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2 Journl of Archeologicl Science 38 (2) 59e62 Contents lists ville t ScienceDirect Journl of Archeologicl Science journl homepge: On the intrinsic ccurcy nd precision of luminescence dting techniques for fired cermics Vsilis Pgonis, *, Reuven Chen, George Kitis c Physics Deprtment, McDniel College, Westminster, MD 257, USA Rymond nd Beverly Sckler School of Physics nd Astronomy, Tel-Aviv University, Tel-Aviv 69978, Isrel c Nucler Physics Lortory, Aristotle University of Thessloniki, 5424 Thessloniki, Greece rticle info strct Article history: Received 4 Septemer 2 Received in revised form 2 Jnury 2 Accepted 23 Ferury 2 Keywords: Thermoluminescence (TL) Opticlly stimulted luminescence (OSL) Luminescence dting Equivlent dose estimtion Qurtz Retrospective dosimetry Authenticity testing Accident dosimetry Kinetic rte equtions Additive dose TL technique SAR technique SAR-TL Phototrnsfer technique Luminescence dting techniques hve een used extensively for rcheologicl nd geologicl smples. Such techniques re sed on thermlly or opticlly stimulted signls. This pper presents simultions of severl luminescence techniques for equivlent dose (ED) estimtion for cermic mterils contining qurtz. The simultions re crried out using recently pulished comprehensive kinetic model for qurtz, consisting of electron nd hole trps nd centers. The complete sequence of the experimentl protocols for severl thermoluminescence (TL) nd opticlly stimulted luminescence (OSL) techniques re simulted using the sme set of kinetic prmeters. The specific simulted protocols re: dditive dose TL protocol, predose technique (oth dditive nd multiple ctivtion versions), phototrnsfer protocol, single liquot regenertive opticlly stimulted luminescence (SAR-OSL) protocol, nd SAR thermoluminescence protocol (SAR-TL). One hundred rndom vrints of the nturl smples were generted y keeping the trnsition proilities etween energy levels fixed, while llowing simultneous rndom vritions of the concentrtions of the energy levels. The reltive intrinsic ccurcy nd precision of the protocols re simulted y clculting the equivlent dose (ED) within the model, for given nturl uril dose of the smple. The intrinsic ccurcy of these techniques is estimted y simulting nturl irrdition of the smples with known uril dose, followed y simultion of the luminescence method used to recover the estimted dose ED. The percent difference etween the uril dose nd the ED vlue represents the simulted ccurcy of the luminescence technique. The reltive intrinsic precision of these techniques is estimted y fitting Gussin proility functions to the ED vlues otined with the model vrints. It is found tht the vrious techniques cn reproduce nturl pleodoses in the rnge mgye Gy with typicl intrinsic ccurcy of þ to %. Techniques sed on single liquot protocols were found in generl to e more precise thn techniques requiring the use of multiple liquots. In ddition, techniques sed on interpoltion of experimentl dt were found to e consistently oth more precise nd ccurte thn those sed on extrpoltion of experimentl dt. Ó 2 Elsevier Ltd. All rights reserved.. Introduction Luminescence techniques re well-estlished experimentl methods for determining the totl cumultive dose from nturl rdition sources for rcheologicl nd geologicl dting, for ccident dosimetry nd for uthenticity testing (Aitken, 985; Wintle, 996; Biliff, 994; Biliff, 997; Roerts, 997; Biliff et l., 2; Wintle, 28; nd references therein). During the pst four decdes ccurte nd precise methods hve een developed for * Corresponding uthor. Tel.: þ ; fx: E-mil ddress: vpgonis@mcdniel.edu (V. Pgonis). estimting the equivlent dose (ED) in fired or unfired smples contining qurtz; such methods re sed either on thermoluminescence (TL) signls, or more recently on opticlly stimulted luminescence signls (OSL). In recent comprehensive review of luminescence techniques for ED estimtion, Wintle (28) summrized the historicl nd technologicl developments in luminescence dting techniques during the pst 5 yers, while in previous pper in this journl Wintle (996) discussed rcheologiclly-relevnt luminescence dting techniques in more generl context. Although TL nd OSL techniques re well-estlished experimentlly, further theoreticl nd modeling work is needed in order to otin etter understnding of the vrious fctors influencing /$ e see front mtter Ó 2 Elsevier Ltd. All rights reserved. doi:.6/j.js

3 592 V. Pgonis et l. / Journl of Archeologicl Science 38 (2) 59e62 oth the precision nd the ccurcy of the vrious experimentl protocols. There hve een severl notle pulished experimentl nd simultion ttempts to estimte the precision nd ccurcy of vrious TL/OSL dting techniques. Biliff nd Hollnd (2) nd Biliff (997) performed comprtive study of dting ricks using severl different TL/OSL techniques, nd y employing oth multiple liquot nd single liquot protocols. Biliff nd Petrov (999) studied the possiility of using the 2 C TL pek in qurtz for retrospective dosimetry. Their study used cermics nd concluded tht single liquot protocols chieved precisions etter thn 5%, nd tht these precisions were much improved over multiple liquot methods. Mejdhl nd Bøtter-Jensen (997) pplied the SARA OSL method to rcheologicl nd geologicl mterils. Their results for 5 smples compred well with those from TL techniques. These uthors lso compred SARA results for 4 sediments with TL nd IRSL estimtes. Liritzis et l. (997) investigted the use of green light stimultion in qurtz dting, using cermics removed from ore holes in res of rcheologicl interest in Greece. They discussed vrious tests nd single liquot correction procedures when using the dditive dose single liquot method of ED determintion. They concluded tht this technique cn e pplied successfully when pproprite corrections re mde for reusing qurtz liquots. Stokes