Non-Destructive, Specular Laser Reflectometry and X-Ray Fluorescence Analysis Applied to Coins of the Gallic Roman Empire

Academic Edi o s: Paola Fe mo and Giuseppe Poli i Recei ed: 7 Ap il 2025 Re ised: 18 May 2025 Accep ed: 26 May 2025 Published: 1 June 2025 Ci a ion: Toschke, Y.; Wolke-Hanenkamp, S.; Wol , E.; Lich enbe ge , A.; Ma in, K.; Nieswand , H.-H.; Imlau, M. Non-Des uc i e, Specula Lase Re lec ome y and X-Ray Fluo escence Analysis Applied o Coins o he Gallic Roman Empi e. He i age 2025,8, 202. h ps:// doi.o g/10.3390/he i age8060202 Copy igh : © 2025 by he au ho s. Licensee MDPI, Basel, Swi ze land. This a icle is an open access a icle dis ibu ed unde he e ms and condi ions o he C ea i e Commons A ibu ion (CC BY) license (h ps://c ea i ecommons.o g/ licenses/by/4.0/). A icle Non-Des uc i e, Specula Lase Re lec ome y and X-Ray Fluo escence Analysis Applied o Coins o he Gallic Roman Empi e Yannic Toschke 1, S e en Wolke-Hanenkamp 1, Eugen Wol 1, Achim Lich enbe ge 2, Ka ha ina Ma in 2, H.-Helge Nieswand 2and Mi co Imlau 1,* 1 Ins i u e o Physics, Depa men o Ma hema ics/In o ma ics/Physics, Osnab ück Uni e si y, Ba ba as aße 7, D-49076 Osnab ück, Ge many; [email p o ec ed] (Y.T.); s e en.wolke-hanenkamp@uni-osnab ueck.de (S.W.-H.); [email p o ec ed] (E.W.) 2Ins i u e o Classical A chaeology and Ch is ian A chaeology, Müns e Uni e si y, Dompla z 20-22, D-48143 Müns e , Ge many; lich enb@uni-muens e .de (A.L.); ka ha ina.ma in@uni-muens e .de (K.M.); hnieswan@uni-muens e .de (H.-H.N.) *Co espondence: mi [email p o ec ed]; Tel.: +49-541-969-2654 Abs ac : Non-des uc i e, specula lase e lec ome y, an indus ially used and easily accessible me hod, is adap ed in numisma ic esea ch o he inspec ion o coins o he Gallic Roman Empi e wi h he objec i e o he alloca ion o min s and/o he iden i ica ion o di e en min ing echniques. Fo his pu pose, he lase - e lec ome ic inge p in s o h ee se ies o coins each consis ing o i e an oniniani (o adia es) o he Gallic Roman Empi e o igina ing om wo min s —T ie and Cologne— a e sys ema ically de e mined, analyzed and co ela ed wi h he co esponding XRF elemen analysis. The esul s show ha he use o an inexpensi e ed-emi ing lase sys em (wa eleng h 632.8 nm) wi h a beam diame e d< 0.5 mm and a sample moun ha can be adap ed o he indi idual shape and hickness o he coins leads o signal in ensi ies ha can be sys ema ically eco ded o e a la ge angula ange wi h a e y good signal- o-noise a io (SNR > 10). While he signals canno be used o assign indi idual coins o min s, we discuss he possibili y o a s a is ical analysis. Al hough each coin se consis s o only i e samples and hus equi es u he s udy, he esul s he e sugges ha he se s can be dis inguished om each o he , ha he e is a co ela ion o he sil e concen a ion and ha i is possible o es ima e he e ac i e index n. Keywo ds: Roman coins; su ace inspec ion; non-des uc i e lase me hod; X- ay luo escence PACS: 78.40.-q; 78.68.+m; 78.70.En 1. In oduc ion X- ay pho oelec on spec oscopy (XPS), X- ay luo escence spec oscopy (XRF), Lase - abla ion- and Mul icollec o -induc i ely coupled plasma-mass spec ome y (LA-ICP-MS, LA-MC-ICP-MS) a e well-es ablished me hods in numisma ics o quali y samples ega d- ing hei chemical o a omic composi ion [ 1 – 3 ]. In pa icula , ex ensi e wo k has been ca ied ou on p o enance de e mina ion o min o o igin using elemen al and iso opic composi ion o sil e ia XRF [ 4 – 6 ]. The e a e also co esponding XRF handheld ins u- men s o use a he exca a ion si e a e he coins ha e been cleaned, o in local museums ab oad [ 7 ]. Due o hei ela i ely high p ice poin o up o a ew Eu 10.000, howe e , hey a e only a ailable o a limi ed ex en . Fo his eason, he coope a ion behind his p ojec He i age 2025,8, 202 h ps://doi.o g/10.3390/he i age8060202 He i age 2025,8, 202 2 o 20 pu sued a i s a emp in he adap a ion o a non-des uc i e, cos -e ec i e lase -based me hod o he use in numisma ics ha was o iginally in oduced o he inspec ion o me al su aces in indus y by Rischmuelle e al. [ 8 ]. The echnical complexi y o he me hod is compa a i ely low, so ha he ans o