Reflectance

Pigment identification and tonal variations

From the analysis of the first derivative RIS cube, ten distinct spectral endmembers were identified in the portrait (Fig. 2). The woman’s flesh tones, clearly the most complex portion of the painting with respect to materials mixing and layering, are represented by five different endmembers, constituting five unique mixtures predominantly comprised of ochre pigments of varying amounts mixed with a white pigment to adjust their hues. Her white garments are also represented by three endmembers, as the artist used shading and bright tones to create a 3D effect. RIS analyses suggested relatively straightforward applications in the pink–purple garment, her jewelry, the leaves, and the highlight of the ringlets in her hair, a material which we will see was also used in the flesh tones. The first derivative RIS endmembers (Fig. 2d), their hues, and the constituent painting materials they are composed of, identified through complementary reflectance, luminescence, XRF, and FTIR analyses, are listed in Table 1. Their chemical mapping is visualized in Fig. 2b.

Fig. 2
figure2

a Three-band image of portrait A.N. 32.4 extracted from the reflectance cube. b Spectral angle map of first derivative endmembers extracted (d). The equivalent reflectance spectra are in c

Table 1 First derivative endmember results from the RIS studies, for which materials assignment is attributed by complementary imaging, FORS, XRF, and FTIR analyses

The spectral endmembers (Fig. 2c, d) represent various intimate mixtures containing a hematite-rich red ochre, a goethite-rich yellow ochre, natrojarosite (((text{Na})text{Fe}^{3+}_{3}(text{OH})_{6}(text{SO}_{4})_{2})), madder lake, copper (Cu(II)) carboxylate, and lead white (cerussite/hydrocerussite). Hematite features a characteristic inflection point at 585 nm and absorption at 660 nm ((^{6}text{A}_{1text{g}}(^{6}text{S})) (rightarrow)(^{4}text{T}_{2text{g}}(^{4}text{G}))), a peak maximum at 750 nm and broad NIR absorption at (sim) 870 nm ((^{6}text{A}_{1text{g}}(^{6}text{S}))(rightarrow)(^{4}text{T}_{1text{g}}(^{4}text{G}))). Goethite is identified by a shoulder at 445 nm ((^{6}text{A}_{1text{g}}(^{6}text{S}))(rightarrow)(^{4}text{A}_{1text{g}}),  (^{4}text{E}_{text{g}}(^{4}text{G}))), an inflection at 550 nm and absorption at 670 nm, as well as a peak maximum at 765 nm and a broad NIR absorption centered at 925 nm ((^{6}text{A}_{1text{g}}(^{6}text{S}))(rightarrow)(^{4}text{T}_{1text{g}}(^{4}text{G}))) [62, 63].

First derivative reflectance spectral analysis helped to determine endmembers representing different mixtures of primarily red and yellow ochre pigments used for multiple flesh tone hues in the woman’s face and neck. The large peaks’ maxima from (sim) 550 to 590 nm correspond to the inflection points of the ferric oxide/oxyhydroxide minerals in the pigments, which can be distinguished by comparison to reference reflectance spectra. The secondary peaks from (sim) 615 to 750 nm provide absorption information corresponding to those at 660–670 nm in the reflectance spectra. Smaller secondary peaks can indicate high amounts of pigment, causing an absorption saturation, or mixtures with a black pigment.

