Correlated x-ray fluorescence and ptychographic nano-tomography on Rembrandt’s The Night Watch reveals unknown lead “layer”

The Night Watch, one of the most famous masterpieces by Rembrandt, is the subject of a large research and conservation project. For the conservation treatment, it is of great importance to understand its current condition. Correlated nano-tomography using x-ray fluorescence and ptychography revealed a—so far unknown—lead-containing “layer”, which likely acts as a protective impregnation layer applied on the canvas before the quartz-clay ground was applied. This layer might explain the presence of lead soap protrusions in areas where no other lead components are present. In addition to the three-dimensional elemental mapping, ptychography visualizes and quantifies components not detectable by hard x-ray fluorescence such as the organic fraction and quartz. The first-time use of this combination of synchrotron-based techniques on a historic paint micro-sample shows it to be an important tool to better interpret the results of noninvasive imaging techniques operating on the macroscale.

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Supplementary Text Figs. S1 to S16 Table S1 Legend for movie S1 References
Other Supplementary Material for this manuscript includes the following:

Additional information samples of the ground of The Night Watch
Figure S1 shows the painting The Night Watch by Rembrandt van Rijn.The white circles indicate the locations where paint samples were taken during Operation Night Watch.These samples are used to make a comparison of the ground layer in these samples.

Inorganic composition of Rembrandt's quartz-clay ground
The material used for the ground of The Night Watch consists mainly of quartz and clay minerals.In Table S1 the identified components of the quartz-clay ground are listed, together with the method of identification.Iron is part of the ground due to its presence in different clays.Iron is also a component of the mineral goethite (α-FeO(OH)).MA-XRD on the painting confirmed the presence of goethite in areas where the ground is exposed.Furthermore, SR--XRD studies performed on paint samples at beamline P06 showed the presence of celadonite (K(Mg,Fe 2+ )(Fe 3+ ,Al)[Si4O10](OH)2, mica group mineral), a component of the pigment green earth.Fig. S2f shows the 3D rendering of the potassium (K) signal collected by tomographic XRF.Potassium is heterogeneously distributed throughout the main part of the sample volume.Potassium is a very common element in minerals and can substitute e.g.sodium atoms in albite (feldspar), a mineral detected in Rembrandts' ground by MAand SR--XRD studies.The newly formed mineral is called K-feldspar or microcline.S2c shows the 3D rendering of calcium in the sample.Calcium is mainly present as gypsum and calcite; this mineral was identified with both MA-XRD as well as SR--XRD.Calcite is often used in paints as a filler next to being employed as a white pigment.In many soils and clays, calcium carbonates are also present.Either the calcite and gypsum were added to the clays used for the ground layer or were already present in the clay used for the ground.MA-XRF results showed the presence of titanium in areas where the ground was exposed.With MA-XRD, no crystalline components containing titanium were found at the surface of the paint; however, SR--XRD studies performed on cross sections of The Night Watch demonstrate that rutile or anatase were present in the ground.Whereas quartz and albite (NaAlSi3O8) were always identified in the ground layer samples, this was not the case for anatase or rutile (TiO2).The 3D rendering of titanium in Fig. 2b shows that titanium is definitely present in the ground.We can distinguish different sets of particles: small spherical particles, small elongated rod-like particles and larger particles.As the XRF set up used in this study is not intended/optimized to detect light elements, we can unfortunately not correlate the titanium distribution to that of oxygen.Looking into the correlation of iron with titanium, we only found very few particles showing a correlation (See Fig. S3).In these particles, also some manganese is present.The correlation between these elements suggests that this might be ilmenite, a titanium-iron oxide mineral (FeTiO3), containing considerable amounts of Mn.Combined SEM-EDX and XRD research conducted in previous research identified ilmenite in many quartz-clay grounds used by Rembrandt, however not in the samples from The Night Watch.Manganese is detected in low intensity in many particles that also contain one or more of the main elements.A small number of particles of zinc and copper are detected.