et l. (2) pplied oth SAR nd SAAD luminescence techniques to sedimentry smples of different origins. Murry nd Olley (22) exmined the reliility of oth pulished nd unpulished SAR-OSL qurtz ges, for which independent ge controls re ville. These uthors concluded tht OSL ges re ccurte nd tht there ws no evidence for systemtic errors for ges extending t lest to 35 k. Thoms et l. (28) used oth SAR-OSL nd TL techniques to study heted mterils of rcheologicl importnce from vrious prts of Indi. In generl, they found resonly good greement etween the SAR-OSL nd TL ges nd the corresponding rcheologicl ges. There hve lso een severl notle pulished simultion ttempts to estimte the precision nd ccurcy of vrious TL/OSL techniques (McKeever et l., 997; Biley, 2; Biley, 24; Admiec et l., 24, 26; Kitis et l., 26; Pgonis et l., 23, 26, 28). Duller (27) discussed the nture of rndom nd systemtic sources of uncertinties in mesurements of the equivlent dose ED during single liquot regenertive dose mesurements. He exmined two different pproches to estimting the uncertinty in ED in the liner dose response region of the OSL signl, nd found tht oth these pproches gve results very close nd consistent with ech other. Severl uthors hve used different pproch, sed on kinetic models for qurtz. Pgonis nd Crty (24) used modified version of the model y Chen nd Leung (998, 999) to simulte the complete sequence of experimentl steps tken during the dditive dose version of the predose technique. This simultion study ws expnded y Pgonis et l. (28) using the comprehensive qurtz model y Biley (2). These uthors simulted oth the dditive dose nd the multiple ctivtion versions of the predose technique, s well s the very successful single liquot regenertive opticlly stimulted luminescence (SAR-OSL) protocol. Biley (24) used Monte- Crlo pproch in which stndrd qurtz model ws used s strting point nd 3 versions of the prmeters were generted y rndomly selecting concentrtion vlues within 8% of the originl vlues, using uniformly distriuted rndom numers. For ech of these vrints the full sequence of irrdition nd therml history of the smples were simulted, nd the SAR-OSL protocol ws simulted in order to otin n estimte of the precision of the SAR protocol. Thompson (27) performed Monte-Crlo simultions of SAR-OSL dosimetry mesurements to investigte the ehvior of the mesured equivlent dose (ED) s function of sored dose (pleodose). It ws found tht the men ED vlue overestimted the pleodose, prticulrly for lrger luminescence mesurement uncertinties nd for lrger pleodoses. This pper descries n effort to simulte the complete experimentl protocols for severl luminescence techniques for fired cermic mterils, nd to estimte their reltive intrinsic ccurcy nd precision. To the est of our knowledge, there re no pulished simultion studies of these different TL nd OSL techniques using the sme kinetic model. The intrinsic ccurcy nd precision re estimted y simulting rndom vritions of the concentrtions of electrons nd holes in nturl qurtz smples. The simultions re crried out using recently pulished comprehensive model for qurtz (Pgonis et l., 28), nd y generting one hundred rndom vrints of the concentrtions of electron nd hole trps in the model. The intrinsic ccurcy of these techniques is estimted y simulting nturl irrdition of the smples with known uril dose, followed y simultion of the luminescence method used to recover the estimted dose ED. The percent difference etween the uril dose nd the ED vlue represents the ccurcy of the luminescence technique. The reltive intrinsic precision of these techniques is estimted y fitting Gussin proility functions to the ED vlues otined with the model vrints. These uncertinties in the ED vlues re clerly of rndom rther thn systemtic nture, due to the rndom distriutions used for the concentrtions in the model. It is found tht the vrious luminescence techniques cn reproduce nturl pleodoses in the rnge mgye Gy with n intrinsic ccurcy nd precision of to %. The rnge of doses simulted in this pper ws chosen s representtive of typicl nturl doses for fired cermics of rcheologicl interest. Techniques sed on single liquot protocols nd on interpoltion methods were found to e more ccurte nd precise thn techniques requiring the use of multiple liquots nd extrpoltion techniques. It is importnt to emphsize tht this pper ttempts to simulte the intrinsic ccurcy nd precision of the vrious luminescence techniques; the ctul overll mesured experimentl precision of ech technique will of course contin severl dditionl sources of experimentl uncertinties, which re not the suject of this pper. Furthermore, this pper ddresses ED estimtion for fired qurtz smples only (such s cermics), while smples contining unfired qurtz or sedimentry qurtz will e the suject of seprte study. 2. Description of the model The simultions in this pper re crried out using the comprehensive qurtz model developed y Pgonis et l. (28). This model is sed on previous model y Biley (2) tht ws developed on the sis of empiricl dt. Fig. shows the energy level digrm in the model used in this pper. The computer code, the set of differentil equtions nd the choice of prmeters were presented recently y Pgonis et l. (28), nd will not e repeted here. For esy reference rief description of the vrious energy levels nd their relevnce in the vrious luminescence dting techniques is presented in this section. The vlues of the kinetic prmeters used in these simultions re shown in Tle. The originl model y Biley (2) consists of 5 electron trps nd 4 hole centers, nd hs een used successfully to simulte wide vriety of TL nd OSL phenomen in qurtz. This model ws expnded y Pgonis et l. (28) to include two dditionl levels nd, s descried elow. Level in the model represents shllow electron trpping level, which gives rise to TL pek t w C with heting rte of 5 K/s. The TL nd OSL signls from this trp ply mjor role in the predose nd phototrnsfer techniques simulted in Sections 3.2 nd 3.3of this pper. In ddition,