ma ion owa ds a handheld ool, especially o use in a museum o ield use seems e y likely. Speci ically, he o iginal me hod enables he de e mina ion and di e en ia ion o (ul a-) hin dielec ic laye s on aluminum pa s, so-called con e sion laye s, and plays an impo an ole in he quali y con ol o co osion p o ec ion o aluminum componen s. Fo his pu pose, he lase -based me hod makes use o he physical phenomenon o lase ligh in e e ence and is capable o di e en ia ing laye hicknesses well below a hickness o 100 nm, and e en below 10 nm on su aces wi h oughness in he ange o ≈ 300 nm. I was demons a ed ha he me hod is sensi i e o he o ali y o he su ace mo phology and he de ec ed signal he e o e con ains in o ma ion abou a ious su ace p ope ies such as oughness, abso p ion and sca e ing cen e s, de ec s and he index o e ac ion. Agains his backg ound, he idea a ose o adop he p inciples o his me hod o inspec he su ace laye sys em o ancien coins wi h he goal o de eloping a po able, low-cos measu ing ins umen o he alloca ion o min s and/o he iden i ica ion o di e en min ing echniques on si e a exca a ion si es. As an example, he subjec o in es iga ion is h ee se ies o Roman coins, each consis ing o i e an oniniani/ adia es o he Gallic Roman Empi e (= i een coins in o al). The Gallic Roman Empi e exis ed om 260 o 274 AD as a sepa a e s a e 1 and was uled by empe o s om he Roman mili a y and had i s capi als in Cologne and T ie . The empe o s o he Gallic Roman Empi e min ed hei own coins ollowing he ypical Roman min ing adi ion. One o he empe o s was Vic o inus, who uled om 269 o 271 as Impe a o Caesa M. Pia onius Vic o inus In ic us Augus us 2 . He was a success ul gene al and became empe o in 269. His uling was accep ed in he p o inces o Gallia, Ge mania and B i annia. In 271, he was killed in a p i a e con lic close o Cologne and subsequen ly was consec a ed. Vic o inus min ed gold coins (mainly au ei) and sil e denomina ions ( e y ew dena ii and lo s o an oniniani/ adia es3). F om a ypological poin o iew, he i een coins unde s udy in his con ibu ion can unambiguously be classi ied and a ibu ed o wo di e en min s (called Min I and Min II in wha ollows), assigned wi h a high deg ee o p obabili y o Cologne and T ie . De ails o he geog aphical loca ion, he posi ions o Min I and Min II and o he hoa ds a e shown in he maps in Figu e 1. He i age 2025,8, 202 3 o 20 Figu e 1. (a) Geog aphical loca ion o Cologne and T ie in Wes e n Eu ope. (b) Ci y map o T ie c. 450–800 AD . : Posi ion o Min I, a chaeologically con i med. : Posi ion o he wo hoa ds FMRD IV, 3/4, 3068.3 and 3068.8 (Pe zhold [ 14 ], p. 37). (c) Map 3: Geog aphical loca ion o Cologne and B auweile . : Posi ion o Min II, no a chaeologically con i med. : Posi ion o he B auweile hoa d. Al hough he an oninianus was claimed o be a sil e coin, i , a his poin in ime, in ac was billon con aining a e y low deg ee o sil e and consis ing mainly o b onze. The e o e, due o wea he ing and wea , he coins p ima ily show hei co oded b onze co e, oday. Technically, he coins we e min ed om p e- ab ica ed lans. The sil e coa ing was applied by whi e boiling, a chemical p ocess ha b ings he ew sil e elemen s in he me al o he su ace (Klos e kämpe [ 15 ]; Zwicky-Sobczyk, S e n [ 16 ], pp. 394–395; K a [ 17 ], pp. 17–21). Two dies we e used o min ing: One die, which was as ened in an an il, was o he ob e se. The o he die, which was held by hand, was on he hamme side and p oduced he e e se imp ession. Eng a e s p oduced he dies manually—as ypical o p e-indus ial p oduc ion—so ha hey should display speci ic indi idual cha ac e is ics ha impac ed on he p oduc , he coin. Conside ing he sensi i i y o he lase -based me hod, i is expec ed ha hese cha ac e is ics can be dis inguished in he de ec ed signal so ha i becomes possible o assign coins o hei o iginal min . The lack o de ailed ex sou ces on he Gallic Empi e unde lines he impo ance and ele ance o coins as di ec his o ical es imonies. Thus, as he e a e almos no min ma ks o iden i ica ion, he ques ion o min localiza ion is no i ial. By iden i ying he min s and naming hem, a