The artist applied extensive shading on the woman’s facial features using a range of darker tones, such as her eyelids, the sides of her nose, her ears, and neck, as well as her forehead, tip of her nose, and chin. The hues in her face comprise deep red-brown, light pink, yellow, and white tones. First derivative endmembers 1, 4, 6, 9 and 10 show varying amounts of a red ochre, a yellow ochre, natrojarosite and lead white to decorate and accentuate certain areas of her face. Endmember 1, found in forehead and facial shading, has spectral features at 456 nm (shoulder), 582 nm (inflection), 670 nm (absorption), 752 nm (peak maximum), and 901 nm (NIR absorption), which clearly shows a mixture of hematite-rich red and goethite-rich yellow ochres. The white pigment was identified by XRF as lead white due to the presence of Pb L(_{alpha }) and L(_{beta }) characteristic X-ray energies measured at 10.55 and 12.61 keV, respectively, and the M(_{alpha }) emission at 2.34 keV. This lead white pigment is believed to be a mixture of cerussite ((text{PbCO}_{3})) and hydrocerussite ((text{Pb}_{3}(text{CO}_{3})_{2}(text{OH})_{2})), produced by placing lead sheets above acidic baths that are sealed for extended periods of time to induce corrosion that produces both lead white phases [27, 64]. Though the characteristic OH stretching feature of hydrocerussite was absent at 1449 nm in the FORS spectra [65, 66], it is quite rare for natural cerussite to be used. Natrojarosite, a Na-rich jarosite, was identified by a small characteristic absorption due to the electronic transition at (sim) 433–435 nm ((^{6}text{A}_{1text{g}}(^{6}text{S})) (rightarrow)(^{4}text{A}_{1text{g}})). FORS and XRF confirmed the presence of a Na-rich jarosite mineral due to the lack of K in the XRF spectra and the presence of the 1543 nm first O–H stretching overtone in the infrared portion of the FORS spectra [67]. The difference in radii of Na vs K as well as their charge/radius values also manifest in diagnostic shifts in the absorption spectra, such as the feature located at 433 nm, which is indicative of natrojarosite [68, 69]. Natrojarosite has been previously identified in other mummy portraits as well as in Hellenistic and Roman mural paintings and funerary stelae [10, 47].

Endmember 6 contains red and yellow ochres, mixed with lead white (inferred from Pb peaks in XRF data), to produce a white-pink flesh tone but presents a unique mixture based on the spectral features’ positions at different wavelengths compared to endmember 1. Endmember 4, which maps to the olive green-toned ringlets in the hair braid across her forehead and the proper right eyeline under her eyebrow, is a mixture of yellow ochre, lead white, natrojarosite (identified by a 435 nm narrow absorption), and possibly a black pigment to darken the hue. The final flesh tone, mapped by endmember 9 on her ear and proper left eyeline, is a deep red hue produced by a rich application of red ochre.

Natrojarosite was also found throughout the white garments, in different tones mapped by endmembers 2, 7 and 8, mixed with lead white and Egyptian blue (the latter identified by luminescence mapping, to be discussed in the next section). Regions appearing brighter such as noticeable brush strokes and dots show stronger signatures of natrojarosite (endmember 2). Weaker signals were found in the veil and the earring of the woman. The white garments also feature dark and yellow-toned stripes, most likely to create shadows and highlights imitating the appearance of the knot and folds in the cloth. The yellow stripes were mapped by endmember 8, while the darker stripes were mapped by endmember 7, which has an (sim) 630 nm absorption in the reflectance spectrum. Because the white hues were produced by a mixture with natrojarosite (which has an absorption at (sim) 640–650 nm), lead white, and Egyptian blue, the complexity of the intimate mixture does not permit the latter’s identification based only on a reflectance signature.

The orange-red bole, which was used as a preparatory layer and outline decoration for the gold jewelry, was mapped by endmember 10 (also found in small amounts in the flesh tone) which contains a mixture of red and yellow ochres, as well as a subtle presence of natrojarosite. Endmember 5, which maps to the green leaves over the pink and white garments, features a spectral profile similar to that of copper carboxylate, most likely produced by mixing copper acetate (i.e. verdigris) with heated beeswax. FTIR analysis on a sample acquired from green applied over the white garment identified verdigris by characteristic bands at 2924, 2853, 1591, 1555, and 1417 cm(^{-1}). Thus, verdigris appears to be the source material for the copper carboxylate pigment.

Endmember 3, which identified madder lake by its double absorption at 514 and 547 nm, was mapped to the pink–purple garment; however, it will be shown that this did not map all applications of the pigment in the portrait, due to low amounts, as well as being mixed and layered with other pigments, thus masking/modifying its characteristic reflectance signature.

