EELS elemental mapping with unconventional methods. I. Theoretical basis: image analysis with multivariate statistics and entropy concepts.

Electron energy loss filtered images recorded within a transmission analytical electron microscope are now widely used for the mapping of the elemental distribution of a given atomic species in a specimen prepared as a thin film. Such an image processing may produce both valuable results and artifacts if a careful inspection of all the hypotheses needed by the calculation is not carried out. This paper presents some general statistical methods for a contrast information analysis of a noisy image data set. After a brief introduction of different concepts such as contrast, variance, information and entropy, two unconventional approaches for image analysis are explained: the relative entropy computed with respect to a pure random and signal-free image and the factorial analysis of correspondence (a branch of multivariate statistics). In the companion article (part II), these concepts are applied to real experiments and the results compared with those obtained with a conventional method. Although electron energy loss spectroscopy is the only technique considered here, these methods for image analysis can be applied to a wide variety of noisy data sets (spectra, images, ...) recorded from various sources (electrons, photons, ...).

EELS elemental mapping with unconventional methods. II. Applications to biological specimens.

This article presents two applications of image analysis and processing using the unconventional methods described in the companion paper (part I). Both the information analysis via relative entropy measurement and mapping and the factorial analysis of correspondence are demonstrated to be valuable tools for building an elemental map from a set of noisy energy-filtered images recorded in an analytical transmission electron microscope. Although the only technique considered here is electron energy loss spectroscopy, there is no doubt that such methods can be applied to a wide variety of similar problems: only a reduced number of underlying hypotheses are needed.

Electron energy loss chemical mapping of low Z elements in biological sections.

A STEM VG HB 501 equipped with a Gatan spectrometer has been interfaced to a PDP 11-34 computer. Digital energy filtered images have been recorded with several energy windows on both sides of a characteristic level, so that the exact background can be stripped under the core loss signal for each pixel. Results concern the distribution of nitrogen (K-edge at 402 eV), oxygen (K-edge at 532 eV) and iron (L23 edge at 705 eV) in embedded sections of bone marrow. The present performances of the system allow the detection of composition variations of 1 to 2% for these elements, with a lateral accuracy of the order of 5 nm in a section of 50 nm thickness. Individual ferritin molecules distributed within the section are clearly imaged and analyzed with the characteristic iron edge.

About the use of electron energy-loss spectroscopy for chemical mapping of thin foils with high spatial resolution.

Core-loss energy-filtered images have been suggested as a substantial contribution to the development of an analytical electron microscope with high spatial resolution. However, for many problems in complex materials, the characteristic signals can only be detected as slope variations of the continuously decreasing background. Therefore further data processing techniques are needed to extract satisfactorily the true chemical information. A discussion of the present limits and of the existing solutions clearly shows that the method can only be developed at the expense of more elaborate systems such as simultaneous detection channels (quite well suited to the STEM instruments). Typical numbers for realistic situations illustrate the field of application of the technique.

Contribution of electron energy loss spectroscopy to the development of analytical electron microscopy.

The combined use of an electron energy loss spectrometer and an electron microscope provides some chemical information at the nanometer scale. The physics of the interaction processes between the incident electron beam and the thin sample foil is reviewed in terms of energy and momentum transfer. This analysis of the content of an electron energy loss spectrum allows us to establish rules for a satisfactory use of the information and to discuss the detection limits of this newly developed microanalytical technique.