A set of computer programs for determining defocus and astigmatism in electron images

A set of programs has been developed for determining the defocus and astigmatism of an electron image from the modulation of the Fourier transform due to the contrast transfer function (CTF) of a microscope. The set consists of four programs. The first one, SCTRAVGFT, averages the Fourier transform azimuthally over several sectors and makes a table of Fourier amplitudes as a function of spatial frequency. The second one, PLTCTFX, is an X-Windows program that fits theoretical CTFs to background corrected and smoothed Fourier amplitudes for each sector. The third one, CTFFIT, determines the mean defocus and astigmatism by non-linear least-squares fitting. The fourth one, PCTFREFN, uses the first program internally to average over points with the same CTF values and refines the mean defocus and astigmatism. This set of programs is particularly useful when the modulation of a Fourier transform by the CTF is weak or a transform appears to be highly astigmatic.