What is the contrast transfer function?
The image formation in bright field electron microscopy can be described by the action of the contrast transfer function (CTF) H(k). Accordingly, the relationship between the object o(r) and the image contrast i(r) can be written as i(r) = o(r)* h(r), where * stands for the convolution operation, and h(r) is the point spread function, which is the Fourier transform of H(k). Thus, following the convolution theorem, I(k) = O(k)H(k). The shape of the CTF, H(k), depends on several parameters (for details, see Frank, 2006): defocus [A] – which describes the deviation in the focus of the objective lens from the “Gaussian focus.” spherical aberration coefficient [mm] – which describes the (third order) spherical aberration of the wave front in the objective lens. source size [1/A] – which describes the illumination divergence, expressed as a size in the back focal plane (hence a quantity in reciprocal space). defocus spread – which describes the spread of defocus due to the spread of electron
