Fig. 1

Process of phase retrieval. a Electron hologram. b Digital diffractogram obtained by fast Fourier transform (FFT). The yellow circle in (b) indicates a selected specific frequency zone for FFT^-1 of the diffractogram. c and d Real and imaginary parts of a complex image reconstructed from the hologram via FFT^-1. e and f Results of real and imaginary parts after applying the noise reduction to (c) and (d), respectively. g Reconstructed phase image obtained by calculating \(\tan^{-1}i/r\), where \(i\) and \(r\) are the imaginary part of (f) and the real part of (e), respectively