Complex observation in electron microscopy. I. Basic scheme to surpass the Scherzer limit

A novel observation scheme, termed the complex observation, which is faithful to reconstruct optical images carried by either electromagnetic or material waves in their intrinsic complex form, is proposed. This observation is based completely on the coherent microscopy and comprised of a triple experiment consisted of twin experiments restoring two linear terms corresponding to the real and imaginary part of complex images and an additional experiment to cancel the square term which is in company with either linear term. A linear combination of three images obtained through the triple experiment is able to exhibit a complex quantity in the form to be numerically manipulated without rupture according to the formal theory of image formation. Manipulation of the phase and the intensity of primary waves penetrating through objects is the key in this observation. The basic scheme is applied to settle the long-standing issue in electron microscopy that the point resolution is impaired by the modulated contrast transfer, which originates from lens aberrations and defocusing. A computer simulation illustrates a modulation-free image with a drastic improvement on the contrast as well as the point resolution compared with the three originals utilized for the image reconstruction.