Determination of the sequence and thicknesses of multilayers in an easel painting

doi:10.1016/S0168-583X(99)00484-X

Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms

Volume 155, Issue 4, September 1999, Pages 447-451

https://doi.org/10.1016/S0168-583X(99)00484-X Get rights and content

Abstract

In this article we propose the application of an improved algorithm to determine the sequence and the thicknesses of paint multilayers. The concentration profiles of colour pigments are deduced using the PIXE technique for different proton energies on the AGLAE accelerator (LRMF, Le Louvre). As an example, this technique has been applied to an actual easel painting worked out at the Ecole du Louvre. The sequence of the paint layers was unknown to the experimentalists, but had been noted by the painter in the course of her work. The mathematical procedure and some results are presented, which are fully confirmed by the artist.

Introduction

In the framework of her studies in History of Art at the Ecole du Louvre, one of us (Guilló) [1] has worked out a painting designed to be used for testing various physical techniques of characterisation: it exhibits several features which are to be experimentally and non-destructively determined, such as underlying inscriptions, pentimenti, more or less thick layers of varnish, etc. Hence a succession of investigations using X-rays, infra-red or ultra-violet radiation,… have been performed at the Laboratoire de Recherche des Musées de France in the Palais du Louvre. When making her work, the painter had noted the stages of its achievement, and especially the order of the paint layers at a number of well defined locations.

Our team has already published several articles [2], [3] showing how PIXE analyses performed with protons of various energies allow one to determine the sequence of pigments in the paint matter, that is the succession of `elemental' paint layers, and, in a second stage, the concentration profiles of these pigments, i.e. the thicknesses of these layers. Pigment mixtures can be evidenced using the same techniques. In the present work, we have applied this method to determine the order and the thicknesses of the paint layers so as to confirm the validity of the mathematical techniques we have proposed. It is useless to stress the advantages which can be gained from the knowledge of these features: they are an important source of information about the artist’s technique. The results are complementary to those given by the classical methods used at the LRMF (see above).

Section snippets

Analysis of the elemental paints used by the artist

On the painting we have tried to define several unmixed colours used by the artist: red, blue, black, chestnut, yellow etc. Elemental analyses at low proton energy (1 MeV) have been performed at several selected points. This energy was low enough for the major elements in the surface layer to be the only detectable ones: owing to surface absorption, the elements in the underlying layers are far less visible. Table 1 and Fig. 1 show such a list of major elements which can be regarded as colour

Sequences of paint layers

We have measured the number of X-rays emitted by the elements detected in the material. The X-ray emission is induced by protons of variable energy E_p. A previous paper [2] has shown that the slope of the curve $ln N_{x} =f(E_{p})$ is, after a correction which takes into account the atomic number of the considered element, an increasing function of the thickness of the material under which this element is located. In Ref. [2] we have established that the lower the proton energy used for the experiments

Determining the layer thicknesses

The concentration profile function C(x) can be resolved on a basis φ_i(x) as $C(x)= ∑ i C_{i} φ_{i} (x).$ In Eq. (1) this yields $N_{x} = ∑ i C_{i} ∫_{0}^{∞} σ(E) exp (−μx/ cos θ)φ_{i} (x) d x.$

So as to get easier computations, we choose for φ_i(x) Gaussian functions centered at various given depths. The widths of these Gaussians must be as small as possible, but not less than the distance between two consecutive ones. Through analyses performed with various proton energies $E_{j}, m$ amplitudes C_i can be deduced from the measurement of N_j numbers

Discussion and conclusion

Using Table 1 and Fig. 3, we may consider that, at the point C, the colour sequence consists of chestnut, possibly mixed with black, on a yellow layer followed by a black one on the canvas. The proportion of black, marked by Fe only, seems to be weak as indicated by the ratio of the numbers of X-rays emitted by Fe and Mn. The Fe and Mn profiles are clearly somewhat distant from the surface: this suggests the presence of a slight surface layer of varnish which cannot be detected by PIXE and

Acknowledgements

We are most indebted to A. Roquebert, who proposed this collaboration, and to J.P. Mohen, who gave us the opportunity of using the AGLAE accelerator facility.

References (7)

G. Lagarde et al.
Nucl. Instr. and Meth. B
(1997)
I. Brissaud et al.
Nucl. Instr. and Meth. B
(1996)
P. Midy et al.
Nucl. Instr. and Meth. B
(1998)

There are more references available in the full text version of this article.