4 V. Pgonis et l. / Journl of Archeologicl Science 38 (2) 59e CONDUCTION BAND i= o C TL i=2 23 o C TL i=3 i=4 OSL F OSL M i=5 Deep i= i= j=6 R j=7 R 2 j=8 L-center j=9 K-center VALENCE BAND Fig.. Schemtic digrm of the comprehensive qurtz model of Pgonis et l. (28) used in this pper. The prmeters in the model re given in Tle. the TL signl from this C TL pek is used to correct for sensitivity chnges occurring during simultions of the dditive dose TL technique in Section 3.. Level 2 represents generic 23 CTL trp, typiclly found in mny qurtz smples. The TL signl from this trp hs een used successfully in severl comprehensive studies (see for exmple Biliff nd Hollnd (2); nd references therein). Levels 3 nd 4 re usully termed the fst nd medium OSL components nd they yield TL peks t w33 C s well s give rise to OSL signls. The OSL from levels 3 nd 4 forms the sis of the very precise nd ccurte SAR-OSL protocols (Wintle nd Murry, 26). The TL nd OSL signl from the fst OSL component (level 3) plys mjor role in the dditive TL, SAR-OSL nd SAR-TL techniques simulted in Sections 3., 3.4 nd 3.5 of this pper. Level 5 is deep electron center which is considered thermlly disconnected. Levels 6 nd 7 re thermlly unstle, non-rditive recomintion centers ( hole reservoirs ). These two levels ply crucil role in the predose sensitiztion mechnism which forms the sis of the predose dting technique. Level 8 is thermlly stle, rditive recomintion center often termed the luminescence center (L). Level 9 is thermlly stle, non-rditive recomintion center termed killer center (K). Levels nd re the two new levels dded to the originl Biley model y Pgonis et l. (28), nd were introduced in order to simulte the experimentlly oserved thermlly trnsferred OSL (TT-OSL) signls nd sic trnsferred OSL (BT-OSL) signls. Level in the model represents the source trp for the TT-OSL signl nd is slightly less thermlly stle trp with high dose sturtion. It is ssumed tht electrons re thermlly trnsferred from level into the fst component trp (level 3). This trp (level ) is ssumed to e emptied opticlly in nture y long sunlight exposure. Although the model does not contin explicitly ny of the slow OSL components which re known to e present in qurtz, level hs very similr therml nd opticl chrcteristics to such slow OSL components discussed in the literture (Biley, 24). Level is elieved to contriute most of the BT-OSL signl in qurtz; these trps re more thermlly stle thn either level 3 or level, nd correspond to TL pek t w36 C when the smple is heted with heting rte of 5 K/s. We will refer to this TL pek s the 37 C TL pek, nd the corresponding TL signl is simulted during simultions of the dditive TL nd SAR-TL methods descried in Sections 3. nd 3.5 in this pper. It is lso noted tht the originl Biley (2) model does not contin n energy level corresponding to this 37 C TL pek. In the rest of this pper it will e demonstrted tht y using the model in Fig. nd the set of prmeters in Tle, it is possile to simulte the complete experimentl protocols for severl TL/OSL dting techniques. Tle 2 shows the simultion steps for the dditive dose TL technique. Tles 3 nd 4 show in schemtic form the steps simulted in the dditive dose nd in the multiple ctivtion versions of the predose technique. The simultion steps in Tle The kinetic prmeters used in the comprehensive qurtz model of Pgonis et l. (28) shown in Fig.. N i re the concentrtions of electron trps or hole, s i re the frequency fctors, E i re the electron trp depths elow the conduction nd or hole trp depths ove the vlence nd, A i (i ¼.5, nd i ¼, ) re the conduction nd to electron trp trnsition proility coefficients, A j (j ¼ 6.9) re the vlence nd to hole trp trnsition proility coefficient nd B j (j ¼ 6.9) re the conduction nd to hole center trnsition proility coefficients. Other prmeters relted to the photoioniztion cross-sections of the opticlly sensitive trps re the photo-eviction constnt q i, the therml ssistnce energy Eth i. Level # Description N i (cm 3 ) E i (ev) s i (s ) A i B i (cm 3 s ) B i (cm 3 s ) q i (s ) E i th (ev) C TL pek.5e7.97 5e2 e C TL pek e7.55 5e4 e 8 3 Fst OSL (33 C TL pek) 4e e3 5e Fst OSL (33 C TL pek) 2.5e8.8.5e3 5e Deep trps 5e 2 e e 6 Hole reservoir 3e8.43 5e3 5e 7 5e 9 7 Hole reservoir e.75 5e4 e 9 5e 8 L-center 3e 5 e3 e e 9 K-center.2e2 5 e3 e 4 3e TT-OSL trp 275 C TL pek 5e e3 e C TL pek 4e9.6 5e2 6e 2

5 594 V. Pgonis et l. / Journl of Archeologicl Science 38 (2) 59e62 Tle 2 The simultion steps for the dditive TL technique. Multiple liquots re used.. Simultion of the qurtz nturl smple s discussed in the text. 2. Irrdite smple in lortory with dose D i t dose rte of Gy/s. 3. Het smple to 5 C e Record mximum of TL signl for the peks t 3, 33 nd 37 C. 4. Repet steps 2e3 for the sequence of doses,.5,,.5, 2 nd 2.5 Gy to reconstruct the doseeresponse curve TL vs. dose. Clculte the ccrued dose ED y liner or non-liner extrpoltion to the x-xis, s shown in Fig. 2 nd c. The following dditionl steps to corrected for sensitivity chnges on the qurt smple were used in some of the simultions: 5. Irrdite smple in lortory with test dose TD ¼ 5 Gy t dose rte of Gy/s. 6. Het smple to 5 C e Record mximum of TL signl for C pek. Use this signl S s mesure of the sensitivity of the smple. Tle 4 The simultion steps for the multiple ctivtion version of the predose technique. A single liquot is used for ll mesurements. The test dose is kept constnt t. Gy in ll steps of this tle. The signls mesured in ll steps re those of the CTL pek.. Simultion of the qurtz nturl smple s discussed in the text. 2. Give test dose (TD). Mesure S o. 3. Het to 5 C(first therml ctivtion). 