Spherical aberration coefficient (Cs) defines the quality of objective lens. The accurate determination of the spherical aberration coefficient Cs is very important to many applications of EM techniques, such as electron holography [1,2], image processing and deconvolution , and electron crystallography of proteins .
The values of Δf (defocus value), Cs (spherical aberration coefficient), and D (standard deviation of the Gaussian distribution of defocus due to the chromatic aberration) can be obtained by TEM image deconvolution. Of these three factors, Cs and D can be determined experimentally. With the estimated values of Cs and D, a set of structure factor of ED (electron diffraction) F(h) can be calculated from equation of Fourier transform (Iim(u)) for a given value of Δf.
Figure 3735 shows the example of an improved analysis by deconvoluting the high resolution TEM images taken from K2O·7Nb2O5 crystals. The space group is P4bm and unit cell parameters of these materials are a = b = 27.5 Å and c = 3.94 Å. Figure 3735 (a) is the expected image at 0.3 nm spatial resolution of the unit cell projected along the c axis. Figures 3735 (b) and (c) shows two experimental high resolution TEM images, taken in the  direction, with different defocus values. The two images are clearly different and their contrasts nearly inverse to each other. By applying the deconvolution technique, described above, to the two images, both the deconvoluted images in Figures 3735 (d) and (e) have similar features and contrasts to those of the expected image in Figures 3735 (a), i.e., they all have four heptagonal channels surrounded by hexagonal, pentagonal, tetragonal, and trigonal channels.
Figure 3735. Image deconvolution of the high resolution TEM images of K2O·7Nb2O5. a: Expected TEM image at 0.3 nm resolution. b and c: Experimental TEM images with defocus values at about 290 nm and 240 nm, respectively. d and e: Deconvoluted TEM images of b and c, respectively. 
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