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

Abstract

Non-destructive, specular laser reflectometry, an industrially used and easily accessible method, is adapted in numismatic research to the inspection of coins of the Gallic Roman Empire with the objective of the allocation of mints and/or the identification of different minting techniques. For this purpose, the laser-reflectometric fingerprints of three series of coins each consisting of five antoniniani (or radiates) of the Gallic Roman Empire originating from two mints—Trier and Cologne—are systematically determined, analyzed and correlated with the corresponding XRF element analysis. The results show that the use of an inexpensive red-emitting laser system (wavelength 632.8 nm) with a beam diameter $d<0.5$ mm and a sample mount that can be adapted to the individual shape and thickness of the coins leads to signal intensities that can be systematically recorded over a large angular range with a very good signal-to-noise ratio (SNR $>10$). While the signals cannot be used to assign individual coins to mints, we discuss the possibility of a statistical analysis. Although each coin set consists of only five samples and thus requires further study, the results here suggest that the sets can be distinguished from each other, that there is a correlation to the silver concentration and that it is possible to estimate the refractive index n.

1. Introduction

X-ray photoelectron spectroscopy (XPS), X-ray fluorescence spectroscopy (XRF), Laser-ablation- and Multicollector-inductively coupled plasma-mass spectrometry (LA-ICP-MS, LA-MC-ICP-MS) are well-established methods in numismatics to qualify samples regarding their chemical or atomic composition [1,2,3]. In particular, extensive work has been carried out on provenance determination to mint of origin using elemental and isotopic composition of silver via XRF [4,5,6]. There are also corresponding XRF handheld instruments for use at the excavation site after the coins have been cleaned, or in local museums abroad [7]. Due to their relatively high price point of up to a few Eur 10.000, however, they are only available to a limited extent. For this reason, the cooperation behind this project pursued a first attempt in the adaptation of a non-destructive, cost-effective laser-based method for the use in numismatics that was originally introduced for the inspection of metal surfaces in industry by Rischmueller et al. [8]. The technical complexity of the method is comparatively low, so that the transformation towards a handheld tool, especially for use in a museum or field use seems very likely. Specifically, the original method enables the determination and differentiation of (ultra-)thin dielectric layers on aluminum parts, so-called conversion layers, and plays an important role in the quality control of corrosion protection of aluminum components. For this purpose, the laser-based method makes use of the physical phenomenon of laser light interference and is capable of differentiating layer thicknesses well below a thickness of 100 nm, and even below 10 nm on surfaces with roughness in the range of ≈300 nm. It was demonstrated that the method is sensitive to the totality of the surface morphology and the detected signal therefore contains information about various surface properties such as roughness, absorption and scattering centers, defects and the index of refraction. Against this background, the idea arose to adopt the principles of this method to inspect the surface layer system of ancient coins with the goal of developing a portable, low-cost measuring instrument for the allocation of mints and/or the identification of different minting techniques on site at excavation sites. As an example, the subject of investigation is three series of Roman coins, each consisting of five antoniniani/radiates of the Gallic Roman Empire (=fifteen coins in total).

The Gallic Roman Empire existed from 260 to 274 AD as a separate state1 and was ruled by emperors from the Roman military and had its capitals in Cologne and Trier. The emperors of the Gallic Roman Empire minted their own coins following the typical Roman minting tradition. One of the emperors was Victorinus, who ruled from 269 to 271 as Imperator Caesar M. Piavonius Victorinus Invictus Augustus2. He was a successful general and became emperor in 269. His ruling was accepted in the provinces of Gallia, Germania and Britannia. In 271, he was killed in a private conflict close to Cologne and subsequently was consecrated. Victorinus minted gold coins (mainly aurei) and silver denominations (very few denarii and lots of antoniniani/radiates3).

From a typological point of view, the fifteen coins under study in this contribution can unambiguously be classified and attributed to two different mints (called Mint I and Mint II in what follows), assigned with a high degree of probability to Cologne and Trier. Details of the geographical location, the positions of Mint I and Mint II and of the hoards are shown in the maps in Figure 1.

Although the antoninianus was claimed to be a silver coin, it, at this point in time, in fact was billon containing a very low degree of silver and consisting mainly of bronze. Therefore, due to weathering and wear, the coins primarily show their corroded bronze core, today. Technically, the coins were minted from pre-fabricated flans. The silver coating was applied by white boiling, a chemical process that brings the few silver elements in the metal to the surface (Klosterkämper [15]; Zwicky-Sobczyk, Stern [16], pp. 394–395; Kraft [17], pp. 17–21). Two dies were used for minting: One die, which was fastened in an anvil, was for the obverse. The other die, which was held by hand, was on the hammer side and produced the reverse impression. Engravers produced the dies manually—as typical for pre-industrial production—so that they should display specific individual characteristics that impacted on the product, the coin. Considering the sensitivity of the laser-based method, it is expected that these characteristics can be distinguished in the detected signal so that it becomes possible to assign coins to their original mint.