4. Give test dose (TD). Mesure S N. 5. Give Clirtion dose. 6. Het to 5 C to empty the trps. 7. Give test dose (TD). Mesure quenched sensitivity S N 8. Het to 5 C (second therml ctivtion). 9. Give Test Dose (TD). Mesure S N þ.. Clculte ED using S o, S N, S N þ nd S N in equtions (2) or (3). the phototrnsfer protocol re given in Tle 5. Finlly Tles 6 nd 7 outline the steps during the SAR-OSL nd SAR-TL single liquot protocols. 2.. Simultion of the therml nd irrdition history of nturl qurtz smples All simultions presented in this pper contin the following initil steps e6 to represent the therml nd irrdition history of the qurtz smples. Steps e4 re dopted from the suggested simulted history of qurtz smples in Biley (2). In order to simulte the zero event (such s the firing of cermics in ntiquity) s relisticlly s possile, n dditionl step 5 ws dded, which simultes heting the smple t 7 C for h. In step 6 the nturl uril dose of Gy is simulted y using very low nturl dose rte of Gy/s t 2 C. A similr simultion step ws used in the simultion work y Pgonis et l. (28). Nturl qurtz smple. Set ll trp popultions to zero. 2 Geologicl dose- Gy t Gy/s t 2 C. 3 Geologicl time- het to 35 C. 4 Illuminte for s t 2 C, simulting repeted dylight exposures over long period of time. 5 Het smple to 7 C for h, to simulte the high temperture firing of cermics in ntiquity. 6 Buril dose- Gy t 2 C t very low nturl dose rte of Gy/s. We hve studied the effect of vrying the prmeters in steps e5 ove during this simultion of the nturl qurtz smple. It ws found tht step 5 (heting of the cermic smple for h t 7 C) is the criticl step in the simultion sequence, while Tle 3 The simultion steps for the dditive dose version of the predose technique. Multiple liquots re used in this technique. The test dose is kept constnt t. Gy in ll steps of this tle. The signls mesured in ll steps re those of the C TL pek.. Simultion of the qurtz nturl smple s discussed in the text. 2. Give test dose, usully. Gy. Mesure initil sensitivity S o using the C TL pek. 3. Het to 5 C. 4. Give test dose. Mesure thermlly ctivted sensitivity S N. 5. Use new Aliquot; give test dose. Mesure S o for normliztion purposes. 6. Give Clirtion dose (use w ED y using tril nd error). 7. Het to 5 C (therml ctivtion). 8. Give test dose. Mesure thermlly ctivted sensitivity S N þ. 9. Repet steps 2e8 using dded doses of 2, 3, etc. in step 6 to otin the sensitivities S N þ 2, S N þ 3, etc. Otin the grph of the sensitivity S vs. dded dose nd estimte the vlue of ED y liner extrpoltion, s shown in Fig. 4. chnges in steps e4 ove do not ffect the results of the simultions significntly. The reson for step 5 eing the most importnt step in the simultion of the nturl qurtz smple, is tht during this high temperture nneling the concentrtions of the trps nd centers in the model re zeroed within the simultion; this is commonly referred to s the zero event. We hve investigted the effect of chnging the prmeters in steps e5 on the estimted ED vlues, y vrying their numericl vlues over wide rnges. Specificlly the geologicl dose in step 2 ws incresed up to 6 Gy, the geologicl time temperture in step 3 ws chnged up to C nd the illumintion time nd temperture in step 4 were similrly chnged over severl orders of mgnitude. All of these drstic vritions of the prmeters resulted in chnge of the estimted ED of less thn.2%, which is well within the numericl ccurcy of the results of the simultions. We conclude tht the exct prmeters used in steps e4 ove re not criticl for the results of the simultion. The detils of the high temperture nneling (step 5) re of prmount importnce in the results of the simultions. We incresed the nneling temperture in step 5 up to C, with no pprecile chnges in the results of the simultion. However, it ws found tht smller nneling tempertures in the rnge 5e6 C gve n overestimte of the ED vlues during the simultions. This overestimtion is not surprising, since one would expect such lower nneling tempertures to result in n incomplete zeroing event, nd hence residul luminescence signl. Such residul signls would led to overestimtion of the ED vlues. The suject of incomplete firing of cermics in ntiquity is rther importnt reserch topic, however, it flls outside the scope of this pper. Tle 5 The simultion steps for the phototrnsfer technique. A single liquot is used for ll mesurements.. Simultion of the qurtz nturl smple s discussed in the text. 2. Het to 6 C to cler C trps. 3. Irrdite with et test dose of. Gy. 4. Het to 6 C to mesure the initil sensitivity S o e record height of C TL pek. 5. UV or opticl stimultion for min (phototrnsfer step). 6. Het to 6 C to mesure the new sensitivity S N e record height of C TL pek. 7. Prolonged UV irrdition to cler the deep donor trps. 8. Het to 6 C to cler C trps. 9. Irrdite with et test dose of. Gy.. Het to 6 C to mesure the sensitivity S o e record C TL pek.. Give clirtion et dose w ED of Gy. 2. Het to 6 C to cler C trps. 3. UV or opticl stimultion for min (phototrnsfer step). 4. Het to 6 C to mesure the sensitivity S e record C TL pek. 5. Clculte ED using eqution (4).

