document: Some methods use 1D radial profiles obtained from circular averaging of 2D experimental PSD [4,8,11] or by elliptical averaging [17]. An inadequacy of circular averaging is that it neglects astigmatism. Astigmatism distorts the circular shape of the Thon rings and thus decreases their modulation depth in the obtained 1D profile. A few algorithms that consider astigmatism involve concepts such as dividing the PSD into sectors where Thon rings are approximated by circular arcs [15,21], applying Canny edge detection to find the rings [17] prior to elliptical averaging, determining the relationship between the 1D circular averages with and without astigmatism [22], or using a brute-force scan of a database containing precalculated patterns as in ATLAS [23]. Some other approaches for estimating CTF parameters do a fully 2D PSD optimization [12,14,18,20] but they usually regulate and fit numerous parameters by an extensive search that does not guarantee convergence. Furthermore, only a few schemes that were developed for defocus estimation provide an error analysis [23,24].
doc_bio_tags: O O O B I I O O B I O B I I O O O B I O O O O B I O O O O B B O O O O O O B I O O O O O O O O O B I O O O O O B O O O O O O B O O O B I O O O O O O O B I I O O O O O O O B I O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O B O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
extractive_keyphrases: 1d profile 1d radial profiles 2d experimental psd 2d psd optimization astigmatism atlas canny edge detection circular averaging ctf elliptical averaging psd thon rings