Background Subtraction for Trace-element Analysis – Analytical Comparison of Methods

For wavelength-dispersive fluorescence analysis, the background is a nonlinear function of 2θ, and a linear interpolation between two background angles gives an erroneously high estimate. This discussion systematically develops and compares interpolation methods analytically, to demonstrate their strengths, weaknesses, and correct use. The background can be estimated from measurement at a single angle, or it can be interpolated as a function of 2θ, using coefficients determined empirically or by using Lagrange polynomials. Three or more background angles can be used to compensate for curvature. However, it is preferable to linearize the background by transforming either 2θ or intensity. Most background subtraction methods, including measurement of a single background, and the commonly used two-background “shape-factor” method, implicitly transform 2θ. Background interpolated by using a 2θ transform is not affected by a change in tube intensity or by a constant change in background, but requires a reference blank sample that may not be universally applicable. Interpolation of log intensity values is not affected by changes in tube intensity, and does not require a reference blank. Measured background normalized to the background estimated from sample composition is not affected by tube intensity or by a constant change in background. INTRODUCTION The problem of background subtraction in wavelength-dispersive analysis is well known. Since the continuum background is a nonlinear function of 2θ (or energy), linear interpolation generally leads to erroneously high background estimates. Using closely spaced background angles reduces the errors, but does not eliminate the curvature. Improving the accuracy of interpolation is crucial for improving the analytical accuracy and for minimizing the number of background angles required. The background is complex, with multiple components due to scattering from the sample and instrument parts. As shown in Fig. 1 and reference [1], diffraction by the sample in particular adds a component that is difficult to estimate a priori. Therefore, background subtraction must remain largely an empirical art. Copyright (c)JCPDS-International Centre for Diffraction Data 2002, Advances in X-ray Analysis, Volume 45. 441