anking al eady becomes ob ious. The a ibu ion and he judgmen as ‘main min ’ ha e implica ions o he unde s anding o he o ganiza ion o he Gallic Empi e, o ins ance, esul ing in he ques ion whe he he e is a capi al nea he limes o mo e inside he Empi e (c . [ 12 ], pp. 26 .). Ci cula a gumen s complica e he ma e : by de ining one ci y as he capi al o he Empi e, one consequen ly loca es he main min he e. O he o he way ound: he main place o min ing is conside ed he Empi e’s capi al. The wo di e en min s we e usually dis inguished by o mal c i e ia (s yle, le e ing, e e se mo i es and, mos c ucial, po ai ypes) (Bland [ 18 ], p. 65 and p. 70; Besley, Bland [ 19 ], p. 62; Bland, Bu ne [20], p. 290 ).4: • Min I s uck adia es wi h d aped and cui assed bus s ( ype D1: he empe o wea s a cui ass co e ed by a mili a y coa held oge he wi h a ibula a he on shoul- de ). The min was o ganized in wo wo kshops (o icinae), which we e occasionally ma ked by addi ional min ma ks in he ield. In he s udy, only coins om o icina B we e included. He i age 2025,8, 202 4 o 20 • Min II issued cui assed po ai s which migh show a bulge o a man le a he back shoulde ( ype B1). The coins we e p oduced by a single wo kshop (o icina). The p ecise iden i ica ion o he wo min ing si es was and is hea ily dispu ed in esea ch (c . Mai a [ 12 ], pp. 23–50, chap e 2) and he a ibu ions changed o we e modi ied as ep esen ed by Figu e A1. I is only in ecen yea s ha a ce ain consensus seems o ha e eme ged, based p ima ily on hoa d ind analysis. O e a long pe iod, Cologne was seen as he impo an and main min o he Gallic Empi e, whe eas he o he , he sou he n min ,Min II o subsidia y min 5 was usually loca ed a T ie 6 . Hoa ds and a chaeological inds ound in he a eas a ound hese p oposed min ing places in ecen decades now make he opposi e iew plausible 7 . Decisi e a e he p opo ional a ios o he places in ques ion and numisma ic objec s (coppe ba s, lans, unci cula ed adia es, e c.) om he o icial T ie min 8 . The e o e, cu en ly, T ie is ega ded as he place o Min Iand Cologne as place o Min II (c . also Table 1). Fo he s udy, coins wi h he e e se ype o Aequi as we e selec ed om he Cologne min . They s em om wo di e en issues (phase I and phase II). Table 1. Alloca ion changes and modi ica ions o he wo min ing si es, Min I and Min II, espec- i ely. Numbe s o Vic o inus coins, aken om he ables in Mai a [12], pp. 43 and 44. Hoa d Min I Min II B auweile (nea Cologne) 36% 63% FMRD IV no. 3064.3 (T ie ) 85% 15% FMRD IV no. 3064.8 (T ie ) 88% 12% 2. Ma e ials and Me hods 2.1. Roman Coin Se ies The coin collec ion o he A chaeological Museum o Müns e Uni e si y holds a signi ican collec ion o coins o he empe o Vic o inus. In his s udy, h ee se ies o Roman coins, each consis ing o i e an oniniani/ adia es o he Gallic Roman Empi e, we e cha ac e ized by specula lase e lec ome y and X- ay luo escence analysis. In addi ion, o e e ence, a Eu opean i e-cen coin o he 21 s cen u y was inspec ed, as well, which consis s o a s eel co e wi h coppe coa ing and was p oduced in an indus ial min ing p ocess. Since he die o he 5 cen coin is indus ially p oduced, unlike he Roman coins, his coin can be used as a e e ence in his s udy. De ails o he i een coins a e gi en in Figu e A1. The ypes o he ob e ses and e e ses a e classi ied in acco dance wi h he common e e ence wo ks om Besley [ 19 ], pp. 73–81, o Mai a [ 12 ], pp. 282–294, as gi en in Table 2. Table 2. Type classi ica ion o he ob e ses and e e ses. Ob e se Types B1: Cui assed bus o he empe o igh , adia e D1: D aped and cui assed bus o empe o igh , adia e Re e se Types Aequi as 1: Aequi as (pe soni ica ion o equi y) s anding l., holding scales in he igh hand and co nucopia in he le a m Pax 1: Pax (pe soni ica ion o peace) s anding l., holding oli e-b anch in he igh hand and a ans e se scep e in he le a m He i age 2025,8, 202 5 o 20 The pho og aphs o Table 3( aken wi h a digi al came a, ype EOS50, Canon Deu sch- land GmbH, K e eld, Ge many) show an example o one Roman coin om each o he h ee se ies. Pho og aphs o all coins can be ound in Appendix A. I is a he