The lack of detailed text sources on the Gallic Empire underlines the importance and relevance of coins as direct historical testimonies. Thus, as there are almost no mint marks for identification, the question of mint localization is not trivial. By identifying the mints and naming them, a ranking already becomes obvious. The attribution and the judgment as ‘main mint’ have implications for the understanding of the organization of the Gallic Empire, for instance, resulting in the question whether there is a capital near the limes or more inside the Empire (cf. [12], pp. 26 f.). Circular arguments complicate the matter: by defining one city as the capital of the Empire, one consequently locates the main mint here. Or the other way round: the main place of minting is considered the Empire’s capital. The two different mints were usually distinguished by formal criteria (style, lettering, reverse motives and, most crucial, portrait types) (Bland [18], p. 65 and p. 70; Besley, Bland [19], p. 62; Bland, Burnett [20], p. 290 f).4:

• Mint I struck radiates with draped and cuirassed busts (type D1: the emperor wears a cuirass covered by a military coat held together with a fibula at the front shoulder). The mint was organized in two workshops (officinae), which were occasionally marked by additional mint marks in the field. In the study, only coins from officina B were included.
• Mint II issued cuirassed portraits which might show a bulge of a mantle at the back shoulder (type B1). The coins were produced by a single workshop (officina).

The precise identification of the two minting sites was and is heavily disputed in research (cf. Mairat [12], pp. 23–50, chapter 2) and the attributions changed or were modified as represented by Figure A1. It is only in recent years that a certain consensus seems to have emerged, based primarily on hoard find analysis. Over a long period, Cologne was seen as the important and main mint of the Gallic Empire, whereas the other, the southern mint, Mint II or subsidiary mint5 was usually located at Trier6. Hoards and archaeological finds found in the areas around these proposed minting places in recent decades now make the opposite view plausible7. Decisive are the proportional ratios for the places in question and numismatic objects (copper bars, flans, uncirculated radiates, etc.) from the official Trier mint8. Therefore, currently, Trier is regarded as the place of Mint I and Cologne as place of Mint II (cf. also

Table 1. Allocation changes and modifications for the two minting sites, Mint I and Mint II, respectively. Numbers for Victorinus coins, taken from the tables in Mairat [12], pp. 43 and 44.

Hoard	Mint I	Mint II
Brauweiler (near Cologne)	36%	63%
FMRD IV no. 3064.3 (Trier)	85%	15%
FMRD IV no. 3064.8 (Trier)	88%	12%

). For the study, coins with the reverse type of Aequitas were selected from the Cologne mint. They stem from two different issues (phase I and phase II).

2. Materials and Methods

2.1. Roman Coin Series

The coin collection of the Archaeological Museum of Münster University holds a significant collection of coins of the emperor Victorinus. In this study, three series of Roman coins, each consisting of five antoniniani/radiates of the Gallic Roman Empire, were characterized by specular laser reflectometry and X-ray fluorescence analysis. In addition, for reference, a European five-cent coin of the 21$\mathrm{st}$ century was inspected, as well, which consists of a steel core with copper coating and was produced in an industrial minting process. Since the die of the 5 cent coin is industrially produced, unlike the Roman coins, this coin can be used as a reference in this study. Details of the fifteen coins are given in Figure A1.

The types of the obverses and reverses are classified in accordance with the common reference works from Besley [19], pp. 73–81, or Mairat [12], pp. 282–294, as given in

Table 2. Type classification of the obverses and reverses.

Obverse Types
B1:	Cuirassed bust of the emperor right, radiate
D1:	Draped and cuirassed bust of emperor right, radiate
Reverse Types
Aequitas 1:	Aequitas (personification of equity) standing l.,
	holding scales in her right hand
	and cornucopia in her left arm
Pax 1:	Pax (personification of peace) standing l.,
	holding olive-branch in her right hand
	and a transverse scepter in her left arm

.

The photographs of

Table 3. Photographs of an example of one Roman coin from each of the three series taken under the same conditions of lighting and digital camera settings. Differences in color and brightness can be concluded from an optical inspection by eye. The inventory numbers accord with the data given in Figure A1.

	Trier	Cologne Phase I	Cologne Phase II
	M 5709	M 5769	M 5775
obverse
reverse

(taken with a digital camera, type EOS50, Canon Deutschland GmbH, Krefeld, Germany) show an example of one Roman coin from each of the three series. Photographs of all coins can be found in Appendix A. It is rather obvious that the individual coins not only differ in shape, thickness, legend and type, but also in the optical color impression and brightness. We here note that all photographs were taken under the same conditions of lighting and digital camera settings (exposure time, sensitivity, etc.) by the photographer of the Archaeological Museum Robert Dylka.

