A Direct VU Factorization Method for Wave Reconstruction of Phase-Shifting Electron Holography

An iterative VU factorization method has recently been proposed for wave reconstruction of temporal phase-shifting (TPS) holography. The electron hologram series are expressed as the multiplication of two matrices V and U, where V contains the modulating phase and U contains the initial phase shifts. To obtain phase values directly, we devise a new VU factorization method (termed newVU-TPS) by supplying the initial phase shifts of a series of TPS holograms. Using hologram simulations and experiments, we verify the applicability of the newVU-TPS method and also evaluate its superiority in comparison to other established TPS reconstruction methods including the principal component analysis (PCA), the least-square (LS) and the VU methods. Moreover, we apply the newVU-TPS method to experimental holograms recorded via direct-detection device (DDD). Our results demonstrate that the proposed newVU-TPS is a fast and accurate reconstruction method for phase-shifting holograms of various sizes, thus enabling phase reconstruction with spatial resolution close to that of the original hologram and phase sensitivity up to about 2π/4000 rad.