Calculation of the angular and energy distribution of multiple scattered electrons using fourier transforms

Improving the reliability of the background extrapolation in transmission electron microscopy elemental maps by using three pre-edge windows

Over the last decades, elemental maps have become a powerful tool for the analysis of the spatial distribution of the elements within specimen. In energy-filtered transmission electron microscopy (EFTEM) one commonly uses two pre-edge and one post-edge image for the calculation of elemental maps. However, this so called three-window method can introduce serious errors into the extrapolated background for the post-edge window. Since this method uses only two pre-edge windows as data points to calculate a background model that depends on two fit parameters, the quality of the extrapolation can be estimated only statistically assuming that the background model is correct. In this paper, we will discuss a possibility to improve the accuracy and reliability of the background extrapolation by using a third pre-edge window. Since with three data points the extrapolation becomes over-determined, this change permits us to estimate not only the statistical uncertainly of the fit, but also the systematic error by using the experimental data. Furthermore we will discuss in this paper the acquisition parameters that should be used for the energy windows to reach an optimal signal-to-noise ratio (SNR) in the elemental maps.

Automated most-probable loss tomography of thick selectively stained biological specimens with quantitative measurement of resolution improvement

We describe the technique and application of energy filtering, automated most-probable loss (MPL) tomography to intermediate voltage electron microscopy (IVEM). We show that for thick, selectively stained biological specimens, this method produces a dramatic increase in resolution of the projections and the computed volumes versus standard unfiltered transmission electron microscopy (TEM) methods. This improvement in resolution is attributed to the reduction of chromatic aberration, which results from the large percentage of inelastic electron-scattering events for thick specimens. These improvements are particularly evident at the large tilt angles required to improve tomographic resolution in the z-direction. This method effectively increases the usable thickness of selectively stained samples that can be imaged at a given accelerating voltage by dramatically improving resolution versus unfiltered TEM and increasing signal-to-noise versus zero-loss imaging, thereby expanding the utility of the IVEM to deliver information from within specimens up to 3 microm thick.

Mechanism of image formation for thick biological specimens: exit wavefront reconstruction and electron energy-loss spectroscopic imaging

With increasing frequency, cellular organelles and nuclear structures are being investigated at high resolution using electron microscopic tomography of thick sections (0.3-1.0 microns). In order to reconstruct the structures in three dimensions accurately from the observed image intensities, it is essential to understand the relationship between the image intensity and the specimen mass density. The imaging of thick specimens is complicated by the large fraction of multiple scattering which gives rise to incoherent and partially coherent image components. Here we investigate the mechanism of image formation for thick biological specimens at 200 and 300 keV in order to resolve the coherent scattering component from the incoherent (multiple scattering) components. Two techniques were used: electron energy-loss spectroscopic imaging (ESI) and exit wavefront reconstruction using a through-focus series. Although it is commonly assumed that image formation of thick specimens is dominated by amplitude (absorption) contrast, we have found that for conventionally stained biological specimens phase contrast contributes significantly, and that at resolutions better than approximately 10 nm, superposed phase contrast dominates. It is shown that the decrease in coherent scattering with specimen thickness is directly related to the increase in multiple scattering. It is further shown that exit wavefront reconstruction can exclude the microscope aberrations as well as the multiple scattering component from the image formation. Since most of the inelastic scattering with these thick specimens is actually multiple inelastic scattering, it is demonstrated that exit wavefront reconstruction can act as a partial energy filter. By virtue of excluding the multiple scattering, the 'restored' images display enhanced contrast and resolution. These findings have direct implications for the three-dimensional reconstruction of thick biological specimens, where a simple direct relationship between image intensity and mass density was assumed, and the aberrations were left uncorrected.

Quantitative energy-filtered electron microscopy of biological molecules in ice

The theoretical and experimental bases for quantitative electron microscopy of frozen-hydrated specimens are described, with special considerations of energy filtration to improve the images. The elastic and inelastic scattering from molecules in vacuum and in ice are calculated, and simple methods to approximate scattering are introduced. Multiple scattering calculations are used to describe the scattering from vitreous ice and to predict the characteristics of images of frozen-hydrated molecules as a function of ice thickness and accelerating voltage. Energy filtration is predicted to improve image contrast and signal-to-noise ratio. Experimental values for the inelastic scattering of ice, the energy spectrum of thick ice, and the contrast of biological specimens are determined. The principles of compensation for the contrast transfer function are presented. Tobacco mosaic virus is used to quantify the accuracy of interpreting image intensities to derive the absolute mass, mass per unit length, and internal mass densities of biological molecules. It is shown that compensation for the contrast transfer function is necessary and sufficient to convert the images into accurate representations of molecular density. At a resolution of 2 nm, the radial density reconstructions of tobacco mosaic virus are in quantitative agreement with the atomic model derived from X-ray results.

Contrast in the electron spectroscopic imaging mode of a TEM. IV. Thick specimens imaged by the most-probable energy loss

When the zero-loss transmission falls below 10(-3) for biological sections of mass-thickness greater than 70 micrograms/cm2, the energy window in the electron spectroscopic imaging (ESI) mode of an energy-filtering electron microscope (EFEM) can be shifted to the most-probable energy loss of the electron energy-loss spectrum. This enables mass-thicknesses up to 150 micrograms/cm2 or thicknesses of 1.5 microns to be examined. Electron energy-loss spectra of thick carbon films calculated by a Fourier method agree with experimental spectra. Measurements of the electron energy-loss spectroscopy and ESI image intensities with an additional platinum film confirm a scattering model for the calculation of the image intensity. This model considers the angular broadening at the most-probable energy loss by introducing an effective illumination aperture of the order of the full-width at half-maximum of the angular distribution.