ob ious ha he indi idual coins no only di e in shape, hickness, legend and ype, bu also in he op ical colo imp ession and b igh ness. We he e no e ha all pho og aphs we e aken unde he same condi ions o ligh ing and digi al came a se ings (exposu e ime, sensi i i y, e c.) by he pho og aphe o he A chaeological Museum Robe Dylka. Table 3. Pho og aphs o an example o one Roman coin om each o he h ee se ies aken unde he same condi ions o ligh ing and digi al came a se ings. Di e ences in colo and b igh ness can be concluded om an op ical inspec ion by eye. The in en o y numbe s acco d wi h he da a gi en in Figu e A1. T ie Cologne Phase I Cologne Phase II M 5709 M 5769 M 5775 ob e se e e se 2.2. Specula Lase Re lec ome y and X-Ray Fluo escence Analysis The coins we e in es iga ed by specula lase e lec ome y as well as by X- ay luo es- cence (XRF) o chemical analysis. The op ical beam pa h o specula lase e lec ome y is p incipally ske ched in he image o Figu e 2a). A linea ly pola ized lase beam is e lec ed a he su ace o he Roman coin and he magni ude o he in ensi y is measu ed using a pho ode ec o . As illus a ed in Figu e 2b), he magni ude o he de ec ed signal is cha ac- e is ic o he mac o- and mic os uc u e o he su ace and he su ace laye o he coin as i loses ligh due o sca e ing, abso p ion, in e e ence and de ec s. We he e no e ha we assume he p esence o a h ee-laye sys em, i.e., a coppe co e wi h sil e coa ing and an oxide laye on he op. The la e may be sil e oxide and, hus, is anspa en o he inciden lase ligh . By de ec ing he sca e ing in ensi y as a unc ion o angle and ligh pola iza ion, i becomes possible o deduce in o ma ion abou he laye p ope ies—such as hickness, abso p ion loss o chemical elemen s a impu i y concen a ion le el—as well as om he me al/laye in e ace, pa icula ly abou he index o e ac ion and abso p ion loss. I is assumed ha hese p ope ies a e highly cha ac e is ic o he coinage and hus enable he min o be iden i ied. I is no ewo hy o men ion ha his measu ing concep can be ans o med in o a pa icula ly use - iendly measu ing de ice. As a ba e y-ope a ed and po able handheld sys em, i is possible o di ec ly ou pu he o igin o he coin o a leas one p obabili y alue (e.g., on a scale o 1–10) on a display, hus comple ely elimina ing he need o he use o analyze measu emen da a. Fo use s who a e amilia wi h 3D p in ing and minicompu e s (e.g., om he MAKER mo emen [ 29 ]), i is e en possible o se up he en i e echnology in a do-i -you sel measu ing de ice hemsel es. This is mainly due o he small numbe o He i age 2025,8, 202 6 o 20 componen s equi ed and enables mul iple sys ems o be se up. A lase poin e as a ligh sou ce and a sma phone came a as a de ec o a e su icien o educe cos s. Figu e 3shows he echnical ealiza ion o he op ical beam pa h in a labo a o y se up. I s basic design ollows he one in oduced by Rischmülle e al. [ 8 ] o he inspec ion o aluminum su ace coa ings and was adap ed o he op ical analysis o Roman coins o he s udy o he p esen wo k. (a) ai in e e ence abso p ion θθ oxide sil e coppe sca e ing (b) Figu e 2. (a) Op ical beam pa h o specula lase e lec ome y. (b) Ske ch o he expec ed su ace laye on he Roman coins and physical phenomena ha can be expec ed om he in e ac ion o cohe en lase ligh wi h he me al–laye –ai sys em in specula lase e lec ome y: (1) coppe co e, (2) sil e laye and (3) oxide laye . M M 60 cm 30 cm P  /2 PH PH  2  in ou  0,7 0,3 Figu e 3. Expe imen al se up o in es iga ing Roman coins a a wa eleng h o 632.8 nm as a unc ion o angle o incidence θ and pola iza ion s a e. P: pola ize ; λ/ 2: wa epla e; PH: pinholes; BS: beam spli e ; D: Si-pho odiode; M: mi o s. He e, we use a low-powe helium–neon lase a a wa eleng h o 632.8 nm (a e age powe P0= 1 mW, lase class 2) as he ligh sou ce, i.e., only a single lase colo o inspec ion. The wa eleng h is chosen in acco dance wi h he p onounced e lec i i y o coppe me als in he ed spec al ange and because o i s high beam quali y (low beam He i age 2025,8, 202 7 o 20 di e gence, nea ly Gaussian in ensi y p o ile) a low cos s ( ≪ EUR 200). The lase powe is compa able