On the Transport of Intensity Technique for Phase Retrieval

Ultramicroscopy. 2004 Dec;102(1):37-49. doi: 10.1016/j.ultramic.2004.08.004.


The Transport of Intensity technique is becoming a viable alternative to electron holography for phase retrieval in Transmission Electron Microscopy. However, several issues are still to be clarified in order to ascertain the applicability of the technique; among them, the controversy regarding its geometrical or wave-optical nature, as related to the phase detection limit. We show here that the Transport of Intensity is a wave-optical technique that works in a special regime of small defocus where the image intensity is linear with the defocus parameter. By a simple analytical example we show that the Transport of Intensity correctly reconstructs the electron optical phase shift even when the phase is smaller than pi, a value defining the boundary between the geometrical and wave approaches. Another example is given, the reconstruction of a phase jump, accompanied with experimental support showing that phase retrieval by Electron Holography and Transport of Intensity techniques yields results in good agreement.

Publication types

  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Algorithms
  • Holography
  • Image Enhancement / methods*
  • Image Processing, Computer-Assisted / methods*
  • Microscopy, Electron, Transmission*
  • Microscopy, Phase-Contrast / methods