Full contrast transfer function correction in 3D Cryo-EM reconstruction

Over the past years electron cryo-microscopy (cryo-EM) has established itself as an important tool in studying the three dimensional structure of biological molecules up to the resolution of 6-9A. However, as we pursue even higher resolution (i.e., 3-4A), the depth-of-field problem inherent in the contrast transfer function emerges as a limiting factor. This problem has been previously addressed in the research community [1]-[4]. In this paper we develop the full theoretical solution to this problem. we show that the projected image from the electron microscope corresponds to neither a slice, nor an Ewald sphere In the Fourier space, but a couple of quadratic surfaces in that space. the general solutions to this problem for both single and double defocus exposures are developed. Simulations show the correctness of the theory.