2.2. Specular Laser Reflectometry and X-Ray Fluorescence Analysis

The coins were investigated by specular laser reflectometry as well as by X-ray fluorescence (XRF) for chemical analysis. The optical beam path for specular laser reflectometry is principally sketched in the image of Figure 2a). A linearly polarized laser beam is reflected at the surface of the Roman coin and the magnitude of the intensity is measured using a photodetector. As illustrated in Figure 2b), the magnitude of the detected signal is characteristic for the macro- and microstructure of the surface and the surface layer of the coin as it loses light due to scattering, absorption, interference and defects. We here note that we assume the presence of a three-layer system, i.e., a copper core with silver coating and an oxide layer on the top. The latter may be silver oxide and, thus, is transparent to the incident laser light. By detecting the scattering intensity as a function of angle and light polarization, it becomes possible to deduce information about the layer properties—such as thickness, absorption loss or chemical elements at impurity concentration level—as well as from the metal/layer interface, particularly about the index of refraction and absorption loss. It is assumed that these properties are highly characteristic of the coinage and thus enable the mint to be identified.

It is noteworthy to mention that this measuring concept can be transformed into a particularly user-friendly measuring device. As a battery-operated and portable handheld system, it is possible to directly output the origin of the coin or at least one probability value (e.g., on a scale of 1–10) on a display, thus completely eliminating the need for the user to analyze measurement data. For users who are familiar with 3D printing and minicomputers (e.g., from the MAKER movement [29]), it is even possible to set up the entire technology in a do-it-yourself measuring device themselves. This is mainly due to the small number of components required and enables multiple systems to be set up. A laser pointer as a light source and a smartphone camera as a detector are sufficient to reduce costs.

Figure 3 shows the technical realization of the optical beam path in a laboratory setup. Its basic design follows the one introduced by Rischmüller et al. [8] for the inspection of aluminum surface coatings and was adapted to the optical analysis of Roman coins for the study of the present work.

Here, we use a low-power helium–neon laser at a wavelength of 632.8 nm (average power $P_0=1$ mW, laser class 2) as the light source, i.e., only a single laser color for inspection. The wavelength is chosen in accordance with the pronounced reflectivity of copper metals in the red spectral range and because of its high beam quality (low beam divergence, nearly Gaussian intensity profile) at low costs (≪EUR 200). The laser power is comparable to a laser pointer device to ensure eye safety and is much too small for laser-induced phenomena on the metallic coin surfaces, such as for laser ablation, so that a non-destructive interaction is present. The beam is directed at a large angle of incidence ${\theta }_{\mathrm{in}}$ to the surface of the Roman coin and the reflected light intensity R of the specular beam is detected using a silicon photodiode. Geometrically, the direction of the specular beam follows Snell’s law, i.e., the angle of incidence equals the angle of reflection ${\theta }_{\mathrm{in}}={\theta }_{\mathrm{out}}=\theta$, so that the detector is positioned at an angle of $2\theta$ with respect to the direction of the incident beam. The specular reflection becomes affected by light scattering, absorption and interference processes and, thus, $R\left(\theta \right)$ becomes especially characteristic for each individual Roman coin. The method further makes use of the angular dependence of $R\left(\theta \right)$ according to Fresnel equations (cf. Bass [30], Hecht [31]) and its pronounced dependence on the light polarization. For this purpose, two independent rotation stages (Newport Corporation, Irvine, CA, USA, model M-URM80CC) are employed in a $\theta -2\theta$ configuration to determine the signal $R\left(\theta \right)$ automatically. The two rotation stages are adjusted with the same axis of rotation in relation to each other, with stage 1 rotating the sample at angle $\theta$ and stage 2 moving the detector at an angle of $2\theta$. Thus, an angular range of ≈10° up to ≈85° is achieved with angular limitations that are due to spatial restrictions of the mechanical components. The precise control of the angle of incidence ($\theta$) and detection angle ($2\theta$) is achieved by angular encoders. Along the beam path, the laser beam is directed through a combination of a Glan–Thompson polarizer (P) and a $\lambda /2$ wave retarder plate in order to adjust the light polarization (either orthogonal or parallel to the plane of incidence, i.e., s- or p-polarization). A beam splitter (BS) is used to control the power of the incident laser beam via detector D2, thus also enabling a compensation for laser fluctuations. The light scattered from the coin passes two pinholes (PHs), positioned on either side of the sample to limit the solid angle of the specularly reflected light. The detected signals for s- and p-polarized laser light, $R_s(\alpha )$ and $R_p$, are used to determine the reflectometric ratio:

$$\Delta R\left(\theta \right)={\displaystyle \frac{R_s\left(\theta \right)}{R_p\left(\theta \right)}}$$

(1)

that serves as a central measure throughout this study.