6 V. Pgonis et l. / Journl of Archeologicl Science 38 (2) 59e Tle 6 The simultion steps for the SAR-OSL technique. A single liquot is used for ll mesurements.. Simultion of the qurtz nturl smple s discussed in the text. 2. Irrdite smple with dose D i. 3. Prehet s t 26 C. 4. Blue OSL for s t 25 C e record OSL (. s) signl (L). 5. Test dose TD ¼. Gy. 6. Cuthet 2 s t 22 C. 7. Blue OSL for s t 25 C e record OSL (. s) signl (T). 8. Repet steps 2e7 for the sequence of doses,.5,,.5,,.5 Gy to reconstruct the dose. Response curve L/T vs. dose. Estimte ED using interpoltion s shown in Fig Simultion of rndom nturl vritions in qurtz smples Our simultion method is similr to the pulished work y Biley (24) who used Monte-Crlo pproch s follows; stndrd qurtz model ws used s strting point, nd 3 versions of the prmeters were creted to form sttisticl ensemle. The experimentlly oserved vriility in TL nd OSL chrcteristics of qurtz ws simulted y ssuming tht ll the fundmentl trnsition proilities in the model remin constnt, while trp concentrtions re llowed to vry rndomly from the vlues of stndrd qurtz model. The 3 vrints of the model were generted in Biley (24) y rndomly selecting concentrtion vlues within 8% of the vlues in the stndrd model, using uniformly distriuted rndom numers. As discussed in Biley (24, p. 34) some vrition of the trnsition proilities my lso e present in nturl smples, ut this vrition is expected to e reltively insignificnt. For ech of these 3 vrints Biley simulted the full sequence of irrdition nd therml history of the smples, nd the SAR-OSL protocol ws simulted in order to otin n estimte of the precision nd ccurcy of the SAR protocol. Even though our modeling pproch in this pper is similr to the pproch of Biley (24), our gols re rther different. In this pper we re mostly interested in comprtive study of the intrinsic ccurcy nd precision of the simulted protocols. In rel experiment, one dels of course with severl dditionl sources of experimentl uncertinties, s descried for exmple in some detil in the pper y Duller (27). An importnt question concerns the use of Gussin curves to fit the simulted distriution of ED vlues. One could envision the use of inomil, Poisson or nother similr mthemticl distriution insted. Our min reson for using Gussin curve is tht there is relevnt precedent in simultion work using kinetic models in qurtz; previous work y Biley (24) lso used Gussin fitting functions for their distriution of their ED vlues. We used the sme fitting function in this pper s in Biley (24), in order to hve reference comprison stndrd for the mgnitude of the Tle 7 The simultion steps for the SAR-TL technique. A single liquot is used for ll mesurements.. Simultion of the qurtz nturl smple s discussed in the text. 2. Irrdite smple with dose D i. 3. Prehet s t 26 C. 4. Mesure TL y heting to 5 C e record TL signl (L). 5. Test dose TD ¼. Gy. 6. Cuthet 2 s t 22 C. 7. Mesure test dose TL y heting to 5 C e record TL signl (T). Repet steps 2e7 for the sequence of doses,.5,,.5,,.5 Gy to reconstruct the doseeresponse curve L/T vs. dose. Estimte ED using interpoltion s shown in Fig. 9. ccurcy nd precision of the simulted luminescence dting techniques. In ddition, Gussin curves were found to fit the dt resonly well in most cses, nd the R 2 vlue of the fits given in the relevnt figures were found to e etween.8 nd.9. In principle, however, there is no solute compelling reson for using Gussin fitting curves. Sensitivity corrected TL (.u.) TL (.u.) TL mx (23 o C pek),.u. c ADDITIVE DOSE TL TECHNIQUE D= Gy D=.5 Gy D= Gy D=.5 Gy D=2 Gy Temperture, o C ED 23 o C TL pek Added et dose, Gy Sensitivity corrected TL Uncorrected TL ED ADDTIVE TLTECHNIQUE 37 o C TL PEAK Buril dose=.5 Gy Added TL dose, Gy Fig. 2. () Simulted glow curves during the dditive TL technique. () The dose response of the 23 C TL pek is liner in the dose rnge simulted in this pper. (c) The doseeresponse of the 37 C TL pek is superliner in the sme dose rnge (open tringles). After correcting for sensitivity chnges using the height of the CTL pek, the doseeresponse of the corrected TL signl ecomes liner (closed circles). 3 2 Uncorrected TL (.u.)

7 596 V. Pgonis et l. / Journl of Archeologicl Science 38 (2) 59e62 Distriution of N= vrints c ADDITIVE TL TECHNIQUE 23 o C TL PEAK BURIAL DOSE=5 Gy R 2 =.9 Simultion Gussin Fit o C TL PEAK uril vs ED : Line... Buril Dose, Gy.. 33 o C nd 37 o C TL PEAKS.. Buril Dose, Gy 37 o C pek : Line 33 o C TL pek Fig. 3. () Simulted results for the intrinsic precision of the dditive dose TL technique t uril dose of 5 Gy, using rndom vrints of the nturl smples. The histogrm shown is for the 23 C TL peks, nd is fitted to Gussin distriutions s discussed in the text. The simulted steps re given in Tle 2. () The simulted equivlent doses (ED) otined using the dditive dose TL technique for the 23 CTL pek, nd for rnge of uril doses. The error rs represent the stndrd devition s otined from Gussin fits similr to the one shown in (). (c) Sme s in (), for the 33 C nd 37 C TL peks. TL (.u.) S N (.u.) ADDITIVE DOSE PREDOSE TECHNIQUE S N+β 5 5 Temperture, o C ED=.7 Gy 3. Simultions of TL/OSL techniques for ED estimtion 3.. Simultion of the dditive dose technique for TL Historiclly the oldest method of TL is the dditive dose technique, in which different liquots of the qurtz smple re given sequence of dded et doses, nd the TL glow curves re mesured for ech liquot. Three TL peks t 23 C, 33 C nd 37 C were used in the simultions for estimting the ED vlues of fired cermic smples. Typicl simulted steps in this method re shown in Tle 2. The min ssumption ehind this technique is the existence of liner reltionship etween the TL signls nd the irrdition dose. A typicl exmple of simulted glow curves t different et doses is shown in Fig. 2, in which the mximum intensity of ll three TL peks cn e seen to increse with the dded et dose. Fig. 2 shows the dependence of the TL signl from the 23 C on the dded et dose; this dependence is liner within the rnge of the simultions, nmely mgye Gy. The equivlent dose ED of the smple cn e found y liner extrpoltion to the dose xis, s shown in Fig. 2. A different non-liner simulted dose response ws otined for the deeper TL trps t 33 C nd 37 C, s shown in Fig. 2c for S N S o S N S o S N+β Added et dose, Gy S N+2β S N+3β Fig. 4. () Simulted glow curves for the dditive dose predose technique with the test dose TD ¼. Gy, pleodose PD ¼ Gy, clirtion et dose of Gy nd n ctivtion temperture of 5 C. The simulted steps re given in Tle 3. () The simulted vrition of the sensitivity S of the C TL pek with the dded et dose. Liner extrpoltion gives the equivlent dose (ED) of the smple s shown.