Particle size distribution of quartz and aluminosilicate particles
As described in the main text, the ptychography results were used to segment the quartz and aluminosilicate particles.Fig. S4 shows the separate particles in randomized colors.Fig. S5 shows the particles size distribution in voxels.Fig. S10a shows the distribution of lead stearate in sample SK-C-5_003 as collected by SR-µ-XRD.This data was measured at beamline ID13 during beamtime allocated to BAG proposal HG-172.A scan of 95 by 130 m was collected with a dwell time of 10 milliseconds and a step size of 1 m in both directions with an energy of 12.95 keV.It should be noted that the XRD data were collected after the tomographic measurements.The XRD map reveals the absence of lead stearate within the area covered by the tomography measurements.We attribute the disappearance of lead stearate to the high dose of radiation the material was exposed to during the X-ray tomography scan (more than 48 hours) at the synchrotron.Lead soaps are prone to decompose after (extensive) exposure to highly intense synchrotron X-ray beams.This was previously observed by the authors in a paint sample of Girl with a Pearl Earring by Johannes Vermeer (1665, Mauritshuis, The Hague) (2).Distortions or movements of the sample due to instability or beam-induced changes were checked by comparing the projection at 0 to the projection at 180 degrees and the projection at 180.5 degrees with the one at 360.5 degrees (see Fig. S11).While slight tilting of the sample was noted, especially during the first 180 scans, no significant (elemental) changes of the sample were observed.The small differences can mainly be related to a small error in the alignment of the images, detector noise and the use of two detectors at the opposite sides of the sample.The changes are more prominent for the comparison of the sample after the first 181 scans (see Fig. S11 a and  c).This might also be explained because after 159 scans, the measurements had to be stopped for about 12 hours due to technical maintenance of the synchrotron electron beam.During this time, the hutch was opened and the sample might have shifted slightly on the stage.This probably accounts for most changes observed between 0° and 180°.Fig. S11b and d show that less changes are observed when comparing the scan at 180.5° and 360.5°.

Limitations of correlative ptychography and XRF tomography
The described technique comes with some limitations for it to become a more commonly used analytical technique.At this time, the measurements are time consuming and results in a large amount of raw data.The ptychographic reconstructions require a lot of computing power.Therefore, measurements can only be done on a limited number of samples and relatively small sample volumes.Beam-induced alterations can also occur during the tomography experiment due to long exposure times of the sample to the beam.The results of such an analysis for the sample in this study can be found in the supporting information (Fig. S11 section 'Beam Damage').No notable elemental changes due to the beam were observed, but we did observe some loss of crystallinity.For answering certain research questions, transmission X-ray microscopy might be an alternative for visualizing a complete sample in 3D in comparison to ptychography.TXM requires less post-collection data processing.Another option could be to repeat the XRF study of a sample at both a hard and soft X-ray beam line to obtain information from low Z elements.A downside would be that the sample must be much smaller to avoid over-absorbance of the beam in the soft X-ray regime.To speed up the measuring time, fewer angles could be measured at a loss of tomographic resolution.If a quantification of the electron density is desired, we would advise to scan the sample on a pin instead of inside an embedding medium.To identify components with similar elemental composition, correlated tomographic XRD could be collected.We expect that ongoing developments in synchrotron brilliance, automatized data processing and increasing computing power will overcome these limitations in the (near) future.
Fit model XRF Figure S12 shows the sum XRF spectrum of all pixels collected in one angle (0°) during the XRF tomography together with the fit model created in PyMCA.(55)

Segmentation of ptychography data
In Figure S13, the result of one of the ptychography projections after the iterative reconstruction is shown.To the left and right of the sample the embedding medium can be seen, while the center of the image shows the strong intensity originating from the sample.In conservation/heritage science it is common practice to embed the small and precious paint fragments in a small resin block.In this study, Technovit 2000LC was used.This methyl acrylate cures with the use of blue light.Due to the presence of this embedding medium, we do not have air in the measured area which can be used as background.Fig. S14 shows the histogram of the ∂ (the refractive index decrement, which represents the change in phase velocity, see Wittwer et al. (11) for more detailed information) of the 3D dataset shown in Fig. 5a.There are no distinguishable Gaussians in the histogram that would relate to different components based on a difference in electron density between materials.Different efforts to use thresholding to differentiate the lower part of the electron density to separate the contribution from the embedding medium, the oil used for the paint, and conservation treatment materials such as the wax resin lining were unsuccessful.This was probably due too similar electron densities of these organic materials.Additionally, the embedding material absorbs part of the X-rays before they reach the samples and measuring an embedded sample is therefore not the best procedure for ptychography, especially if you want to look at very subtle differences in electron density as is the case for the organic fractions.

Estimation of spatial resolution of the 3D reconstructions
To estimate the spatial resolution of the reconstructed 3D volumes, line profiles of sharp edges on ortho slices of both the 3D XRF data set and ptychography data set were measured.A Gaussian profile was fitted over the change in intensity of the grey values along the line.This was done by using an in-house developed MATLAB script.More details on the method can be found in Bossers et al. (15) and Wise et al. (19) Figure S15 shows the spatial resolution estimation of the XRF results, calculated on sharp edges within ortho slices of the copper (Fig. S15a) and strontium (Fig. S15b) data sets.These elements were selected due to their high contrast in particles and low contrast in the background, unlike an element such as lead of which low concentrations are present in many of the voxels in the 3D data set.The achieved average 3D spatial resolution for the XRF data set was 591 nm. Figure S16 shows the spatial resolution estimation of the ptychographic reconstruction.Two line profiles were measured in the central ortho slice from the 3D reconstructed ptychography dataset.The achieved average 3D spatial resolution of the ptychography dataset was 595 nm.