A special feature of the setup is the sample holder that was developed for this study (cf. photograph of Figure 4) and produced using 3D filament printing technology (filament: polylactic acid, PLA) to account for the various shapes and thicknesses of the individual samples at low costs. The holder is designed for a simple exchange of the coins and can also be easily adapted to various sizes, thicknesses and shapes by using a series of 3D-printed, exchangable holders. The laser spot with diameter of ≈2 mm was positioned at a flat region of the surface in order to retain the low laser beam divergence in the reflected signal.

From a practical viewpoint the measurement protocol comprises the following five steps which can be carried out on site at the excavation location or at the museum:

(1)

Select an appropriate sample mount; insert and fix the coin; mount the holder onto the rotation stage.

(2)

Rotate the polarizer in vertical position (s-polarization) and perform an angular scan to determine $R_{\mathrm{s}}\left(\theta \right)$.

(3)

Rotate the polarizer in horizontal position (p-polarization) and perform an angular scan to determine $R_{\mathrm{p}}\left(\theta \right)$.

(4)

Determine and plot the ratio $\Delta R\left(\theta \right)$ according to Equation (1).

(5)

Unmount the Roman coin and continue from the beginning with the next one.

The duration of this measurement cycle for one coin depends on the chosen measurement parameters, particularly on angular resolution, angular positioning time and integration time per angular position. It can thus certainly reach tens of minutes per coin. If realized as handheld tool, however, the duration can be optimized to the inspection of 1–2 coins per minute to enable the measurement of a larger set of coins per hour. Naturally, the measurement process can be further automized up to the case that besides inserting and removal of the coins the resulting reflectometric ratio $\Delta R$ is displayed upon pressing a button. The dimension of the laboratory setup depicted in Figure 3 measures (width× height× depth) 50 cm × 20 cm × 40 cm at a weight of ≈5 kg. For use at the excavation site or in the museum, a transformation into a compact (size of a shoe box) and portable tool is possible. This type of transformation to an automatized out-of-the-lab measurement device was already successfully demonstrated for a very similar setup in Toschke [32] that was used for the study of embossed aluminum small components.

Additionally, chemical composition analysis is performed for all coins using a XRF spectromter (type Axios, Malvern Panalytical Ltd., Malvern, UK) equipped with the Omnian SW LTU software package and the Helium Archive for data fitting and quantification. This technique enables the non-destructive elemental analysis of samples by detecting characteristic secondary X-rays emitted from the elements present. The main elements investigated include Ag, Al, Ca, Cl, Cu, Fe, Na, Ni, P, Pb and S. During the measurement, a primary X-ray beam excites the atoms in the sample, causing the emission of element-specific fluorescence radiation. The helium purge system is employed to reduce absorption effects from air, thereby enhancing the detection of light elements such as Na and Al.

3. Results

3.1. Specular Laser Reflectometry

Figure 5 shows plots of the reflectometric ratio $\Delta R$ (cf. Equation (1)) as a function of angle $\theta$ sorted according to the three series Trier (left), Cologne phase I (middle) and Cologne phase II (right). The data represent an angular range of ${10}^{\circ }<\theta <{87}^{\circ }$ and were measured at a wavelength of $\lambda =632.8$ nm in all cases.

In the first step of the data analysis, it is necessary to limit the size of the data set to a few (here: three) parameters with which characteristic properties of the plots shown are described. As these extracted parameters reduce the plots to essential information, they (potentially) simplify the identification of possible correlations between the parameters and the respective mints. In purely qualitative terms, a comparable signal curve can be seen in all plots: a signal builds-up with increasing measurement angle, passes through a maximum and disappears for very large measurement angles. This means that each plot can be reduced to three parameters: (1) the maximum signal strength, (2) the angular position of the signal maximum and (3) the angular width between the rise and fall of the signal maximum. The next step is to analyze the data, taking into account the numerical values and units, in order to find and define suitable parameters. For instance, all 15 data plots exhibit a similar overall shape with $\Delta R\approx 1$ at the smallest and largest angles of $\theta ={10}^{\circ }$ and $\theta \approx {87}^{\circ }$, i.e., beam geometries in which the laser beam strikes the coin surface almost vertically (commonly called normal incidence) and parallel to it (grazing incidence), respectively. In between, $\Delta R$ is always larger than unity with a peak position ${\theta }_{\max }$ (cf. inset of Figure 5) at ≈60° in all cases. The width of the peak, characterized by the full width at half maximum (FWHM, see inset), is ≈10°. Clear differences between the series are found regarding the peak values $\Delta R\left({\theta }_{\max }\right)$; that particular rise from ≈15 (Trier), via ≈24 (Cologne phase I) up to ≈37 (Cologne phase II), i.e., $\Delta R\left({\theta }_{\max }\right)$, is indicated as a promising parameter to identify the provenance of coins. The detailed list of the parameters peak angle ${\theta }_{\max }$(°), peak width FWHM(°) and peak values $\Delta R\left({\theta }_{\max }\right)$ is given in

Table 4. Parameters for the reflectometric peaks depicted in Figure 5: Peak angle ${\theta }_{\max }$(°), peak width FWHM(°) (full width at half maximum), and peak value $\Delta R\left({\theta }_{\max }\right)$ for all coins and sorted according to the three series. Errors reflect the precision in the determination of the respective values from the data set. Average values with the respective standard deviations are added in the last line of each series (bold printed values).

