Figure 14.1.

The Ewald sphere and Prec algorithm. (A) Fourier coefficients in the transforms of electron microscope images (F_Robs) are actually combinations of coefficients (F_L and F_R) that lie on a spherical surface through the 3D transform of the specimen called the Ewald sphere. (B) Prec iteratively recovers the independent values of these coefficients by comparing CTF-corrected observations (F_Rcorr) with the calculated sum (F_Rcalc) that would have been expected from the right (F_Rj) and left (F_Lj) terms of some previous reconstruction, with appropriate phase factors e^iφ_L = (α + iβ)²e^i2χ. Half the difference (F_Δ) is then added to F_Rj and F_Lj to produce the next iteration (F_{Rj + 1} and F_{Lj + 1}).