UNMIXING AND MAPPING PIGMENTS: A STATISTICAL APPROACH FOR ART AND ARTIFACTS

Earth materials such as minerals, metals, Fe-oxides, and others have been historically used as pigments on paintings and artifacts. Since each has its own mineralogical and trace element chemistry, bulk elemental composition can be used to determine which were used or mixed by an artist. Non-destructive analysis using X-ray fluorescence (XRF) spectroscopy is a common tool to determine the elemental composition of pigments. Large elemental composition maps from XRF analysis provide an opportunity to study the distribution of pigments in spatial context.

In this study we test the ability of a multivariate factor analysis called positive matrix factorization (PMF) to statistically unmix a large XRF-based elemental dataset into unique factors from a painting made with known endmember pigments. Positive matrix factorization deconstructs a dataset and assigns it to two matrices, factor profiles (amount of each species in a factor) and factor contributions (proportion of each factor in a sample) that when multiplied replicate the input data. In this case the factor profile is anticipated to correlate to a pigment while the contribution would indicate how much of each pigment was present. Eight natural pigments were acquired and characterized by X-ray diffraction and XRF spectroscopy. They were then mixed at known weight percentages of 20:80, 40:60, 60:40, and 80:20 yielding 112 mixtures and analyzed by XRF spectroscopy. Finally, a painting was made using the eight end member pigments. Elemental analysis of the painting was conducted using two instruments: a Bruker Tracer III-SD pXRF spectrometer at a 3 mm by 3 mm resolution and the Bruker Elio at a 1 mm by 1 mm resolution. Concentrations were calculated using calibration to a set of mudrock standards for the Tracer III dataset and fundamental parameter calibration for the Elio dataset. Elemental concentrations and PMF factor contributions for each data point were mapped to allow for spatial comparison to the original painting.

Preliminary results indicate that; 1) elemental ratios of known two-pigment mixtures lie on mixing lines between their endmember pigments, 2) elemental maps correlate to the original picture, and 3) some factor profiles match well to know end member pigments while others appear to correlated to minerals common to more than one pigment.