Two black colorants were distinguished in this painting. The wooden panel was first primed with a black wash containing P and Ca that suggests the use of bone black. The dark tones in the painting, such as the background and the woman’s hair, contain high levels of Pb, possibly due to a mixture of lead white as there are white/grey tones both in the hair and background, and Fe. The reflectance values in the VNIR stay primarily under 5–7% of the total signal, suggesting that a carbon-based black is the primary component of the black paint. The black pigment was also used for the eyes and eyebrows, layered over the deep red pigment to soften the black tone and produce a range of brown to red hues.

Finally, wax was confirmed in the portrait as a binding media in the FORS spectra acquired from various hues, identified by the position of (text{CH}_{2}) asymmetric/symmetric plus bending fundamental modes at 2311 and 2352 nm, as well as the first overtones of (text{CH}_{2}) asymmetric/symmetric stretching at 1730 and 1763 nm [70,71,72,73] (Fig. 3). FTIR further confirmed the presence of beeswax with characteristic bands at 2954, 2847, 1735, 1712, 1472, 1463, 1175, 730 and 720 cm(^{-1}). The visual characteristics of the binding media also suggest the use of beeswax, and this result is consistent with technical analyses of other mummy portraits that have been well characterized to have been painted with beeswax [47, 74].

Fig. 3
figure3

Characteristic absorptions in the short-wave infrared at 1730, 1763, 2310, and 2352 due to (text{CH}_{2}) bending and stretching modes identify beeswax as the binding medium

Gold and white applications

The gold jewelry and the lead white applications in the veil and eye were challenging to extract representative endmembers to map using the first derivative, which is sensitive to subtle differential changes in the reflectance profile. The specular reflection, or glints, off the gold leaf, which was applied in high relief does not have any spectral information. The gold jewelry was more robustly mapped by a diffuse reflectance endmember showing a broad reflectance (Fig. 4a, b) and characterized by XRF as an alloy of gold and silver, most likely electrum. While VNIR spectral mapping was not effective for lead white, due to the very thin application of the veil and mixtures with other pigments, a first derivative eigenimage produced from the MNF transform emphasized the applications of white in the portrait (Fig. 4c), highlighting features such as the proper left eye and emphasized the veil wrapping around the body of the woman at the bottom of the portrait, giving an enhanced sense of dimensionality to the painting. Additional details such as the fabric mesh of the veil are clearly visible, and it appears that the veil itself has small adornment features, appearing both on the top of her head and along the draped edge on her proper left side.

Fig. 4
figure4

a Mapping of gold applications in the portrait using the endmember in b; c MNF eigenimage that emphasizes white applications in the portrait

Luminescence

First derivative analysis of the reflectance data cube provided identification and a preliminary mapping of madder lake. The robustness of this mapping is limited, though, in regions where its reflectance signature was masked or convoluted by other spectral signatures. The emission profiles, however, once corrected for self-absorption and absorption by other pigments, should remain relatively unchanged by the rest of the pigment palette identified in Table 1, as those materials do not have visible-induced visible photoluminescence. RIS analyses were also unable to reliably identify Egyptian blue.

Endmember extraction from the corrected LIS data cube yielded two distinct endmembers: one featuring a peak emission at 605 nm (EM 1), corresponding to madder lake, and the other in the NIR at 888 nm (EM 2), attributed to Egyptian blue (Fig. 5a). In the portrait there is a pseudo-emission signal in the visible wavelength range not associated with any luminescent pigment that is roughly proportional to the reflectance of the portrait, possibly due to the presence of stray light. Though it does not interfere with Egyptian blue’s emission signal, it does slightly compromise the fluorescence profile of madder lake. We applied linear spectral unmixing to understand how Egyptian blue, madder lake, and the background emission contribute to the total luminescence signal in the image cube. To do so, the Egyptian blue endmember was first corrected by removing the fluorescence peak in the visible wavelength range, which was ascribed to stray light. The two pigment endmembers and a manually-selected reference background emission spectrum (Fig. 5a) were then linearly unmixed to map the distribution of the background emission, madder lake, and Egyptian blue (Fig. 5b–d).