o a lase poin e de ice o ensu e eye sa e y and is much oo small o lase -induced phenomena on he me allic coin su aces, such as o lase abla ion, so ha a non-des uc i e in e ac ion is p esen . The beam is di ec ed a a la ge angle o incidence θin o he su ace o he Roman coin and he e lec ed ligh in ensi y R o he specula beam is de ec ed using a silicon pho odiode. Geome ically, he di ec ion o he specula beam ollows Snell’s law, i.e., he angle o incidence equals he angle o e lec ion θin =θou =θ , so ha he de ec o is posi ioned a an angle o 2 θ wi h espec o he di ec ion o he inciden beam. The specula e lec ion becomes a ec ed by ligh sca e ing, abso p ion and in e e ence p ocesses and, hus, R(θ) becomes especially cha ac e is ic o each indi idual Roman coin. The me hod u he makes use o he angula dependence o R(θ) acco ding o F esnel equa ions (c . Bass [ 30 ], Hech [ 31 ]) and i s p onounced dependence on he ligh pola iza ion. Fo his pu pose, wo independen o a ion s ages (Newpo Co po a ion, I ine, CA, USA, model M-URM80CC) a e employed in a θ− 2 θ con igu a ion o de e mine he signal R(θ) au oma ically. The wo o a ion s ages a e adjus ed wi h he same axis o o a ion in ela ion o each o he , wi h s age 1 o a ing he sample a angle θ and s age 2 mo ing he de ec o a an angle o 2 θ . Thus, an angula ange o ≈ 10 ◦ up o ≈ 85 ◦ is achie ed wi h angula limi a ions ha a e due o spa ial es ic ions o he mechanical componen s. The p ecise con ol o he angle o incidence ( θ ) and de ec ion angle (2 θ ) is achie ed by angula encode s. Along he beam pa h, he lase beam is di ec ed h ough a combina ion o a Glan–Thompson pola ize (P) and a λ/ 2 wa e e a de pla e in o de o adjus he ligh pola iza ion (ei he o hogonal o pa allel o he plane o incidence, i.e., s - o p -pola iza ion). A beam spli e (BS) is used o con ol he powe o he inciden lase beam ia de ec o D2, hus also enabling a compensa ion o lase luc ua ions. The ligh sca e ed om he coin passes wo pinholes (PHs), posi ioned on ei he side o he sample o limi he solid angle o he specula ly e lec ed ligh . The de ec ed signals o s - and p-pola ized lase ligh , Rs(α)and Rp, a e used o de e mine he e lec ome ic a io: ∆R(θ) = Rs(θ) Rp(θ)(1) ha se es as a cen al measu e h oughou his s udy. A special ea u e o he se up is he sample holde ha was de eloped o his s udy (c . pho og aph o Figu e 4) and p oduced using 3D ilamen p in ing echnology ( ilamen : polylac ic acid, PLA) o accoun o he a ious shapes and hicknesses o he indi idual samples a low cos s. The holde is designed o a simple exchange o he coins and can also be easily adap ed o a ious sizes, hicknesses and shapes by using a se ies o 3D-p in ed, exchangable holde s. The lase spo wi h diame e o ≈ 2 mm was posi ioned a a la egion o he su ace in o de o e ain he low lase beam di e gence in he e lec ed signal. F om a p ac ical iewpoin he measu emen p o ocol comp ises he ollowing i e s eps which can be ca ied ou on si e a he exca a ion loca ion o a he museum: (1) Selec an app op ia e sample moun ; inse and ix he coin; moun he holde on o he o a ion s age. (2) Ro a e he pola ize in e ical posi ion ( s -pola iza ion) and pe o m an angula scan o de e mine Rs(θ). (3) Ro a e he pola ize in ho izon al posi ion ( p -pola iza ion) and pe o m an angula scan o de e mine Rp(θ). (4) De e mine and plo he a io ∆R(θ)acco ding o Equa ion (1). (5) Unmoun he Roman coin and con inue om he beginning wi h he nex one. He i age 2025,8, 202 8 o 20 Figu e 4. Pho og aph o he sample holde wi h a Roman coin. The inciden lase beam is isible by he ed ligh spo in he cen e o he coin. The 3D-p in ed holde enables moun ing o coins wi h di e en sizes, shapes and hicknesses, and can be easily exchanged wi h a se ies o di e en holde s. The du a ion o his measu emen cycle o one coin depends on he chosen mea- su emen pa ame e s, pa icula ly on angula esolu ion, angula posi ioning ime and in eg a ion ime pe angula posi ion. I can hus ce ainly each ens o minu es pe coin. I ealized as handheld ool, howe e , he du a ion can be op imized o he inspec ion o 1–2 coins pe minu e o enable he measu emen o a la ge se o