Mint	Sample	${\mathit{\theta }}_{\mathbf{max}}$(°)	FWHM(°)	$\mathbf{\Delta }\mathit{R}\left({\mathit{\theta }}_{\mathbf{max}}\right)$
Trier	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
	Average	59.4 ± 1.7	19.0 ± 1.0	12.0 ± 1.3
Cologne phase I	M 5769	60.9 ± 0.6	24.5 ± 1.0	07.7 ± 0.4
	M 5770	59.8 ± 0.6	13.9 ± 0.8	23.3 ± 0.6
	M 5772	60.5 ± 0.6	21.7 ± 0.9	08.8 ± 0.4
	M 5773	56.6 ± 0.6	18.9 ± 0.9	13.2 ± 0.5
	M 5774	62.1 ± 0.6	16.1 ± 0.8	18.8 ± 0.5
	Average	60.0 ± 0.9	19.0 ± 1.9	14.4 ± 2.9
Cologne phase II	M 5775	61.5 ± 0.6	23.8 ± 1.0	07.0 ± 0.4
	M 5776	58.7 ± 0.6	15.9 ± 0.8	19.9 ± 0.6
	M 5777	59.4 ± 0.6	16.5 ± 0.8	17.3 ± 0.5
	M 5778	62.5 ± 0.6	38.6 ± 1.2	03.3 ± 0.4
	M 5779	57.5 ± 0.6	11.3 ± 0.7	37.3 ± 0.7
	Average	59.9 ± 0.9	21.0 ± 5.0	17.0 ± 6.0

.

The data plots of Figure 5 point to a behavior that is expected for the case that a surface layer giving rise to interference phenomena is not present. Instead, air/metal or air/patina reflection is the dominating physical phenomenon (cf. discussion). This opens up the possibility of modeling the experimental data using the original Fresnel equation for the reflection of polarized light at material surfaces via the procedure described in Tompkins [33]. Accordingly, the data set is re-plotted in Figure 6 by the reciprocal angular dependence $1/\Delta R\left(\theta \right)$ that becomes proportional to the angular reflectivity of parallel polarized light (p-polarized light). We note that, in this case, the minimum at ≈60° is called the principal polarization angle and scales with the refractive index and absorption loss of the material.

The red lines in Figure 6 represent sample results of the modeling procedure with the refractive index and absorption coefficient of the metal, $n_{\mathrm{metal}}$ and ${\kappa }_{\mathrm{metal}}$, as free fitting parameters. A good agreement with the experimental data and $n_{\mathrm{metal}}\approx 1.5$ is obvious in all three cases. Considering a refractive index for air of $n_{\mathrm{air}}=1$ and common values for metal absorption (${\kappa }_{\mathrm{metal}}\approx 0.7$), the determined index $n_{\mathrm{metal}}$ of each of the 15 coin is shown in the plot of Figure 7 sorted according to the following series: Trier, Cologne phase I and Cologne phase II. We note that the error bars resemble the standard deviation obtained from the individual modeling fits.

With the exception of the coins M 5712, M 5774 and M 5778 (marked as green data points in Figure 7), the modeled refractive indexes are found in a limited range of $1.4<n_{\mathrm{metal}}<1.6$ for all samples under study (cf. blue shaded area in Figure 7). Within the individual series, we can deduce the following aspects: The values of the Trier series vary in the range $1.48<n_{\mathrm{metal}}<1.58$ with an average value of ${\overline{n}}_{\mathrm{metal}}=1.53$. The indices of the Cologne phase I series show the highest coincidence for the different coins with a negligible fluctuation in the range $1.49<n_{\mathrm{metal}}<1.5$ and an average value of ${\overline{n}}_{\mathrm{metal}}=1.495$. The Cologne phase II series, in contrast, shows the largest fluctuations of n with values in the range $1.41<n_{\mathrm{metal}}<1.6$ and an average value of ${\overline{n}}_{\mathrm{metal}}=1.5$. Thus, the refractive index of all three series is found within a very small range of deviation (<1.5%) from the average value $n_{\mathrm{metal}}=1.51$, i.e., there are no obvious differences detectable between the coins.

