Transfer theory and image formation in a time dependent aberrationless magnetic field lens

Transfer theory and image formation is studied for the case of a time dependent magnetic field lens consisting of an axially symmetric ellipsoidal coil producing a spatially-homogeneous but time pulsating magnetic field. This system is capable of focusing a pulsed beam of charged particles drifting parallel along the coil axis as well as forming images of an object emitting electrons. This lens avoids the constrains imposed by Scherzer theorem, and has the advantage of being free of spherical aberration. This last property suggest the possibility of using it to increase the resolving power beyond the limits imposed by spherical aberration present in traditional lenses. In this work we develop the transfer theory by solving the corresponding Schrodinger time dependent equation and derive exact expressions for the propagator. Assuming coherent electron pulses incident perpendicularly on the specimen, we then construct transfer functions in the presence of symmetrical apertures and obtain contrast image functions for thin, weak scattering objects in the bright field case.