title: On the transport of intensity technique for phase retrieval.
abstract: 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.
authors.affiliation: Brookhaven National Laboratory, Center for Functional Nanomaterials, Building 480, Upton, NY 11973, USA. beleggia@bnl.gov
authors.forename: M
authors.initials: M
authors.lastname: Beleggia
authors.forename: M A
authors.initials: MA
authors.lastname: Schofield
authors.forename: V V
authors.initials: VV
authors.lastname: Volkov
authors.forename: Y
authors.initials: Y
authors.lastname: Zhu
mesh_terms: D000465:Algorithms; D006696:Holography; D007089:Image Enhancement / Q000379:methods*; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D046529:Microscopy, Electron, Transmission; D008858:Microscopy, Phase-Contrast / Q000379:methods