setting the initial peak paraeters. The pattern file (pattern file is the special file, which contains the coefficients needed to calculate the glow-peak paraeters for the typical TL glow-curve. The inforation read fro the pattern file is the teperature distance between position of each peak and the global axiu, ratio between height of a peak and the easured TL signal in the teperature channel corresponding to the peak position. The starting values of energy are also read fro the pattern file) If any pattern file (nae.fac) is appropriate to your TL glow-curve: Open it by pressing button Open (Figure 4). After opening of a new glow-curve, press the button Reload to rescale the peak paraeters according to the new global axiu. If checkbox autoat is arked the reloading is ade autoatically after opening each new data file. Manual setting If none of predefined pattern files is appropriate to your TL glow-curve: Choose the nuber of peaks (fro 1 to 10). Sign the checkbox click&draw, which allows you to add the peaks in position within the plot area, where you clicked with the ouse (the default energy value 1.7eV). The initial peak paraeters values occur in The peaks paraeters table. To add the next peak select second row in The peaks paraeters table and click on the chart again etc. Figure 4. The starting paraeters A3

14 After setting the initial paraeters, button FIT ust be pressed to start the fitting procedure. Once a successful deconvolution is perfored a pattern file can be autoatically generated by pressing Save button. Then each next glow-curve of siilar shape can be processed using this pattern file. 4.2 Constraints Soeties the best nuerical solution corresponds to unacceptable paraeter values. In such cases user should exploit his previously gathered knowledge about peaks positions, proportions and energies to force the progra to keep fitted values within set liits. In GlowFit user ay set the nuerical liits or percentage range around the initial value. The conditions for the peak paraeters ay be set by pressing button Constraints. To unconstrain the paraeter the checkbox of the appropriate peak paraeter should be unarked. By pressing button % user ay change the nuerical liit into the percentage liit. To back to the nuerical liit button <= should be used. The percentage range on all the peaks paraeters ay be set by pressing button Set All %. The once set conditions ay be used again, in the next session with GlowFit, after using Save and Open buttons. Figure 5. The constraints panel. A4

15 4.3 The fixing of the peak paraeters Soeties it is necessary to fix soe paraeters, e.g. in case of very coplex curves or very low statistics. The fixed paraeters are not changed during the fitting procedure if user arks the appropriate checkbox as on Figure The background Figure 6. The fixing of the peaks paraeters. The background is set to zero by default. However, user ay include the background into the fitting procedure by unarking fixed background paraeters (Figure 7). The background paraeters could be constrained by pressing button <=. Before starting the fit, the subtraction of background is possible by arking subtract checkbox and pressing Apply button. This button without subtract option plots the background with a, b and c paraeters. 5. The fitting quality Figure 7. The background settings. A plot of residuals (relative differences between easured and fitted values in each channel) is presented on screen below the fitting curve (Figure 1). Progra introduces also the nuber of iterations needed to obtain the best peak paraeters. Nuber -2 indicates that the axiu nuber of iterations, 150, wasn t enough to obtain the iniu of χ 2 function. In this case user should continue the fitting procedure with the new starting paraeters, which are the result obtained fro the previous fit. A5

16 5.1 The adjustent The graphical interface enables also to anipulate the glow peaks before and after the fitting, as a anual fit adjustent. This is very helpful in case the iniization ethod failed. In order to adjust a peak paraeter user should ark the appropriate radiobutton (Figure 8) and ove the slide control (left(-) or right(+)) to change this paraeter value. The step of oveent is changeable as shown in Figure 8. Another possibility to adjust the peak paraeters is to type the values straightforward into The peaks paraeters table and confir by double-pressing nter key (Figure 4). Step of oveent 6. Closing Figure 8. The anual adjustent of the peak paraeters. The application can be closed by selecting Close fro the ain enu. Figure 9. The progra closing. A6

17 7. Overview Button FIT Constraints Clear Fits Open Meaning to fit the TL glow-curve (the new window with description DON indicates the end of the fitting procedure) to set the constraints on the fitting paraeters to clear all set peaks paraeters to open pattern file this pattern will be valid till opening the new one Pattern Reload to rescale the peak paraeters according to the curve global axiu (do it after file opening each new curve or ark autoat to do it autoatically) Save to save the pattern file Save data to save the iportant data to the report file and the plot coordinates to filenae.plo file Apply to show the background with a, b, c paraeters (when subtract is checked the background will be taken away fro the data source) double-click on to change the linear scale into the logarithic (to back into linear scale doubleclick the chart again) 8. rrors In case of any error, please restart the progra and be so kind to send e-ail to author describing the proble. Monika.Puchalska@ifj.edu.pl A7