For comparison, the specular laser reflectometry was additionally applied to a European 5 cent piece and analyzed using the Fresnel formula. In this case, a refractive index of $n=1.56$ was determined. Thus, there is a small, but notable, difference from the values of the Roman coins (by ≈3% smaller), that cannot be disregarded.

3.2. X-Ray Fluorescence Analysis

The results for the surface composition of the coins, as determined from the analysis using X-ray fluorescence, are presented in

Table 5. Results of the XRF analysis for all 15 samples under consideration and sorted according to the three series (Trier, CGN I = Cologne phase I, CGN II = Cologne phase II). The values of the constituents are given in percentages and are summed up in the last column. We note that elements with values below $0.4\%$ are neglected, so that the sum remains below 100%.

Mint	Sample	Ag	Al	Ca	Cl	Cu	Fe	Ni	Pb	S	Si	Sn	Sum
Trier	M 5709	2.6	0.6	1.5	0.8	81.3	2.0	0.4	0.7	5.1	2.2	-	97.2
	M 5711	5.2	-	-	14.8	76.8	-	-	1.0	1.0	-	-	98.8
	M 5712	4.1	0.4	-	2.3	87.6	-	-	1.2	1.3	1.1	0.5	98.5
	M 5713	3.8	0.9	-	0.9	85.8	-	-	3.8	-	3.9	-	99.1
	M 5714	4.3	-	-	5.9	83.7	-	-	3.3	0.4	0.7	-	98.3
CGN I	M 5769	5.6	0.7	0.9	2.2	84.6	-	-	0.9	1.0	2.6	-	98.5
	M 5770	7.0	-	0.5	12.3	74.3	-	-	3.0	1.2	0.8	-	99.1
	M 5772	6.9	-	-	7.6	72.7	-	-	10.2	1.0	0.8	-	99.2
	M 5773	6.2	0.4	-	3.6	85.7	-	-	1.7	0.7	1.1	-	99.4
	M 5774	6.5	0.4	-	5.1	82.7	-	-	0.9	0.8	0.8	1.7	98.9
CGN II	M 5775	6.0	0.4	0.7	0.8	88.5	-	-	1.0	0.5	1.0	-	98.9
	M 5776	9.0	0.5	-	0.9	85.1	-	-	3.5	-	1.0	-	100.0
	M 5777	6.5	1.3	-	1.4	79.8	-	-	4.1	0.5	4.8	-	98.4
	M 5778	10.1	-	-	0.7	85.4	-	-	2.6	-	0.7	-	99.5
	M 5779	6.7	0.6	0.5	2.2	85.9	-	-	0.9	0.9	1.1	-	98.8

and sorted according the three series.

A total of eleven chemical elements are resolved with copper being the dominant contribution in all coins and percentages between 72.7% and 88.5% with average values of 83.04% (Trier), 80% (Cologne phase I) and 84,95% (Cologne phase II), respectively. Besides some individual elements, such as chloride (Cl) for the samples M 5711 and M 5770 or lead (Pb) for the sample M 5772, all detectable elements remain at concentrations well below the 10% margin. While the majority of elements at the impurity level are distributed very differently throughout the entire sample set, the presence of silver is clearly noticeable in all of the coins. Here, the values vary between 2.6% and 10.1% with averages of 4% (Trier), 6.44% (Cologne phase I) and 7.66%, i.e., with a slight tendency of larger Ag contents in the coins of the two Cologne series.

4. Discussion

The data set of Figure 5 unambiguously validates the principle functionality of the developed optical setup for specular laser reflectometry applied to Roman coins. The key measure, the reflectometric ratio $\Delta R$, can be detected with sufficiently high precision, i.e., with a measurement error of below 5% and a signal-to-noise-ratio (≡maximum-to-minimum signal ratio) of $SNR>10$ in most of the cases. In particular, $\Delta R$ ranges from 1 up to an extremum of 37 with typical values in the order of 10. As a result, the detected angular scans $\Delta R\left(\theta \right)$ reveal a functional continuous development with a characteristic shape and a pronounced maximum peaking at the angle of $\theta \approx {60}^{\circ }$. All measurements can be reproduced within the error margins and are characterized by the peak angle ${\theta }_{\max }$, the full width at half maximum (FWHM) of the peak and the peak value $\Delta R\left({\theta }_{\max }\right)$ for each of the inspected Roman coins. As expected, the coins show no surface ablation after the measurements, as the laser power (and in particular the power density) is much below the laser-induced damage threshold of copper, see Murphy, Ritter [34]. Taking laser safety, low energy power consumption (<300 W), the use of rechargeable batteries, the possibilities for automatization and reduction of dimension and weight of the setup, and the table-top technologies for rapid prototyping in the field of Open Science, Toschke [32], into account, a transformation of the method towards a handheld measurement tool at excavation sites or in a museum is possible, in principle.