coins pe hou . Na - u ally, he measu emen p ocess can be u he au omized up o he case ha besides inse ing and emo al o he coins he esul ing e lec ome ic a io ∆R is displayed upon p essing a bu on. The dimension o he labo a o y se up depic ed in Figu e 3measu es (wid h × heigh × dep h) 50 cm × 20 cm × 40 cm a a weigh o ≈ 5 kg. Fo use a he exca a ion si e o in he museum, a ans o ma ion in o a compac (size o a shoe box) and po able ool is possible. This ype o ans o ma ion o an au oma ized ou -o - he-lab measu emen de ice was al eady success ully demons a ed o a e y simila se up in Toschke [32] ha was used o he s udy o embossed aluminum small componen s. Addi ionally, chemical composi ion analysis is pe o med o all coins using a XRF spec om e ( ype Axios, Mal e n Panaly ical L d., Mal e n, UK) equipped wi h he Om- nian SW LTU so wa e package and he Helium A chi e o da a i ing and quan i ica ion. This echnique enables he non-des uc i e elemen al analysis o samples by de ec ing cha ac e is ic seconda y X- ays emi ed om he elemen s p esen . The main elemen s in es iga ed include Ag, Al, Ca, Cl, Cu, Fe, Na, Ni, P, Pb and S. Du ing he measu emen , a p ima y X- ay beam exci es he a oms in he sample, causing he emission o elemen - speci ic luo escence adia ion. The helium pu ge sys em is employed o educe abso p ion e ec s om ai , he eby enhancing he de ec ion o ligh elemen s such as Na and Al. 3. Resul s 3.1. Specula Lase Re lec ome y Figu e 5shows plo s o he e lec ome ic a io ∆R (c . Equa ion (1)) as a unc ion o angle θ so ed acco ding o he h ee se ies T ie (le ), Cologne phase I (middle) and Cologne phase II ( igh ). The da a ep esen an angula ange o 10 ◦<θ< 87 ◦ and we e measu ed a a wa eleng h o λ=632.8 nm in all cases. In he i s s ep o he da a analysis, i is necessa y o limi he size o he da a se o a ew (he e: h ee) pa ame e s wi h which cha ac e is ic p ope ies o he plo s shown a e desc ibed. As hese ex ac ed pa ame e s educe he plo s o essen ial in o ma ion, hey (po en ially) simpli y he iden i ica ion o possible co ela ions be ween he pa ame e s and he espec i e min s. In pu ely quali a i e e ms, a compa able signal cu e can be seen in all plo s: a signal builds-up wi h inc easing measu emen angle, passes h ough He i age 2025,8, 202 9 o 20 a maximum and disappea s o e y la ge measu emen angles. This means ha each plo can be educed o h ee pa ame e s: (1) he maximum signal s eng h, (2) he angula posi ion o he signal maximum and (3) he angula wid h be ween he ise and all o he signal maximum. The nex s ep is o analyze he da a, aking in o accoun he nume ical alues and uni s, in o de o ind and de ine sui able pa ame e s. Fo ins ance, all 15 da a plo s exhibi a simila o e all shape wi h ∆R≈ 1 a he smalles and la ges angles o θ= 10 ◦ and θ≈ 87 ◦ , i.e., beam geome ies in which he lase beam s ikes he coin su ace almos e ically (commonly called no mal incidence) and pa allel o i (g azing incidence), espec i ely. In be ween, ∆R is always la ge han uni y wi h a peak posi ion θmax (c . inse o Figu e 5) a ≈ 60 ◦ in all cases. The wid h o he peak, cha ac e ized by he ull wid h a hal maximum (FWHM, see inse ), is ≈ 10 ◦ . Clea di e ences be ween he se ies a e ound ega ding he peak alues ∆R(θmax) ; ha pa icula ise om ≈ 15 (T ie ), ia ≈ 24 (Cologne phase I) up o ≈ 37 (Cologne phase II), i.e., ∆R(θmax) , is indica ed as a p omising pa ame e o iden i y he p o enance o coins. The de ailed lis o he pa ame e s peak angle θmax ( ◦ ), peak wid h FWHM(◦) and peak alues ∆R(θmax)is gi en in Table 4. 