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PIXE analysis of historical paintings: Is the gain worth the risk?
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Citation Excerpt :
The comparison of the spectra allows to deduct the depth profiles of the paint layer stack. The theoretical grounds of this technique were early established [8] and tested on artificial paint layer sequences [9,10]. One of the first applications of differential PIXE to a historical painting was a dual energy study at 2 and 4 MeV of the “Christus und Maria Magdalena” attributed to Cranach the Elder (1515–1520) [11].
The PIXE analysis of easel paintings constitutes a challenging task. Despite recognized merits and a few emblematic applications, PIXE has never been routinely applied to these fragile, complex and precious targets. The present work discusses the place of PIXE in the study of easel paintings and opens up perspectives for a more systematic usage of this analytical technique. Progress achieved since decades in the implementation of PIXE to study such fragile cultural heritage artefacts is reviewed, notably at the LABEC laboratory in Italy and at the AGLAE facility of the C2RMF in France. Two specific techniques developed for paintings are detailed and exemplified on Renaissance painting masterpieces: differential PIXE for paint layers depth profiling and multi-scale elemental mapping for the imaging of pigment distribution. Beam-induced damage, a major concern, notably depends on the employed beam fluence in particle/cm² or μC/cm². After recalling previous works on damage induced in chemical products comparable to pigments, we present the behaviour under different fluences of protons of a few MeV (1–300 μC/cm²) of targets having high resemblance to historical easel paintings: pellets of specially synthesized lead white pigments, layers of lead white mixed with linseed oil and areas containing lead white of two 19th century paintworks. The results shed new lights on the behaviour of paintworks under the beam and pave the way to strategies for damage mitigation. In particular, the lowering of PIXE performance induced by the decrease of the beam fluence sets a trade-off between risk of damage and gained information which also impacts the PIXE scanning protocol for paintings. As an illustration of an adequate adjustment of this balance, we report the exploratory application of PIXE mapping to a large area of a 19th century easel painting without damage. The recorded elemental maps are compared to elemental maps collected on the same area using laboratory-based scanning XRF.
Concentration profiles in paint layers studied by differential PIXE
2008, Nuclear Instruments and Methods in Physics Research, Section B: Beam Interactions with Materials and Atoms
Citation Excerpt :
Generally they are two methods of changing the irradiated depth: by tilting the sample with respect to the beam [1–3], which changes the projectile impact angle, and by varying the projectile energy [4–6]; for larger impact energies, projectiles penetrate deeper into the target. Depth–resolution measurements with PIXE have been performed on several materials: paint layers (studying their sequence and thickness) [7–11], glasses (measuring the weathering-depleted layer) [2] and metals (plating and surface enrichment of nobler metals) [12–18]. For most of applications, variation of the projectile energy was preferred to the tilting method, which requires precise mechanical adjustment [1]; it is also impractical for large objects like oil paintings.
Differential PIXE measurements varying the proton energy were used to probe the concentration profiles of metal-based pigments in paint layers. The algorithms developed earlier for metal targets were improved and enhanced to include light elements; the necessary information on chemical compounds has to be provided by complimentary methods. The de-convolution method employs slicing the target into layers characterized by mean production depths; the matrix inversion is replaced by a min χ² problem. Two different methods of normalization are used: setting the sum of weight fractions of particular compounds to unity, and direct measurements of the projectile number, in our case through the argon line excited in the air. The efficiency of the two methods was compared for paint layers in frescoes, showing that smother concentration profiles are obtained using the measured proton numbers. Conversion of the layer areal densities into geometrical thicknesses is discussed.
3D Micro-PIXE at atmospheric pressure: A new tool for the investigation of art and archaeological objects
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The paper describes a novel experiment characterized by the development of a confocal geometry in an external Micro-PIXE set-up. The position of X-ray optics in front of the X-ray detector and its proper alignment with respect to the proton micro-beam focus provided the possibility of carrying out 3D Micro-PIXE analysis. As a first application, depth intensity profiles of the major elements that compose the patina layer of a quaternary bronze alloy were measured. A simulation approach of the 3D Micro-PIXE data deduced elemental concentration profiles in rather good agreement with corresponding results obtained by electron probe micro-analysis from a cross-sectioned patina sample. With its non-destructive and depth-resolving properties, as well as its feasibility in atmospheric pressure, 3D Micro-PIXE seems especially suited for investigations in the field of cultural heritage.
Differential PIXE for investigating the layer structure of paintings
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This paper reports an example of how the differential PIXE technique can be successfully applied to the investigation of wood or canvas paintings. The work analysed is a famous wood painting by Leonardo da Vinci, the “Madonna dei fusi” (ex-Reford version, 1501), chosen for a pilot study in a wide international project aimed at analysing Leonardo’s works of art by means of non-destructive techniques. While illustrating the results obtained concerning the identification of pigments and the discrimination of the stratigraphy of layers, the merits and limits of differential PIXE in general are pointed out.
The differential PIXE set-up at the Van de Graaff laboratory in Florence
2002, Nuclear Instruments and Methods in Physics Research, Section B: Beam Interactions with Materials and Atoms
PIXE analysis performed with protons of different energies makes it possible to obtain information about the depth sequence of different elements within the analysed sample. In this paper we report on the differential PIXE set-up installed at the external-beam facility of the KN3000 accelerator in Florence. In order to change beam energy on the sample, our choice was to insert energy degraders between beam exit window and sample. 25 μm Upilex foils are used to degrade the beam: with 3 MeV protons, the energy loss is about 500 keV; higher energy losses are obtained by sandwiching more foils. Measurements of lateral beam profiles and of energy loss and straggling after the Upilex foils are reported, compared to those obtained with other materials such as aluminium and copper. We also investigated the possible damage to the foil due to beam irradiation. Preliminary applications of this set-up to the stratigraphic analysis of samples of archaeometrical interest are described.
Non-invasive investigations of paintings by portable instrumentation: The MOLAB experience
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¹: Present address: CERAP, Université Paris I – Panthéon-Sorbonne, France.

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Determination of the sequence and thicknesses of multilayers in an easel painting

Abstract

Introduction

Section snippets

Analysis of the elemental paints used by the artist

Sequences of paint layers

Determining the layer thicknesses

Discussion and conclusion

Acknowledgements

Nucl. Instr. and Meth. B

Nucl. Instr. and Meth. B

Nucl. Instr. and Meth. B