4.1. Reflectometric Ratio

We will first discuss possible differences in the reflectometric ratio $\Delta R$ within the three series, but—more important—between the series themselves—all with regard to the question whether it is possible to correlate characteristic features of the determined experimental data to either Trier or Cologne, i.e., whether it is possible to clearly assign the coins to one of the two mints. For this purpose, we will focus on the comparison of the angular position ${\theta }_{\max }$ where the individual maxima of $\Delta R\left(\max \right)$ are reached and the FWHM values of the peak as well as on the comparison of the absolute values of $\Delta R\left({\theta }_{\max }\right)$ themselves according to Table 4.

Considering all spectra, the variation for ${\theta }_{\max }$ is determined in the range of $56.6^{\circ }<{\theta }_{\max }<65.5^{\circ }$, i.e., within $\Delta \theta =8.9^{\circ }$ for the Trier series, in comparison with $\Delta \theta =5.5^{\circ }$ and $\Delta \theta =5^{\circ }$ for the Cologne I and II series. It is very likely that this difference can be attributed to the fact that the error in the determination of ${\theta }_{\max }$ is smaller for the Cologne series due to the comparably larger $\Delta R$ values. This interpretation is supported by the respective average values ${\overline{\theta }}_{\max }$ that are found at comparable positions, remarkably within a very limited range of $59.4^{\circ }<{\overline{\theta }}_{\max }<{60}^{\circ }$ tantamount to a deviation from the average value as small as $\pm 0.3^{\circ }$ (≡$\pm 0.5\%$). We thus conclude that either the angular position of the maximum ${\theta }_{\max }$ or its variation resemble properties that are characteristics for (at least one of) the three series. A similar conclusion can be deduced from the analysis of the FWHM values of the reflectometric peaks: While the distribution of the values scatters significantly ($\Delta$FWHM = 27.2° for Cologne phase II, 10.6° for Cologne phase I and 6.0° for Trier) and correlates with the $\Delta R$ value, the average values again coincide in a very limited range of 19.0°$<\overline{\mathrm{FWHM}}<$ 21°, tantamount to a deviation from the average of $\pm$1° (≡$\pm 6\%$), i.e., in the order of the FWHM errors. In contrast, at first sight from Figure 5, there is an obvious dependence of the peak value $\Delta R\left({\theta }_{\max }\right)$ on the three series. In more detail, there is a significant rise from Trier (8.5) to Cologne phase I (23.3) to Cologne phase II (37.3) for the respective largest values of $\Delta R\left({\theta }_{\max }\right)$. The same holds for the average values $\overline{\Delta R}\left({\theta }_{\max }\right)$ with an increase of 12.0 to 17. These characteristics are so pronounced and exceeding the errors that the scattering of the distribution of the $\Delta R$ values within each of the three series can be disregarded. In other words, it can be concluded that it is not the individual values of the reflectometric data that allow a statement to be made about the classification, but the statistical consideration of the averaged data of the coin sets. Obviously, statistics based on a set of only five coins each must be classified as less meaningful and of limited validity. In terms of the results of a pilot study, however, this observation motivates further systematic studies with larger coin sets, but also the examination of a possible correlation with the XRF data, as presented below.

4.2. Layer Inspection

The fact that the reflectometric ratio $\Delta R\left(\theta \right)$ is larger than unity for all coins under study (see Figure 5) points to the fact that the signals are not affected by interference phenomena. It is therefore very reasonable to assume that there is no layer on the coin metal surfaces—or layers that are negligible for the analysis—contrary to our model assumption in the illustration of a metal–layer system in Figure 2b). The impact of interference in a surface layer on specular laser reflectometry was originally investigated by Rischmueller et al. in Rischmüller [8] with pretreated (conversion-coated) industrial aluminum sheets as an example. Precisely tailored layer thicknesses were synthesized by a controlled pre-treatment protocol (conversion coating) to uncover the relation between layer thickness d and the peak value $\Delta R\left({\theta }_{\max }\right)$. Figure 8 (adapted from Rischmüller [8]) highlights the discovered changes of the angular dependence $\Delta R\left({\theta }_{\max }\right)$ with layer thicknesses in the range of 36 nm < d < 70 nm (PT1 to PT5). The results for a reference sample (cf. data for ‘Ref’) that does not obey a surface layer ($d=0$) is additionally plotted for comparison.