0 5 10 15 20 25 30 35 40 ∆R T ie Cologne phase I Cologne phase II Angle o Incidence (°)θ 20 30 40 50 60 70 80 20 30 40 50 60 70 80 20 30 40 50 60 70 80 θmax ∆R( max)θ FWHM Figu e 5. Re lec ome ic a io ∆R acco ding o Equa ion (1) as a unc ion o angle θ in he ange 10 ◦<θ< 87 ◦ a a wa eleng h o λ= 632.8 nm and so ed acco ding o he h ee coin se ies: T ie (le ), Cologne phase I (middle) and Cologne phase II ( igh ). The inse (T ie plo ) schema ically shows he pa ame e s θmax , FWHM and ∆R(θmax) ha a e de e mined om he da a se s, lis ed in Table 4and used o u he analysis and discussion. Table 4. Pa ame e s o he e lec ome ic peaks depic ed in Figu e 5: Peak angle θmax ( ◦ ), peak wid h FWHM( ◦ ) ( ull wid h a hal maximum), and peak alue ∆R(θmax) o all coins and so ed acco ding o he h ee se ies. E o s e lec he p ecision in he de e mina ion o he espec i e alues om he da a se . A e age alues wi h he espec i e s anda d de ia ions a e added in he las line o each se ies (bold p in ed alues). Min Sample θmax(◦)FWHM(◦)∆R(θmax) T ie M 5709 56.8 ±0.6 15.9 ±0.8 16.3 ±0.5 M 5711 60.3 ±0.6 21.9 ±0.9 08.5 ±0.4 M 5712 65.5 ±0.6 19.7 ±0.9 10.8 ±0.5 M 5713 56.6 ±0.6 18.1 ±0.9 13.0 ±0.5 M 5714 57.9 ±0.6 19.2 ±0.9 11.3 ±0.5 A e age 59.4 ±1.7 19.0 ±1.0 12.0 ±1.3 He i age 2025,8, 202 16 o 20 ha o he me als ha e a sui able coa ing as i is he case o con e sion laye s on aluminum, so ha an expansion o he s udy o hyd oxide laye s o gold o oxidized sil e (ancien ) coins emains p omising. Finally, howe e , i should be emphasized ha all he esul s shown he e a e based on he limi ed se ies o coins o i e samples each and a e he e o e o a pilo na u e. A alida ion o he ob iously s ongly s a is ical me hodology wi h mo e ex ensi e sample se s is absolu ely necessa y in he nex s ep, bu is e y p omising. Au ho Con ibu ions: Concep ualiza ion, Y.T., A.L., K.M., H.-H.N. and M.I.; me hodology, Y.T.; so wa e, Y.T.; alida ion, Y.T.; o mal analysis, Y.T.; in es iga ion, Y.T.; esou ces, K.M., H.-H.N., A.L. and M.I.; da a cu a ion, K.M., H.-H.N., A.L. and M.I.; w i ing—o iginal d a p epa a ion, Y.T., K.M., H.-H.N. and A.L.; w i ing— e iew and edi ing, S.W.-H., E.W., A.L., K.M., H.-H.N. and M.I.; isualiza ion, Y.T., S.W.-H. and E.W.; supe ision, A.L. and M.I.; p ojec adminis a ion, A.L. and M.I.; unding acquisi ion, A.L. and M.I. All au ho s ha e ead and ag eed o he published e sion o he manusc ip . Funding: This esea ch is pa o he p ojec s Op ocubes and quan umexpedi ion and was unded by he Ge man Fede al Minis y o Educa ion and Resea ch (BMBF) and Ge man Fede al Minis y o Resea ch, Technology and Space (BMFTR) wi hin he unding p og ams “Pho onics Resea ch Ge many” wi h con ac numbe 13N15229 and 13N15230 and “Quan um ak i ” wi h con ac numbe 13N16719. The au ho s a e esponsible o he con en s o his publica ion. Da a A ailabili y S a emen : The o iginal da a p esen ed in he s udy a e openly a ailable in he OsnaDa a eposi o y o Osnab ück Uni e si y a h ps://doi.o g/10.26249/FK2/QO3ASW. Acknowledgmen s: The au ho s hank Ka s en Kömpe (Ino ganic Chemis y Di ision, Depa men o Biology/Chemis y o Osnab ück Uni e si y) o p o iding X- ay luo escence spec a and o discussion and Robe Dylka om he A chaelogical Museum o aking he pho og aphs o all coins unde s udy. Con lic s o In e es : The au ho s decla e no con lic s o in e es . He i age 2025,8, 202 17 o 20 Appendix A In .-no. Measu emen s Legend and Type o Ob e se & Re e se RIC V,2 Elme 1941 Beachy Head (= Bland 1979) B auweile (= Ziegle 1983) T ie (= Demo 1984) Cune io (= Besley – Bland 1983) No manby (= Bland – Bu ne 1988) Mai a 2014 RIC V,42 5709 2.18g; 23.0mm; 7h 5711 2.56g; 19.8mm; 12h 5712 2.75g; 19.8mm; 6h 5713 2.81g; 19.6mm; 5g 5714 3.05g; 20.2mm; 7h 5769 3.02g; 20.1mm; 7h 5770 2.87g; 19.6mm; 8h 5772 2.77g; 20.3mm; 1h 5773 2.69g; 21.3mm; 2h 5774 2.85g; 21.9mm; 8h 5775 2.56g; 19.1mm; 7h 5776 3.91g; 21.2mm; 7h 5777 2.65g; 20.7mm; 2h 5778 2.67g; 22.5mm; 8h 5779 2.51g; 20.3mm; 8h p. 172 no. 526 [T ie ] … p. 117 no. 573-601 [Cologne] … p. 44 nos. 175-177 [Cologne] … p. 148 no. 2530 (“issue 3, phase 2“ min I o p incipal min ] … p. 337 no. 1406 [min I =p incipal min =T ie ] … no. 588 (issue 3, phase 2) (c. la e 269 – mid 270) [T ie , wo kshop B] “Min I” = T ie Ob . IMP C VICTORINVS P F AVG. Vic o inus [D1] Re . PA-X AVG / V - *. Pax1 … no. 118 (AD 269-271) [Cologne] … p. 68 no. 682 (“6. Emission, e wa gegen Ende 269”. [Cologne] p. 67 able 3: “issue III, 1 s phase”; p. 98 nos. 1705- 1788 [ Cologne , officina A] p. 184 no. 565 [Cologne] … p. 72 able 4 and p. 99 no. 2746: “issue I, 3 d phase” [T ie ] – … p. 44 nos. 182-183 [T ie ] … p. 150 no. 2562 ( min II o b anch min issue 1c”) p. 184 no. 567 [Cologne] … p. 337 no. 