A set of programs has been developed for determining the defocus and a
stigmatism of an electron image from the modulation of the Fourier tra
nsform due to the contrast transfer function (CTF) of a microscope. Th
e set consists of four programs. The first one, SCTRAVGFT, averages th
e 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 ba
ckground corrected and smoothed Fourier amplitudes for each sector. Th
e third one, CTFFIT, determines the mean defocus and astigmatism by no
n-linear least squares fitting. The fourth one, PCTFREFN, uses the fir
st program internally to average over points with the same CTF values
and refines :he 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.