Qualitatively, all spectra resemble a behavior with an extremum value of $\Delta R\left({\theta }_{\max }\right)$ and starting/end values of $\Delta R=1$ that is similar to the one observed for Roman coins in our study. In particular, we would like to point to the plot of the reference sample (gray shaded, filled circles in Figure 8) that passes through a maximum at $\Delta R\approx 3.0$. However, the plots PT1–PT2 show two distinct characteristics that must be distinguished from our study: (i) the angle ${\theta }_{\max }$ of the respective extremum shifts from 65° to 78° with increasing layer thickness and (ii) the peak value $\Delta R_{\max }$ decreases with increasing layer thickness. The latter particularly falls below the value 1 for the samples PT3–PT5, so that the angular dependence of $\Delta R\left(\theta \right)$ flips from passing through a maximum to passing through a minimum. For PT4 and PT5, the special case of $\Delta R\left({\theta }_{\max }\right)\approx 0$ results. This change in $\Delta R$ is attributed to the interference of wave pairs that arise from the reflection at the layer surface and at the layer–metal interface (cf. Figure 2b). Depending on the layer thickness, the wave pair can be mutually phase shifted so that destructive interference occurs. In the optimum case of a phase shift by 180°, the signal intensity of the s-polarized wave vanishes and $\Delta R$ becomes zero. Due to this effect, it is possible to sense the presence and thickness of surface layers of metals with very high precision. Applied to the results of our study, that show reflectometric ratios with values much larger than unity, the absence of an interference phenomenon must be concluded. It may result either from the absence of a surface layer ($d=0$) in agreement with the reference sample (see Figure 8) or from extremely thick layers larger than the laser wavelength ($d>>\lambda$) or from a surface layer with strong light absorption, e.g., by a patina on the antoniniani/radiates. In the latter cases, the reflection at the layer–metal interface does not reveal sufficient signal intensity for interference. Instead, the angular dependence $\Delta R\left(\theta \right)$ is determined by the Fresnel equations, Hecht [31], and—considering coins of the same metal—the refractive index scales with the angular position of ${\theta }_{\max }$, as it is supported by direct comparison of the data of Table 4 and Figure 7. In this context, the small difference to the refractive index of a European five-cent coin can straightforwardly be explained by minor differences in the metal composition.

4.3. X-Ray Fluorescence

X-ray fluorescence (XRF) analysis identified the metallic silver surface layer of the coins, but also copper as a result of its metallic core. It is thus straightforward to assume a corrosion layer—if at all present—of silver oxide (or silver sulfide), and/or, due to the large concentration of copper, of cupric oxide (CuO) and cuprous oxide (Cu₂O, $n=2.0$). In the presence of an appropriate oxide layer, the lack of an interference signal can be explained, if the layer thickness is much larger than the laser light wavelength of $\lambda =632$ nm, i.e., in the order of micrometers (and more). XRF measurements further indicate only trace amounts of tin on the surface, suggesting that a tin–bronze alloy is unlikely to be present. The exact chemical state of the silver—whether native or part of a compound—remains unclear. However, the visual appearance of sample M 5778 suggests the presence of native silver, which aligns with XRF results indicating the highest silver content among all analyzed samples. Despite the limited number of samples, the XRF results reveal a significant (statistical) trend: coins attributed to the Cologne mint exhibit a higher silver content. This observation is found in agreement with the (statistical) trend of the reflectometric ratio $\overline{\Delta R}\left({\theta }_{\max }\right)$ and potentially indicates the existence of distinct production lines or deterioration. In detail, Figure 9b) shows the averaged values of the reflectometric ratio as a function of the averaged silver concentrations $\overline{\Delta R}\left({\theta }_{\max }\right)\left(\overline{c}\left(\mathrm{Ag}\right)\right)$. Note that respective averaging refers to the three individual sets, i.e., to a number of five coins for each data point. In comparison to the individual dependence $\Delta R\left(c\right(\mathrm{Ag})$ shown in Figure 9a), a linear dependence becomes obvious. This enables the calibration of the reflectometric signals with the XRF results by linear fitting, as depicted by the red line in Figure 9b). The calibration is of particular importance in the view of the application of specular laser reflectometry as a low-cost handheld alternative tool for the analytical inspection of Roman coins at the excavation site and/or in a museum.

5. Conclusions

Our study reveals that specular laser reflectometry turns out to be a useful technique (i) to differentiate sets ($\gg$5) of different coin series via the averaged reflectometric ratio, (ii) to determine the surface silver content of a set of coins by correlation with averaged X-ray fluorescence analysis and (iii) for the determination of the average value ${\overline{n}}_{\mathrm{metal}}$ of the refractive index of a set of coin metals at the air–metal or air–patina interface. Compared with existing analytical techniques (such as X-ray fluorescence), it reveals the important possibility of a transformation into a portable measuring device at excavation sites and/or in a museum. At the same time, it turned out that it cannot be applied for a characterization of individual copper coins and that interferometric signaling fails. It cannot be ruled out that other metals have a suitable coating as it is the case for conversion layers on aluminum, so that an expansion of the study to hydroxide layers of gold or oxidized silver (ancient) coins remains promising. Finally, however, it should be emphasized that all the results shown here are based on the limited series of coins of five samples each and are therefore of a pilot nature. A validation of the obviously strongly statistical methodology with more extensive sample sets is absolutely necessary in the next step, but is very promising.