User:V21c2006

Diffractogram is a type of image generated by doing forward Fourier_transformof the Wave_functionof electron beam on the image plan. In Transmission_electron_microscopy, the wave function of the exit electron beam that passes through the specimen and objective lens can be expressed as: Ψ(r)= a(r) exp[i φ(r)] where an amplitude a(r) and phase φ(r). The intensity distribution I (r) in the image plan is expressed as: I (r) = │FT^-1{FT{a(r)exp[iφ(r)]}exp[iχ(u)]}│² where χ(u) indicates the extra phase to the wave function resulting from defocus and spherical aberration. Then diffractogram is the result of forward Fourier transform of the image intensity I (r) and can be expressed as: Diffractogram =│ FT{ I (r) }│² = │FT{a(r)exp[iφ(r)]exp[iχ(u)]} │² Diffractogram is different from Diffraction_pattern, whose intensity is not affected by the extra phase χ(u) since the intensity of diffraction pattern is expressed as: = │FT{a(r)exp[iφ(r)]}exp[iχ(u)] │² = │FT{a(r)exp[iφ(r)]}│²

E. Voelkl. Using diffractograms to evaluate optical systems with coherent illumination. OPTICS LETTERS, 2003, 28 (23), 2318-2321</ref>