Movie S1.
3D rendering of Pb (L3) distribution in yellow, Ca (K) distribution in cyan, Fe (K) distribution in red, Ti (K) distribution in green and ptychographic signal in grey.

Figure S3 .
Figure S3.Correlation study between iron, titanium and manganese.a) Correlation plot with Fe-K on the X axis and Ti-K on the Y axis.The cluster of voxels with a correlation between Fe and Ti is encircled in dark blue.b).Correlation plot with Fe-K on the X axis and Mn on the Y axis b) 3D rendering of the Fe K signal in red.The orange circle indicates the ilmenite particle.c) 3D rendering of the four clusters indicated in a. e) Zoom in on the ilmenite particle in the orange circle, showing the distribution of Mn in purple, f) Ti in green and g) Fe in red.

Figure S4 .
Figure S4.Segmentation of the quartz and aluminosilicate particles in 3D.a) Lead distribution in grey and segmented quartz and aluminosilicate particles in randomized colors b,c) 3D rendering of quartz and aluminosilicate particles.

Figure S5 .
Figure S5.Distribution of particle size of quartz and AlxSiyMgz , excluding three outliers with a volume above 75000 voxels.Each voxel is 200 x 200 x 200 nm.

Figure S7 .
Figure S7.Presence of red lead confirmed with Raman spectroscopy.a) Light microscopy image of bottom of sample (SK-C-5-093) that was collected after the knife attack in 1975 on The Night Watch(37) b) The Raman spectrum collected on the red particles is shown in blue and a reference spectrum of red lead is shown in red.
Figure S8.Lead protrusions (white spots) observed on the surface of the painting under normal light 5 µm photography.

Figure S9 .
Figure S9.Formation of lead carboxylates after introduction of a wax resin mixture to lead oxide.The lead carboxylate band is located between 1490-1670 cm -1 .The time series is shown from dark blue to yellow and spans a period of 70 hours at a temperature of 40 degrees Celsius.

Figure S11 .
Figure S11.Study into beam-induced changes.2D fitted elemental distribution of the sample at 0° (red) and 180° (green) for a) iron, c) lead andat 180.5° (red) and 360.5° (green) for b) iron and d) lead.A small misalignment can be seen after 180-degree rotation in both the Fe-K and Pb-L3 distribution.

Figure S13 .
Figure S13.Reconstructed 2D X-ray ptychography projection which resulted after 1000 iterations using the ePIE algorithm(11).At the edges of the image, information is lacking for a correct reconstruction.Left and right of the sample signal from the embedding medium is observed.The contrast of the image is enhanced for clarity.

Figure S14 .
Figure S14.Histogram of the ptychography data in Fig. 5a.The x-axis shows the ∂ (refractive index decrement).The y-axis shows the number of counts (in logarithmic scale).

Figure S15 .
Figure S15.Study of the 3D spatial resolution of the XRF dataset.a) Reconstructed ortho slice of the Cu-K data set in XZ orientation (voxel size 200 nm).The green box shows a zoom-in of the area where a line profile (red line) was measured.The graph on the right shows the data points on this line and the fitted Gaussian profile in red, the calculated half width half maximum (HWHM) is taken as an estimation of the achieved resolution of the 3D dataset.b) Reconstructed ortho slice of the Sr-K data set in XY orientation (voxel size 200 nm).The blue box shows a zoom-in of the area where a line profile (red line) was measured.The graph on the right shows the data points on this line and the fitted Gaussian profile in red, the calculated half width half maximum (HWHM) is taken as an estimation of the achieved resolution of the 3D dataset.

Figure S16 .
Figure S16.Study of the 3D spatial resolution of the ptychographic dataset.On the left a reconstructed ortho slice of the ptychography data set in XY orientation is shown (voxel size 45.3 nm).The blue box shows a zoom-in of the area where two line profiles (red and orange line) were measured.The graphs on the right show the data points on these lines and the fitted Gaussian profile in red and orange, the calculated half width half maximum (HWHM) is taken as an estimation of the achieved resolution of the 3D dataset.

Table S1 .
Composition of the quartz-clay ground, identified as part as Operation Night Watch and previous analytical studies on The Night Watch