The theoretical basis of electron emission holography and tomography

We investigate the theoretical foundation of electron emission holography for surface structure analysis by using the Lippmann-Schwinger integral equation to examine the reconstruction integral for electron holography. We elucidate the physical content of single-energy electron emission holograms and demonstrate the non-uniqueness of the holographic image. We examine the physical meaning of images obtained by the coherent superposition of multi-energy holograms in the weak scattering limit. We show that the coherent superposition of holographic image fields is an electron tomogram of the scattering potential. This establishes close connection between recently proposed methods for image improvement in electron holography and conventional image reconstruction schemes by computerized tomography. An optimal reconstruction algorithm, which retrieves a 3D image of the scattering potential in the weak scattering limit, is proposed.