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 MSA 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 multiple 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.
  • Mindquilts site page requests ~2000/day are approaching a million/year. [backlinks]
  • Requests for a "stat-counter linked subset of pages" since 4/7/2005: .


  • Above: The Fresnel Propagator without, and with, Spherical Aberration

    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 32x32, 64x64, and 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 32x32, 64x64, and 128x128.
    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.

    Specimens in preparation...
  • Holey Carbon Film: 32x32, 64x64, and 128x128.
  • Amorphous Specimen: 32x32, 64x64, 128x128.
  • Polycrystalline Specimen: 32x32, 64x64, 128x128.
  • Atom-Thick Graphite 2D-PolyCrystal: 32x32, 64x64, 128x128.

  • 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 aberration-free lens.

    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, to philfSPAMX@newton.umsl.edu. Copyright 1996 by Phil Fraundorf, Dept. of Physics & Astronomy/Center 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 :)