Timo de Wolff

Non-destructive, depth resolved investigation of corrosion layers of historical glass objects by 3D Micro X-ray fluorescence analysis

3D Micro X-ray fluorescence analysis was used for the investigation of reverse-glass paintings. The material-specific combination used in reverse-glass paintings leads to damage phenomena reinforced by glass corrosion. To elucidate the mechanism of corrosion processes taking place in the glass object depth profiles of mobile elements are of interest. In order to obtain elemental depth profiles of such kind of fragile objects the method of choice should be non-destructive. Our first results demonstrate the usefulness of the 3D Micro-XRF measurements for this kind of investigations. The assumption that certain binding media may initiate corrosion processes beginning at the interface glass/binding material could be confirmed.

A compact 3D micro X-ray fluorescence spectrometer with X-ray tube excitation for archaeometric applications

In this work, the applicability of a new 3D micro X-ray fluorescence (3D Micro-XRF) laboratory spectrometer for the investigation of historical glass objects is demonstrated. The non-destructiveness of the technique and the possibility to measure three-dimensionally resolved fluorescence renders this technique into a suitable tool for the analysis of cultural heritage objects. Although absorption and resolution effects complicate qualitative analysis of the data, layered structures can be distinguished from homogeneous samples without the need for full quantification. Different manufacturing techniques were studied in this work with the help of hand-made reference samples. With the gained knowledge it could be shown for the investigated historical glass object, that black enamel as a stained glass contour colour was used in a cold painting. The object was not fired after the application of the black enamel, but instead the adhesion of the paint was solely provided through organic binding agents and the backing with metal foils. Thus, for the manufacturing of the object, a mixture of cold painting technique with a stained glass color was used. Quantitative measurements with a 3D Micro-XRF setup at the Berlin synchrotron BESSY II confirm the assumptions drawn on the basis of the qualitative investigation with the 3D Micro-XRF spectrometer with X-ray tube excitation.

Performance of a polycapillary halflens as focussing and collecting optic—a comparison

Polycapillary halflenses are widely used to focus X-ray radiation onto a small spot. Additionally they can reduce the field of view of a semiconductor detector when placed in front of one. In 3D micro X-ray fluorescence spectroscopy (3D Micro-XRF) with synchrotron radiation, two polycapillary halflenses are used in a confocal geometry. Up until now, characterization measurements in the focal plane have only been performed in the case of the lens focusing parallel radiation. Assumptions have been made, that in the other case, when isotropic radiation from a spot source is transported to a detector, the acceptance distribution in the focal plane is also Gaussian. We performed measurements with an electron beam as well as a proton beam which confirm this assumption. In addition, a comparison between measurements in collecting and focusing mode show differences in spot size and transmission. These differences exemplify the fact that there is not one global spot size or transmission function of a polycapillary halflens. Illumination and divergence effects can alter both characteristic lens parameters.

3D Micro-XRF for Cultural Heritage Objects: New Analysis Strategies for the Investigation of the Dead Sea Scrolls

A combination of 3D micro X-ray fluorescence spectroscopy (3D micro-XRF) and micro-XRF was utilized for the investigation of a small collection of highly heterogeneous, partly degraded Dead Sea Scroll parchment samples from known excavation sites. The quantitative combination of the two techniques proves to be suitable for the identification of reliable marker elements which may be used for classification and provenance studies. With 3D micro-XRF, the three-dimensional nature, i.e. the depth-resolved elemental composition as well as density variations, of the samples was investigated and bromine could be identified as a suitable marker element. It is shown through a comparison of quantitative and semiquantitative values for the bromine content derived using both techniques that, for elements which are homogeneously distributed in the sample matrix, quantification with micro-XRF using a one-layer model is feasible. Thus, the possibility for routine provenance studies using portable micro-XRF instrumentation on a vast amount of samples, even on site, is obtained through this work.

Amoebas, nonnegative polynomials and sums of squares supported on circuits

We completely characterize sections of the cones of nonnegative polynomials, convex polynomials and sums of squares with polynomials supported on circuits, a genuine class of sparse polynomials. In particular, nonnegativity is characterized by an invariant, which can be immediately derived from the initial polynomial. Furthermore, nonnegativity of such polynomials f coincides with solidness of the amoeba of f, i.e., the Log-absolute-value image of the algebraic variety

Reconstruction of confocal micro-X-ray fluorescence spectroscopy depth scans obtained with a laboratory setup.

{\mathcal {V}} (f) \subset (\mathbb {C}^*)^n

Lower Bounds for Polynomials with Simplex Newton Polytopes Based on Geometric Programming

V(f)⊂(C∗)n of f. These results generalize earlier works both in amoeba theory and real algebraic geometry by Fidalgo, Kovacec, Reznick, Theobald and de Wolff and solve an open problem by Reznick. They establish the first direct connection between amoeba theory and nonnegativity of real polynomials. Additionally, these statements yield a completely new class of nonnegativity certificates independent from sums of squares certificates.

Lopsided approximation of amoebas

Amoebas and coamoebas are the logarithmic images of algebraic varieties and the images of algebraic varieties under the arg-map, respectively. We present new techniques for computational problems on amoebas and coamoebas, thus establishing new connections between (co-)amoebas, semialgebraic and convex algebraic geometry and semidefinite programming. Our approach is based on formulating the membership problem in amoebas (respectively coamoebas) as a suitable real algebraic feasibility problem. Using the real Nullstellensatz, this allows to tackle the problem by sums of squares techniques and semidefinite programming. Our method yields polynomial identities as certificates of non-containment of a point in an amoeba or coamoeba. As the main theoretical result, we establish some degree bounds on the polynomial certificates. Moreover, we provide some actual computations of amoebas based on the sums of squares approach.