Ultimate resolution and information in electron microscopy II. The information limit of transmission electron microscopes

Does a monochromator improve the precision in quantitative HRTEM?

“…The precision that might be gained by slightly deviating from Scherzer defocus is hardly significant. The intrinsic energy spread standard deviation DE of the electron source has been set to 0:35 eV, which corresponds to a full width at half maximum (FWHM) value of 0:82 eV, being a typical value for a Schottky Zr=W FEG microscope (see, for instance, [8]). The remaining microscope parameters used are given in Table 1.…”

“…To further illustrate this principle, Fig. 3 shows the attainable precision as a function of DE f for a C s -corrected microscope at Scherzer defocus and an intrinsic energy spread DE equal to 0:75 eV (corresponding to a FWHM value of 1:77 eV), which is a practical value for a LaB 6 electron gun [8]. The values of the other microscope and object parameters used are again given in Tables 1 and 2.…”

“…Moreover, with the introduction of a C s -corrector [7], the effect of the beam convergence on the spatial coherence will be reduced drastically and may even vanish completely (when C s is zero). Chromatic aberration will mostly be the predominant factor governing the information limit [8]. It results from a spread in defocus values which results from fluctuations in accelerating voltage, lens current and thermal energy of the electron, where the thermal energy fluctuation is often the dominating term.…”

“…This effect has to be taken into account when the performance of a monochromator in quantitative HRTEM is evaluated. This might be done by using a modified definition of the information limit that includes the SNR [8,12]. In the present work, however, an alternative performance measure is proposed, which allows quantitative evaluation based on the SNR dependent statistical measurement precision.…”

Modal decomposition of a propagating matter wave via electron ptychography

“…It defines the transfer properties of the imaging lens in a transmission electron microscope (TEM), determining the extent of the 'information limit' -i.e. the highest spatial frequency that can be transferred through the electron optics, and hence the highest resolution that can be obtained in the image [6,7]. This is particularly important in the field of imaging nanoscale biological structures such as large proteins and viruses because contrast in the image of such weaklyscattering structures must be enhanced by large defocus in the object lens [8], which, in the presence of partial coherence, greatly reduces the width of the information limit and hence limits resolution.…”