IT-16-P-3028 Phase mapping at the interface retrieved by FFT based transport of intensity equation

   Phase retrieval using transport of intensity equation (TIE) is convenient and powerful to obtain electrostatic potential of materials, because it needs only three transmission electron microscope (TEM) images taken at different foci. In our previous results, potential map of gold nanoparticles adsorbed on a thin amorphous carbon (a-C) film was successfully obtained with high spatial resolution (1nm). However, it is difficult to obtain potential map of two-phase interface. In this study, we investigate how to obtain the phase map of the boundary between a-C and vacuum regions quantitatively.
  TEM observation was taken by 50pm-resolved R005 equipped with cold field emission gun and double aberration-correctors. Figure 1(a-c) shows three TEM images of under-focus 1000 nm, just-focus and over-focus 1000 nm. The TIE retrieved phase map using these three images is given in (d). Figure 1(e) and (f) are the line profiles along the blue lines indicted in (a) and (d). We notice that the mean intensity of vacuum, thin C-film and thick C-film regions are different in the original TEM image and the intensity profile does not reflect the expected phase shift among these regions. Moreover, a strong low-frequency contrast appeared in the phase map.
  We found the reasons of such discrepancy. Firstly, the periodic boundary condition required for FFT process of solving the TIE equation influences the retrieved phase map. Secondly, brightness difference exists in the focal-series TEM images, which is caused by the variation in objective lens current. Since the intensity difference applied to TIE is obtained by subtracting the over-focus TEM image from the under-focus one, the difference in image brightness causes deviation in the intensity differences. For example, all the values of ΔI are negative in the vacuum area. However, they should only oscillate around zero according to the wave theory.
  We consider that applying padding or mirror methods to the process is effective to satisfy the boundary condition, and aligning the current center rather than the voltage center of objective lens can eliminate the inhomogeneous illumination when taking a focal-series TEM images.