Practical Electron Microscopy and Database

The local intensity distribution I(r) of HRTEM image is a function of the amplitudes and phases of the transmitted and diffracted electron beams of the exist wave from the TEM specimen. I(r) can be given by [1 - 2],

          ---------------------- [4145a]
                   
                    
                    
                    
                     ------------- [4145b]

where,
         ψ_i -- The complex electron wave on detector or photographic film
         U₀ -- The amplitude of the transmitted electron beam
         U_g -- The amplitude of the diffracted electron beam
        θ₀ -- The phase of the transmitted electron beam
        θ_g -- The phase of the diffracted electron beam
        χ(g) -- The phase change χ(g)

The phase change χ(g) reflects the influence of the contrast transfer function of the objective lens. The first term in Equation 4145b represents the background intensity of the HRTEM image while the other terms give cosine fringes of various periodicities and amplitudes due to the local intensity modulation produced by constructively and destructively interfere at the image plane.
         
         

[1] K. Ishizuka, Ultramicroscopy 5 (1980) 55.
[2] R. W. Glaisher and A. E. C. Spargo, Ultramicroscopy 18 (1985) 323.