Optimizing the window size for multiple least squares fitting of electron energy loss spectra

Abstract

The purpose of this study was to determine the effect of the fitting window size used with the linear least squares fit method when quantitating trace elements with electron energy loss spectroscopy. Theory and computer simulation with a simple model of two 'signals' show that, when the background underlying the signal is slowly varying and the signal is localized, there exists a minimum window optimal for fitting raw spectra. The width of the minimum fitting window can be determined directly from the reference standard spectrum of the signal alone and the estimates of signal and background are related. Use of narrower than the minimum window will increase the fitting uncertainty of the signal and yield less reliable results. More complicated experimental spectra must be fitted to more than two standards and a simple analytical expression of the minimum fitting window cannot be derived, but can be determined empirically. Our study shows that the empirical value obtained from experimental spectra is only slightly larger than the theoretical value derived from the simple model, indicating that this conclusion is still valid. When fitting difference spectra with a slowly varying background, the estimates of signal and background are independent and windows wider than the size of the signal will yield the same fitting uncertainty. In the presence of a non-slowly varying background, common in difference spectra, the minimum window size depends on the fine structure of the signal and the background.

Quantitative EFTEM mapping of near physiological calcium concentrations in biological specimens

“…However, in many biological applications it is important to analyze large fields of view rapidly, which is difficult to achieve with current STEM/EELS setups. From the spectral image data acquired with STEM/EELS, it is possible to extract precisely the elemental signal by multiple linear least square fitting (MLLS) of reference spectra [11,39,40]. For our present purpose we can consider the STEM/EELS analysis to provide an accurate measure of the calcium concentration.…”

Progress in Electron Energy Loss Spectroscopy, Elemental Mapping and Elemental Tomography of Biological Structures

“…The current state of the art in EELS instrumentation includes: spectrum-imaging in the STEM [9]; energy filtering electron microscopy (EFTEM) using in-column or post-column filters equipped with highly efficient charge-coupled device (CCD) detectors [10]; sophisticated methods for spectral and image analysis [11][12][13]; and most recently attempts to collect 3-D elemental distributions from sectioned cells by energy-filtered electron tomography [14].…”

“…As originally appreciated by Henry Shuman and Andrew Somlyo, all of the above developments are essential for successful application of EELS to biological systems, which present a formidable challenge in terms of their radiation sensitivity and the small numbers of atoms of specific elements that are found in cellular structures [8]. The current state of the art in EELS instrumentation includes: spectrum-imaging in the STEM [9]; energy filtering electron microscopy (EFTEM) using in-column or post-column filters equipped with highly efficient charge-coupled device (CCD) detectors [10]; sophisticated methods for spectral and image analysis [11][12][13]; and most recently attempts to collect 3-D elemental distributions from sectioned cells by energy-filtered electron tomography [14].…”