LAUSR

The transverse wavefunction of a free electron can be structured with the use of off-axis diffraction holograms [1, 2]. Uses for structured electron wavefronts require exceedingly precise control of over this degree of freedom [3, 4]. Algorithms for the generation off-axis hologram patterns designed to produce an exact desired phase and amplitude in a specific diffraction order exists for phase only type holograms [5], which is useful for spatial light modulators in light optics. Implementations of these algorithms have been shown for material holograms for electrons [6], but the non-zero amplitude loss due to high angle scattering through the material give non-exact outputs. Here we present an exact solution to this problem allowing for production of precisely shaped electron wavefronts from amplitude and phase shifting material off-axis holograms for electrons. This is done by casting the transfer function in the thin hologram approximation as the sum of diffraction orders and inverting the thickness and phase profile of the hologram to be written as a function of the desired output.