8 V. Pgonis et l. / Journl of Archeologicl Science 38 (2) 59e the cse of the TL pek t 37 C. The response of this pek ws found to vry lmost qudrticlly with the irrdition dose, phenomenon tht is well known from vriety of TL studies (Wintle, 28). A similr simulted non-liner ehvior ws found for the 33 C TL pek (this dt is not shown here). This qudrtic dose dependence hs een previously ttriuted to competition effects etween different TL trps in qurtz (Chen nd McKeever, 997). The non-liner dose dependence of the TL signl is one of the mjor prcticl prolems ssocited with TL dting. In some cses the non-linerity cn e removed y mking sensitivity correction to the TL signl. We hve simulted this sensitivity correction y dding few steps to the simultion steps, s shown in Tle 2. These steps consist of irrditing the smple with test dose of 5 Gy, followed y mesurement of the TL signl from the CTL pek. The mximum height of this C TL signl is used s mesure of the sensitivity S of the smple; the corrected TL signl is otined y dividing the TL signl from the 33 Cor37 CTL peks y this sensitivity S. The result of pplying is shown in Fig. 2c, where it cn e seen tht the sensitivity-corrected TL signl Distriution of ED vlues Simulted PREDOSE TECHNIQUE ADDITIVE DOSE VERSION BURIAL DOSE.5 Gy R 2 =.96.4 Simulted : Line... Buril Dose, Gy Fig. 5. () Simulted results for the intrinsic ccurcy nd precision of the dditive dose predose technique t uril dose of.5 Gy, using N ¼ rndom vrints of the nturl smples. The simulted steps re given in Tle 3. The solid line represents est-fit Gussin curve to the simulted dt. () The simulted equivlent doses (ED) otined using the dditive dose predose technique nd for rnge of uril doses. The error rs represent the stndrd devition s otined from Gussin fits similr to the one shown in (). ecomes liner with the dose. The ED vlue cn now e found y extrpolting the fitted liner curve to the dose xis. The results of simulting vrints of the dditive dose TL technique using the 23 C TL pek re shown in Fig. 3. The distriution of the ED vlues ws fitted with Gussin distriution function shown s dshed line. The eqution for the fitted Gussin distriution N(D) is of the form: TL (.u.) Distriution of ED vlues c Simulted MULTIPLE ACTIVATION PREDOSE TECHNIQUE S o S N S N-quenched S N+β Temperture, o C S N So Buril Dose, Gy S N+β BURIAL DOSE 5 Gy R 2 =.939 Simultion : Line S N-quenched.. Fig. 6. () Simulted glow curves during the multiple ctivtion predose technique. The simulted steps re given in Tle 4. () Simulted results for the intrinsic precision of the multiple ctivtion predose technique t uril dose of Gy, using N ¼ rndom vrints of the nturl smples. (c) The simulted equivlent doses (ED) otined using the multiple ctivtion predose technique nd for rnge of uril doses. 8

9 598 V. Pgonis et l. / Journl of Archeologicl Science 38 (2) 59e62! NðDÞ ¼Aexp ðx x oþ 2 2s 2 ; () where the constnt A represents the numer of vrints t the pek of the distriution which is centered t x o nd hs stndrd TL (.u.) Distriution of ED vlues c PHOTOTRANSFER TECHNIQUE Temperture, o C S N S β S o BURIAL DOSE. Gy R 2 = Buril Dose, Gy Simultion #2 : Line Simultion # Fig. 7. () Simulted glow curves during the phototrnsfer technique. The simulted steps for this technique re given in Tle 5. () Simulted results for intrinsic precision of the phototrnsfer technique t uril dose of. Gy, using N ¼ rndom vrints. (c) The simulted equivlent doses (ED) otined using the phototrnsfer technique nd for rnge of uril doses. devition s. The stndrd devition s otined in this mnner represents mesure of the intrinsic precision of the technique. In the exmple of Fig. 3 the ccumulted nturl dose ws 5 Gy nd the fitted Gussin curve yields n verge ED ¼ 3.9 Gy, with stndrd devition s of.2 Gy. We conclude tht this dting protocol underestimtes the uril dose y w2%, nd tht the intrinsic precision of this technique is s/ed ¼.2/3.9 Gy ¼.5%. This procedure of simulting vrints nd finding the stndrd devition s from the est-fitted Gussin distriution ws repeted for severl uril doses etween mgy nd Gy, with the results shown in Fig. 3. The : dshed line in this figure indictes the idel cse in which % of the uril dose is recovered using the simulted technique. The mount of devition of the dt points in Fig. 3 from the : line is mesure of the intrinsic ccurcy of the technique. The smll error rs in this figure re the stndrd devition s otined from the Gussin fits, nd represent the intrinsic precision of this technique. The results of Fig. 3 show tht the dditive TL method using the 23 C pek cn reproduce the ED vlues ccurtely in the rnge mgye2 Gy. The intrinsic precision of this technique is seen to e very good, in the rnge 2e5%, s indicted y the smll error rs in Fig. 3. Fig. 3c shows the simultion results otined for the dditive TL method using the 33 C nd 37 C TL peks. It cn e seen tht using these two higher temperture TL peks within this model leds to n overestimtion of smll doses etween mgy nd. Gy. However, oth methods seem to e oth ccurte nd precise in the higher dose rnge.2 mgye Gy. We ttriute the systemtic ED overestimtion t lower doses to the following three fctors. Firstly, the TL signl t 33 C is composite one, contining contriutions from oth the fst nd the medium OSL/TL components (levels 3 nd 4 in the model). Secondly, there is n dditionl TL pek t w3 C in the model, shown s smller hump in Fig. 2. This pek overlps with the TL pek t 33 C, nd represents level in the model. Thirdly, using the signl from the C TL pek my not completely correct for sensitivity/superlinerity chnges occurring in the smple. An importnt question out the histogrms presented in this pper concerns the presence of severl simulted dt points which fll well outside the histogrm, s seen for exmple in Fig. 3. We hve repeted the simultions in Fig. 3 using lrger numer N ¼ 3 of smple vrints, in order to check whether the presence of these points is due to our use of N ¼ vrints. The results of simulting N ¼ 3 vrints were found to e identicl to those of Fig. 3. This indictes tht these outlying points re not n rtifct of the simultion process, ut rther they represent the inherent limittions in the ccurcy nd precision of the vrious dting techniques Simultions of the predose technique Two min vritions of the predose technique exist, known s the multiple therml ctivtion technique nd the dditive dose technique. In typicl experimentl ppliction of the predose procedure, test dose TD ¼. Gy is commonly used, s well s clirtion dose with vlue close to the estimted pleodose of the smple. The exct vlue of the clirtion dose to e used in the experiment is usully found y tril nd error. The response to the test dose TD is mesured y heting the smple to 5 C, just ove the C TL pek. The effect of vrious experimentl prmeters on the ccurcy of the predose technique ws simulted in detil in Pgonis nd Crty (24) nd Pgonis et l. (28). Our gol in this pper is to explore the reltive ccurcy nd precision of the two predose techniques, rther thn detiled study of the effect of the vrious experimentl prmeters.

