Interactive Focusing and Astigmatism Adventures on the Web
On the first day after the Jul '96 startup, this page received
226 visits plus 1644 requests for pages in the branches beyond this
trunk! Such responsiveness by the community of interested
microscopists exists in part thanks to the
listserver. On that day only one visitor (whose name we
don't have yet) managed to locate optimum (Scherzer) defocus in
the Challenge series below.
In spite of
years on occasion between updates, activity remains with for
example more than 10,000 epc-series (electron phase contrast) page requests
during the first 23 days of Nov 2005.
A wave-optical (e.g. light or electron) imaging
system is focussed
when it forms
an image of wave intensity passing through the "object plane" which
is of interest. For example, you may want your picture to focus on
the flower in the foreground, or the mountains in the distance. In
electron phase contrast imaging (HR-TEM) of very thin specimens, one
sometimes focusses on an object plane downstream from the specimen,
where the specimen's "wake" gives rise to detectable intensity
differences on the film.
Images have astigmatism
when waves that approach the image plane from different
directions carry their focus from different object planes.
This happens, for example, if the lens of our eye has axial asymmetry.
Traditionally, astigmation (making focus the same in all
directions) and focusing (choosing the correct focus) have
been challenges faced by most microscopists.
Here we offer an
opportunity for new and old microscopists alike to hone their skills
at correcting focus and astigmatism settings,
using calculated electron phase contrast images. As of
April 2005, we are actively developing more specimens and
larger images for this long-active site, so stay tuned...
First, practice focusing with power spectrum
information available to better see what is happening. Begin at
exact "Gaussian focus". Image sizes we are calculating include
128x128. On the
larger size images, you might also ask if there isn't something
in the holey carbon film specimen in addition to the holes...
Then practice astigmatism correction,
with power spectrum information to better see what is happening.
Begin with a corrected image, then make it worse and then better.
Image sizes in preparation include
Now for the challenge! How many steps
will it take you to correct astigmatism and find Scherzer
defocus on one of the specimens below? If you send us a couple
of sentences telling us how many steps it took you, and the
strategy employed in getting it done, we'll try to post your
note for the potential benefit of those looking for strategies
which will work for them.
If you have an applied physics or mathematical
streak, you might also try determining spherical aberration,
defocus step size, and point resolution for the microscope being
simulated in these image calculations. This latter part may
require a few assumptions, e.g. about image field width and
electron wavelength (e.g. 300kV). For ideas how to approach the
problem given a series of micrographs of the same specimen, at
different defocus settings, check out the classic book by
John Spence: Experimental High Resolution Electron Microscopy,
now in its second edition. Solutions to this problem might also
be instructive for prospective instrumentation and materials
physicists, and we would like to either link to such solutions,
or post them if you send them here. The figure at right provides
clues to the way zeros in the power spectrum of amorphous materials
images move around with defocus in the simulations above, and to
the role that
spherical aberration plays in modifying the phase contrast transfer
down stream of the specimen (when the objective is "under" Gaussian
focus) from the "Fresnel propagated transfer" expected for an
The foregoing gives rise to a lovely and robust way
to model thin-specimen images and, by doing it repeatedly i.e.
via multislice, thick specimen images as well. It promises to help us
develop new tools for getting numbers from bio-specimen and
atom/molecule images in the days ahead. Specifically, the
spherical aberration portion of the plot below left predicts
precisely where “zeros” will appear in the power spectrum of an
amorphous specimen image, as a function of defocus and astigmatism.
Since most image fields have some amorphous material in them, this
yields a calibration of instrument response internal to each image.
The images here were first calculated using a
program I put
together some years ago which uses, as I recall, a strong phase
object algorithm from Spence's book, applied to "very thin" specimens.
Newer images are likely to be calculated with similar algorithms,
implemented in Wolfram's Mathematica.
Variations in contrast associated with changing specimen thicknesses
hence may require fancier, e.g. multislice, algorithms. If
someone is willing to provide image sets from more complicated
specimens, real or virtual, we would certainly consider hosting
or linking users to them as well.
Send comments, your answers to problems posed, and/or complaints,
Copyright 1996 by Phil Fraundorf,
Dept. of Physics &
for Molecular Electronics, University of Missouri-StL,
St. Louis MO.
This page contains original material, so if you choose to echo in
your work, in print, or on the web, a citation would be cool.
(Thanks. /philf :)