1428 [min II = Cologne] … no. 641 (issue 1/phase 2, c. mid 269) [Cologne] “Min II” = Cologne phase I “Min II” = Cologne phase II … p. 337 no. 1427 [min II = Cologne] … no. 639 (issue 1/phase 1, c. mid 269) [Cologne] Ob . IMP C PI VICTORINVS P F AVG. Ma ius [B1] R . AEQVITAS AVG. Aequi as 1 … p. 72 able 4 and p. 99 nos. 2743-2745: “issue I, 2 nd phase” [T ie ] – – … p. 150 no. †2561 (min II o b anch min , issue 1b”) Ob . IMP C PI VICTORINVS P F AVG. Vic o inus [B1] Re . AEQVITAS AVG. Aequi as 1 … no. 41 (AD 269-271) “Po ai o Vic o inus” [“unce ain o Sou he n Gallic min ”] … p. 70 no. 701 (“2. Emission, Ende 268 – Mi e 269 / ühe Phase”) [T ie ] … p. 70 no. 702 (“2. Emission, Ende 268 – Mi e 269 / spä e e Phase”) [T ie ] Figu e A1. Tabula lis ing o he min s unde in es iga ion o his s udy. We no e ha an impo an a gumen o he ac ual a ibu ion o he main min I o T ie and min II o Cologne is he e idence o hoa ds om B auweile and T ie (see Table 1in his a icle). I is by coincidence ha he samples analyzed by op ical means ( ypes [ 21 ], nos. 682 and 701–702) a e no ha clea o e en seem o con adic he o he wise ob ious conclusion. He i age 2025,8, 202 18 o 20 Table A1. Pho og aphs o all Roman coins om he h ee se ies aken unde he same condi ions o ligh ing and digi al came a se ings. Di e ences in colo and b igh ness can be concluded om he op ical inspec ion by eye. The in en o y numbe s acco d wi h he da a gi en in Figu e A1. T ie M 5709 M 5711 M 5712 M 5713 M 5714 ob e se e e se Cologne Phase I M 5769 M 5770 M 5772 M 5773 M 5774 ob e se e e se Cologne Phase II M 5775 M 5776 M 5777 M 5778 M 5779 ob e se e e se He i age 2025,8, 202 19 o 20 No es 1On he Gallic Roman Empi e c . König [9]; D inkwa e [10]. 2C . Kienas e al. [11], p. 237. 3 Fo he coins c . Mai a [ 12 ], pp. 82–84, 163–181 and 648–724, and RIC V,4 [ 13 ] pp. 165–194. Radia es a e coins wi h a alue o wo dena ii, also named “an oniniani” a e he empe o M. Au elius An oninus (Ca acalla) who es ablished his new o e - a ed coin in AD 215. The name “ adia es” o igina es om he ays on he empe o ’s head ins ead o he egula lau el w ea h; his o mal cha ac e usually doubles he alue o a coin. 4 Al eady Elme [ 21 ], p. 14, desc ibes di e en s yles: “Die Haup me kmale ü T ie sind: höhe es Relie , au gelocke es Haa , b ei e e Sch ö ling und g öße e Buchs aben, ü Köln: lache es Relie (sei 267), kleine e und zie liche e Buchs aben und auch kleine e Sch ö ling”— a ia ions, ha a e o en ha dly ecognisable. Only wo ypes o Vic o inus’ p edecesso Pos umus ma k Cologne (Colonia Claudia A a Ag ippinensium) as min ing place: Webb [ 22 ] (Pos umus) no. 286 = Mai a [ 13 ] no. 425 (COL CL AGRIP) and Webb [ 22 ] (Pos umus) no. 285 = Mai a [ 13 ] no. 426 (C C A A). The e e se mo i o a pe soni ica ion holding scales and co nucopia is subsequen ly a ibu ed o Cologne. 5C . he es ima ion in Bland [18], p. 78 “ he min o icials o T ie , who we e always sligh ly mo e cu o om he mains eam o poli ical e en s in he Gallic Empi e han hei Cologne colleagues”. 6 In oduced by Elme in [ 21 ], pp. 9, 12 . Cologne had been a mili a y min o he Cen al Empi e be o e. Fo T ie as he second min , see ibidem p. 14 ollowing sca ce li e a y and epig aphic e idence. 7 Mai a [ 13 ], pp. 9–19; see also Mai a [ 12 ], esp. pp. 35 . 42–46. 49 . o Bland, Besley, Bu ne [ 23 ], pp. ix . and xii .; Besley, Bland [19], pp. 57 . al eady a gued o a e-e alua ion bu “p e e o lea e open he ques ion o min -localiza ion” (p. 58). 8 Mai a [ 12 ], pp. 35 . C . Ziegle [ 24 ] (B auweile , nea Cologne) as well as Demo [ 25 ]; R.-Al öldi [ 26 ], pp. 192 . nos. 3064.3 and 3064.8 (hoa ds om T ie ) and Gilles [ 27 ] on he emains o he o icial T ie min , exca a ed in 2005. 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[C ossRe ] Disclaime /Publishe ’s No e: The s a emen s, opinions and da a con ained in all publica ions a e solely hose o he indi idual au ho (s) and con ibu o (s) and no o MDPI and/o he edi o (s). MDPI and/o he edi o (s) disclaim esponsibili y o any inju y o people o p ope y esul ing om any ideas, me hods, ins uc ions o p oduc s e e ed o in he con en .