10 V. Pgonis et l. / Journl of Archeologicl Science 38 (2) 59e L/T (.u.) ED=.7 Gy Recycling rtio=. Zero=.3 OSL SAR PROTOCOL L/T (.u.) Nturl TL signl SAR-TL pek t 23 o C.4 ED=.5 Gy c d Simulted DISTRIBUTION OF RECYCLING RATIOS DISTRIBUTION OF ZERO L/T VALUES Regenertive Dose, Gy RECYCLING RATIO RECYCLING DISTRIBUTION R 2 = ZERO VALUE (L/T) ZERO DISTRIBUTION R 2 = Buril dose, Gy Simultion TD=5 Gy : Line Simultion TD=. Gy Fig. 8. () Simulted L/T signls during the SAR-OSL technique. The simulted steps re given in Tle 6. (), (c) Typicl distriutions of the simulted recycling rtios nd zero intercepts for the SAR-OSL technique. (d) The simulted equivlent doses (ED) otined using the SAR-OSL technique nd for wide rnge of uril doses. c Regenertive Dose, Gy o C TL PEAK : Line Simultion TD= Gy Simultion TD=. Gy.. Buril Dose, Gy 23 o C nd 37 o C TL PEAKS : Line 23 o C TL pek 37 o C TL pek.. Buril Dose, Gy Fig. 9. () Simulted L/T signls during the SAR-TL technique, using the 23 C TL pek in qurtz. The simulted steps re given in Tle 7. () The simulted equivlent doses (ED) otined using the SAR-TL technique for the 33 C TL pek, nd for rnge of uril doses. (c) Similr results for the TL pek t 23 C nd 37 C The dditive dose vrition of the predose technique The dditive dose vrition is multiple liquot technique. The sic sequence of mesurements during the dditive dose technique is shown in Tle 3 (Aitken, 985, p. 53e68). Using first portion of the mteril the TL sensitivities S o nd S N to smll test dose (TD) re mesured s shown in steps 2e4ofTle 3. Using the remining portions of the mteril, the TL sensitivities of the irrdited smples S N þ, S N þ 2, S N þ 3 etc. re mesured s shown in

11 6 V. Pgonis et l. / Journl of Archeologicl Science 38 (2) 59e62 Tle 8 Summry of ll ED vlues nd their uncertinties otined from the simultions in this pper. All vlues re in Gy. Buril dose, Gy Additive TL 23 C pek (s) Additive TL 33 C pek (s) Additive TL 37 C pek (s) Additive predose, C pek (s) Multiple liquot predose, C pek steps 5e9 of Tle 3. Exmples of simulted TL glow curves during this procedure re shown in Fig. 4. The dditive dose vrition of the predose technique voids multiple therml ctivtion of the mteril nd lso is not ffected y the phenomenon of rdition quenching which ws simulted nd discussed in some detil y Pgonis et l. (28). The ovious disdvntge of the dditive dose technique is the need for interclirtion etween the different liquots, nd the necessity for smples exhiiting low S o -vlues (Aitken, 985, p. 63; Pgonis et l., 28). The dose evlution in the dditive dose technique is sed on the ssumption of liner vrition of the sensitivity of the smple with the dose. By extrpolting the grph of the sensitivity S to the dose xis s shown in Fig. 4, one otins n estimte of the equivlent dose (ED) of the smple. The results of simulting vrints of the dditive dose version of predose technique re shown in Fig. 5, nd these were fitted with Gussin distriution s descried previously. This procedure ws repeted for severl uril doses etween mgy nd Gy, with the results shown in Fig. 5, together with the : line. The error rs in this figure represent once more the stndrd devition s otined from the Gussin fits, nd re seen to e much lrger thn those in Fig. 3. The results of Fig. 5 indicte tht the dditive dose vrition of the predose technique systemticlly underestimtes the ED vlues in the complete rnge mgye Gy, nd tht the intrinsic precision of this technique ecomes progressively worse t smller doses The multiple ctivtion vrition of the predose technique The sic sequence of mesurements during the multiple ctivtion technique is shown in Tle 4 nd is sed on the use of single liquot of the smple (Aitken, 985, p. 53e68). The TL sensitivities S o nd S N of the mteril to smll test dose (TD) re mesured s shown in steps 2e4 of Tle 4. The thermlly ctivted sensitivities S N þ nd S N re mesured using the sme liquot, s shown in the rest of Tle 4. Experiments using the multiple ctivtion vrition exhiit the phenomenon of rdition quenching consisting of the sensitivity S N in step 7 eing usully lower thn the sensitivity S N in step 4, due to the et irrdition in step 5 of Tle 4. In ddition, in this technique the liquot undergoes multiple therml ctivtion, which cn cuse chnges to its predose chrcteristics. A sequence of typicl simulted TL glow curves otined using the multiple ctivtion predose technique is shown in Fig. 6. The equtions used in the multiple ctivtion technique re lso sed on the ssumption of liner response of the sensitivity of the smple. The equivlent dose (ED) cn e clculted using the eqution: ED ¼ S N S o S Nþ S N,: (2) When the effect of rdition quenching is tken into ccount, eqution (2) is modified y using the quenched sensitivity S N insted of the sensitivity S N, to otin corrected estimte of the equivlent dose using the eqution (Aitken, 985): ED ¼ S N S o S Nþ S N,: (3) The pplicility of this corrected eqution (3) is discussed in some detil in Pgonis et l. (28). The results of simulting vrints of the multiple ctivtion predose technique re shown in Fig. 6 nd c. The results of Fig. 6c indicte tht the multiple ctivtion version of the predose technique reproduces oth ccurtely nd precisely the ED vlues in the complete rnge mgye Gy. By compring Fig. 6c nd Fig. 5c, it is cler tht the multiple ctivtion version is preferle to the dditive dose version in the cse of the predose technique. This technique ecomes much less ccurte t doses ED > Gy Simultion of the phototrnsfer technique This technique hs wned in populrity due to the development of the more precise/ccurte SAR protocols. However, we include it here to demonstrte tht the mechnism in the phototrnsfer technique is consistent with the model used in this pper. In qurtz phototrnsfer, opticl stimultion trnsfers trpped chrge from opticlly sensitive deep donor levels like the 33 CTL trp, into shllower cceptor levels like the C TL trp (McKeever, 985). The min ssumption ehind this technique is tht frction of the initilly trpped chrge in the deep donor levels is trnsferred into the C TL trp, nd therefore, the TL signl from this trp will likely e proportionl to the rdition dose received y the smple. The equivlent dose ED of the smple cn e found y using clirtion dose of out the sme mgnitude s the nturl dose. The simulted steps in this method re shown in Tle 5. In steps e4 the initil sensitivity S o of the liquot to the test dose of. Gy is mesured, followed y mesurement of the ctivted sensitivity S N in steps 5e6. Step 5 is the min phototrnsfer event, in which UV or opticl stimultion trnsfers chrge from deep opticlly sensitive trps t 33 C (the fst OSL trp of qurtz), into the C TL trp. This chrge trnsfer is ssumed to tke plce through the conduction nd. The deep trps re clered y prolonged UV irrdition in step 7, nd the sensitivity to the test dose is mesured gin in steps 8e. Steps e4 re the clirtion sequence for the phototrnsfer process, where the sensitivity of the liquot to known clirtion et dose is mesured (S ). By ssuming tht the sensitivity signl from the C TL trp is proportionl to the phototrnsferred chrge, the estimted dose ED of the liquot is given y the eqution (McKeever, 985, p. 268):

