In this study, we examine the viability of fiber optics reflectance spectroscopy (FORS) as a method for differentiating red chalk drawing media on paper. Our work was carried out in the context of a research project funded by the German Research Foundation (DFG), in which three international partners are studying a group of about 300 drawings at the Staatliche Kunsthalle Karlsruhe (see funding and acknowledgements). These drawings have been reattributed to the Roman workshop of the Italian architect, etcher, and dealer in antiquities Giovanni Battista Piranesi (1720–1778) in 2014 [1, 2, 3]. Among the drawings are many that were executed in natural red chalk. Since this was one of the most versatile drawing mediums used by 18th-century artists, draftsmen, etchers, and architects alike, it is not surprising that it was favored by Piranesi and his circle. Red chalk has a high and varied color intensity and is exceptionally useful in the etcher’s workshop for copying and transferring drawings mechanically or via counterproofing. It was a medium for masters in particular, since its strong coloring ability and fine grain precluded erasure and correction.
The Karlsruhe drawings illustrate the rich variety of red chalk tonalities (Fig. 1), ranging from the bright orange prevailing in many 16th-century drawings to the dark reddish tones of the 18th century, found especially in French drawings, as already identified by Meder in 1919 [4 p121]. In the Piranesi workshop, where several different draftsmen were employed and closely cooperated, this wide range of red-chalk tonalities appears in a narrowly defined chronological and geographical context. This makes the drawings an ideal group for the study of variations in color, especially since they were kept undisturbed in albums since the early 19th century. Of special interest in FORS analysis are color variations that result from the compositional differences of the chalks and the additional color variations that result from the artists’ application techniques. Smudging, whether intentionally performed, or due to wear, lightens the color; a darker color and a smoother line are produced as a result of oil contact from the tracing of a design, or by the moistening and pressing of a drawing during counterproofing, as has been shown in a study of the 18th-century artist Daniel Chodowiecki (1726–1801) . These variations are visually differentiable, and can be photographically documented, but those methods are insufficient for the systematic color-oriented comparison of a large number of drawings in numerous collections located far apart from each other. FORS presents an interesting option because it allows rapid measurements, is portable, in our setup was contact-free, and could be used for the comparison of the Karlsruhe drawings with authenticated drawings by Piranesi in other collections.
1.1 Factors influencing color variation in red chalk
Geologically, natural red chalk can be classified as a type of ocher [6 p99]. The hue and intensity of its color result from its mineralogical composition, especially its contents of iron oxides and hydroxides. Reddish ochers primarily contain hematite, Fe2O3, whereas goethite, α-FeOOH, is the main Fe-bearing phase in yellowish ochers [7 p70]. The total amount of non-tinting components, such as kaolinite, illite, calcite, gypsum, and dolomite have influence on the lightness of ochers . Natural red chalk from a single mineral deposit can exhibit varying hues and intensities [8 p29], thus artists had a range of tonalities to choose from, even before the advent of fabricated chalks. Morphological differences, including grain size and shape of the Fe oxides and hydroxide crystals, along with their density and presence of impurities in the form of other metal ions, also influence their color appearance. For synthetically produced hematite it has been shown that particle shape and size influences reflection properties: Acicular particles reflect light at higher VIS wavelength ranges more intensively than isometric ones [9; depicted in 10 p135, Fig. 6.12]. Furthermore, the hue of hematite changes from yellowish-red to red-purple as the particle size increases from 0.1 µm to 1.0 µm [11 p57, Fig. 4–1], on to a purplish hue for particle sizes of ~ 1.5 µm [12 p183–184].
Natural red chalk has been found to contain hematite platelets, while fabricated red chalk made from artificial hematite features roundish particles; thus a stronger dependency between particle orientation and color is seen in natural red chalk [13, p176]. This dependency became apparent when field-emission scanning electron microscopy (FESEM) was used to study the effects of red chalk drawing techniques on paper. Wet application resulted in a thick, clumped-up deposit on the paper; dry smudging caused small particles to distribute thinly across the paper surface, with small, iron-rich particles directly attached to the cellulose fibers [6 p110]. Historical sources also indicate that the color of a natural red chalk was manipulated by heating or acid treatment, with varying degrees of success [14 p84, 15 p205].
1.2 Elemental analyses of red chalk and red ocher
Mayer and Vandiver [13 p174, p432] studied hematite and red ocher samples of the Forbes Collection of pigment material, as well as red Conte crayons, using X-ray diffraction (XRD) and scanning electron microscopy (SEM). The samples were composed of 50–80% hematite and 20–50% clay, and quartz. Mayhew et al. analyzed five natural red chalks from different geological sites (in Arizona, Burgundy in France, and three regions in Germany, see Appendix Table A1) using XRD to study their different mineralogical compositions [6 p101–103, see Appendix, Table A1]. In two of the five samples no hematite could be detected. The authors suggested this could be due to the small size of the hematite particles present, or to their low crystallinity. FESEM revealed natural red chalk strokes on paper to be composed of larger secondary plate-like silicate particles covered by smaller, iron-containing particles, presumably hematite [6 p105–106]. Mößbauer spectroscopy was used to quantify iron-bearing minerals (goethite, hematite, and clay minerals) in ochers from Roussillon, France . Hematite concentrations of 1.5–43.2% were detected in eight of the nine samples. Colored iron compounds in ocher have also been classified using the Munsell Color Charts , which are easy to use in field work, and colorimetric methods based on the CIELAB system established by the International Commission on Illumination (commonly known by its French acronym, CIE), a colorimetric system that reproduces human color perception. Both systems utilize data derived from visible (VIS) spectroscopy [7, 16, 17, 18, 19, 20].
In UV-VIS spectroscopy, absorption bands in the reflection or absorption spectrum provide information on the electron transitions taking place in the material. These bands are broad and overlap each other, but they can be amplified and better isolated by calculating derivatives of a spectrum . The color of iron oxide pigments was shown to result from the crystal-field transitions of Fe(III) in an octahedral ligand field . For hematite and goethite, the influence of the ligand-to-metal charge transfer is predominant. It takes place in the UV range, with its absorption edge extending into the VIS range [7 p76]. The electron transfer 2(6A1) → 2(4T1) is made possible by the specific shape of the crystal structure of hematite, in particular, by the face-sharing octahedra, which are not found in yellow iron hydroxides. This structural difference is responsible for the shift of the absorption bands toward higher wavelengths, and thus a color shift from yellow to red [22 p1268].
Elias et al.  were able to detect a correlation between the a* (redness) coordinate of CIELAB and the position of the inflection point of the steep slope of the VIS reflectance spectrum of ocher samples. The higher the redness value a* and the content of hematite found in the total amount of iron oxides were, the further the inflection point shifted toward the higher wavelengths. The inflection points differed depending on the hues of yellow, orange, and red ochers, with the red ocher accordingly at the highest wavelengths (575–580 nm).The non-tinting constituents of the ochers containing hematite as the main color-forming compound had little influence on the position of the inflection point, but influenced the lightness reading. While earlier studies aimed at analyzing the physical properties of red chalk or understanding the connection between color and composition of ochers, in this study, we aim to explore the viability of FORS-derived spectra in combination with compositional analysis and PCA and better describe similarities and differences of modern and historic red chalk on paper.