Fig. 5
figure5

a Endmembers used for linear unmixing. EM 2, corresponding to Egyptian blue, was corrected to remove the stray light background. b Emission mapped in the portrait using the background fluorescence endmember. c Madder lake abundance map produced from the linear unmixing of EM 1. d Egyptian blue abundance map produced from the linear unmixing of corrected EM 2

The LIS abundance map for madder lake (Fig. 5c) shows a broader pigment application compared to the map obtained from the RIS endmember for madder lake. The pink garment, made up of different hues of light and dark pink and purple with varying amounts of white and featuring regions of deterioration, is now more comprehensively mapped. Furthermore, the earrings are better characterized compared to the RIS first derivative mapping for madder lake. A subtle feature of madder paint also appears in the proper right eye of the woman.

The application of Egyptian blue was initially inferred by a visible-induced NIR photograph produced by the Walters Art Museum (Fig. 6a). The photograph shows a strong luminescence arising from the white garments and the green leaves on the pink–purple garment near the woman’s proper left shoulder. There is also a weaker but still distinct luminescence in the outline of the figure’s face, in the proper left cheek, and in the upper lip and chin. The linearly unmixed abundance map for Egyptian blue shows emission from the white garments and the green leaves (Fig. 5d). By relying on a spectral signature rather than total light capture (as done in multiband photography), a more reliable mapping and interpretation of the pigment’s application by the ancient artist to paint the white clothing and the leaves is available; in fact, the green leaves appear to have a stronger mapping in the abundance map than what was identified in the NIR photograph. LIS also overcomes the challenge of attempting to map this pigment using RIS data, as the amounts were too low in the pigment mixtures to reliably assign its absorptions in the visible. However, luminescence mapping within the facial region was less successful, most likely due to the extremely low amount of Egyptian blue.

Fig. 6
figure6

a Visible-induced NIR luminescence photograph (Walters Art Museum). b Combined maps (abundance map for blue endmember, spectral angle map for black endmember) for the second derivative Egyptian blue endmembers in c, overlaid with 10% transparency onto the portrait to show luminescence distribution. d Spectra from mapped pixels in the woman’s face in b, designated by the horizontal arrows, confirm that the luminescence seen in the photograph in a is indeed Egyptian blue, due to the 897 nm spectral feature, and able to be mapped by LIS

To further access weaker emission signals, a second derivative calculation was applied to the LIS cube, and the analyses were localized to the NIR in two spectral ranges: 800–975 nm and 850–1000 nm, where the data contains little to none of the stray light. Two endmembers were selected: the first endmember was found using the SHW (800–975 nm), and the second endmember was found manually from an ROI in the woman’s face (850–1000 nm). The first endmember, mapped in blue pixels in Fig. 6b using an abundance map to show the variation in amount, corresponds to the white garments and leaves. The local minimum for the NIR emission in the second derivative appears at 886 nm, which closely matches the peak emission value of EM 2 applied in the linear unmixing, which accounts for this similar mapping behavior. However, the green leaves are mapped more comprehensively than what was seen in Fig. 5d.

The second endmember, extracted from the facial region, features a weaker, shifted emission at 897 nm which was able to map, in white pixels, some Egyptian blue in the upper lip, the chin, the proper left cheek, and the outlining of the proper right side of her face. This mapping was performed as a spectral angle map to give all pixels equal intensity to show the distribution more clearly as the amount is quite low in the face. To confirm that the mapping’s bright spots in the face (indicated by the red, green, and purple arrows) were Egyptian blue, their associated spectra were extracted and are shown in Fig. 6d. Comparison of these spectra to the second endmember show similar profiles with the second derivative feature of NIR emission at 897 nm.

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