12 V. Pgonis et l. / Journl of Archeologicl Science 38 (2) 59e62 6 (s) Phototrnsfer, C pek (s) SAR-OSL, 33 C pek (s) SAR-TL, 23 C pek (s) SAR-TL, 33 C pek (s) SAR-TL, 37 C pek (s) ED ¼ S N S o =S S o : (4) Typicl results otined y simulting the steps in Tle 5 re shown s Simultion # in Fig. 7, nd the results of simulting rndom smple vrints re shown in Fig. 7. In the exmple of Fig. 7 the two sensitivities S o nd S o re the sme. In second set of simultions we vried the clirtion et dose used in step of Tle 5; insted of using fixed clirtion et dose of Gy, we used clirtion dose equl to. times the nturl dose of the smple. The results of using this optimized clirtion dose re shown s Simultion #2 in Fig. 7c. The results of Fig. 7c indicte tht the phototrnsfer technique cn e used for the whole rnge of doses mgye Gy, when the prmeters re optimized Simultion of the single liquot regenertive dose OSL technique (SAR-OSL) Fig. 8 shows the results of simulting the populr nd very successful single liquot regenertive protocol (SAR) developed during the pst yers (Wintle nd Murry, 26). The SAR technique hs een developed for oth OSL nd TL signls, with the corresponding techniques referred to s SAR-OSL nd SAR-TL. The most importnt prt of the SAR technique is the correction of the mesured OSL/TL signls y mesuring the sensitivity of the smple due to smll test dose. The OSL/TL signl due to n irrdition dose is usully denoted y L, while the corresponding test dose signl is denoted y T. The rtio L/T represents the sensitivity-corrected OSL/TL signl. During the SAR protocol the mesured nturl L/T signl is compred with dditionl L/T signls which re regenerted y irrditing the smples in the lortory. A typicl sequence of steps undertken during the SAR-OSL protocol is shown in Tle 6. In Step 2 the smple is given lortory dose D i, known s the regenertive dose. In step 3 the smple is heted to prehet temperture, typiclly for s t 26 C, in order to empty the shllow thermlly unstle TL trps. In step 4 the smple is opticlly stimulted for s using lue light (typiclly 47 nm), nd the resulting OSL signl (L) is recorded. The opticl stimultion t step 4 is crried out t n elevted temperture of 25 C, in order to void complictions due to the opticlly sensitive TL trp t C. In step 5 the smple is given smll test dose of. Gy, nd in step 6 it is heted for s t lower temperture of 22 C (known s the cuthet), to gin remove electrons from shllow TL trps. Finlly in step 7, the smple is gin opticlly stimulted for s, to mesure the OSL signl (T), which is used to crry out the sensitivity correction for the OSL signl mesured in step 4. Steps 2e7inTle 6 re repeted for sequence of doses D i, with the first dose D i tken to e zero in order to mesure the OSL signl in the nturl smple. Fig. 8 shows the results of simulting the SAR-OSL protocol. The five regenertive doses used were.8,,.2, nd.8, nd two vlues of the test dose were used, nmely. Gy nd 5 Gy. The prehet temperture used in the SAR protocol simultion ws s t 26 C for the regenertive dose mesurements, nd the cuthet used for the test dose mesurements ws 2 s t 22 C. The sensitivity corrected signls L/T were used to reconstruct the doseeresponse curve s shown in Fig. 8, nd interpoltion is used for estimting the ccrued dose y the smple. The simultion results of the SAR-OSL protocol showed good recycling rtios close to unity, nd zero intercepts close to zero. Fig. 8 shows typicl distriution of recycling rtios nd zero intercepts for the vrints in the model. Fig. 8c shows the results of two sets of simultions, which were crried out using test doses of. Gy nd 5 Gy. It is concluded tht the results of the SAR- OSL protocol cn e optimized y choosing pproprite vlues of the test dose. The results of Fig. 8c indicte tht the SAR-OSL technique is oth ccurte nd precise in the rnge of doses. Gye Gy. The intrinsic precision of this technique gets progressively worse t lower doses in this rnge. It is noted tht liner interpoltion is used in ll our SAR-OSL nd SAR-TL simultions. In principle, one would expect tht non-liner interpoltion would give even etter ccurcy in the simultions Simultion of the TL single liquot regenertive dose technique (SAR-TL) Fig. 9 nd shows the results of simulting the SAR-TL protocol developed in nlogy to the SAR-OSL protocol during the pst yers (Wintle nd Murry, 26). The steps in this simultion re shown in Tle 7, nd re crried out using the TL signl from the 23, 33 nd 37 C TL peks in the model. The five regenertive doses used were.8,,.2, nd.8, nd two vlues of the test dose were used, nmely. Gy nd Gy. The prehet temperture used in the SAR-TL protocol simultion ws s t 26 C for the regenertive dose mesurements, nd the cuthet used for the test dose mesurements ws 2 s t 22 C. The results of the SAR-TL protocol showed good recycling rtio close to unity, nd intercepts close to zero. The sensitivity corrected signls L/T were used to reconstruct the doseeresponse curve s shown in Fig. 9, nd interpoltion ws used for estimting the ccrued dose y the smple. The results of Fig. 9 indicte tht the SAR-TL technique is lso sensitive to the test dose used, with more ccurte results otined using test dose of Gy. Fig. 9c shows the corresponding results using the TL peks t 23 nd 37 C. The intrinsic precision of this technique cn e seen to e good throughout the rnge of doses exmined. 4. Conclusions The comprehensive qurtz model of Pgonis et l. (28) ws used successfully in this pper to simulte the complete sequence of experimentl steps tken during severl TL/OSL experimentl