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
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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.
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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
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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. Among hese a i ac s we e
objec s o di e en s ages o comple ion (“Vo p oduk e”), see Knick ehm [28], p. 26.
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Knick ehm, W. O izielle und lokale Münzp äges ä en des gallischen Sonde eichs in und um T ie ; Kleine numisma ische Reihe de
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