A SET OF COMPUTER-PROGRAMS FOR DETERMINING DEFOCUS AND ASTIGMATISM INELECTRON IMAGES

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.