Exploring unknown nanostructures with electrons

Thanks to the speed of JavaScript and HTML5 canvas on modern devices, folks can practice taking transmission electron microscope (TEM) data from "unknowns" through a browser on many platforms. What kinds of cool and/or interesting pictures can YOU capture with this dude?

Note: If the image panels and returning) may help, as we are still learning js/HTML5.

The simulation is for a million-dollar 300 keV transmission electron microscope (TEM) with point-resolution just under 2 . below are blank at first, hitting page reload (or in Chrome going here The left-side panel direct-space image field-width is corresponds to a pattern half-width of 1/d about 112.9 , while the right-side panel diffraction-pattern spatial-frequency cutoff ≈ 128/112.9 ≈ 1.13 cycles/. Off-center spots in diffraction correspond to transverse electron-momentum shifts, following deBroglie, proportional to spatial-frequency. All "unknown" specimens focus and tilt together.

focus: ; # 0
- - - - ⇓ large aperture image ⇓ - - - - - - - - - - - - ⇓ diffraction pattern ⇓ - - - -
Tilt1: 0 o ; Tilt2: 0 o ;
aperture-click d ≈ 3.53 , last d ≈ 3.53 , Δφ ≈ 90 o, cursor d ≈ 0.778 .
- - - - ⇑ digital darkfield ⇑ - - - - - - - - - - - - ⇑ image power spectrum ⇑ - - - -

You may want to choose your own path, but the standard approach to specimen-characterization with electron deBroglie-phase contrast is to first try to minimize astigmatism in the optics, here using the four δf controls. This may be done by minimizing anisotropy associated with amorphous materials in the image (not easy to find in specimens here), or more easily by circularizing zeros in the microscope's contrast transfer function (CTF) which show up as dark, curvy, and specimen-independent lines in the image power-spectrum.

The second step might then be to optimize focus with the over/under controls. This is your call. Otto Scherzer's goal there, for example, was to push the first CTF zero (and its associated Fourier-phase inversion) out to the largest possible spatial-frequency. Another goal might be to maximize contrast transfer for the spatial-periodicities (i.e. diffraction-spots) of specific interest in a given field of view.

The third step, perhaps in concert with the second, is to see how the specimen image and its associated darkfield images change with specimen-orientation. Tilt-button clicks rotate the specimen by one degree per click over orthogonal axes (T1 fixed and T2 rotating), providing "Ewald-slice" access to each specimen's whole reciprocal-lattice. Angles and spacings associated with three non-coplanar periodicities generally let one determine lattice-parameters for part (often all) of any 3D crystal.

The brightness information in the digital darkfield panel (obtained using periodicities in the image) behaves much like intensity in electron-optical darkfield images. However the color (hue) denotes Fourier-phase which allows one to see phase inversions (e.g. due to thickness or a screw-dislocation side-on) as well as vector phase-gradients which correspond e.g. to pico-meter lattice-strains in an otherwise fixed-period object. From these one might for example separately calculate and display isotropic (parallel to periodicity) and shear (perpendicular to periodicity) components of the projected strain.

To test your skill at optimizing focus with the image only, check out our electron phase-contrast challenge here.

An expanded set of image exploration tools for electron detectives is under development using JS/HTML5-canvas on the web here.

Look for improvements to these, plus a platform to do image-analysis on-line with real experimental images as well, in the days ahead.


Thanks to the author of the javascript FFT routines we are using to do the calculations. This page is hosted by the University of Missouri Saint Louis Department of Physics and Astronomy. The person responsible for errors is P. Fraundorf, whose mobile-friendly electron detectives construction is here and whose most ancient webpage on electron phase-contrast focus optimization may be found on the web here.