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Journal of Electron Microscopy Advance Access published online on September 19, 2009
Journal of Electron Microscopy, doi:10.1093/jmicro/dfp046
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© The Author 2009. Published by Oxford University Press on behalf of Japanese Society of Microscopy. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org

Quantitativeness of phase measurement by transport of intensity equation

Masanori Mitome1,*, Kazuo Ishizuka1,2 and Yoshio Bando1

1 National Institute for Materials Science, 1-1 Namiki Tsukuba Ibaraki, 305-0044, Japan and
2 HREM Research Inc., 14-8 Matsukazedai Higashimatsuyama Saitama, 355-0055, Japan

* To whom correspondence should be addressed. E-mail: MITOME.Masanori{at}nims.go.jp

Based on the transport of intensity equation (TIE), a phase map can be readily retrieved from only three images of a focal series. The retrieval procedure does not require an iterative calculation and it is performed very fast with the use of the fast Fourier transform. However, it must be noted that sensitivity depends on the spatial frequency components and difficulties are encountered when phase information is retrieved to be of the same quality for all frequency components. Since the retrieved phase is influenced by conditions in which the focal series was taken, it is important to select the appropriate conditions and parameters used in this process. Optimal conditions to preserve the quantitativeness of phase maps measured by the TIE method are discussed theoretically and they are demonstrated by measuring phase shifts in silver particles. It was found that the high quantitativeness can be obtained by selecting appropriately a defocus difference and a high pass filter constant according to the frequency components for the objects.

Keywords     phase retrieve, transport of intensity equation, inner potential

Received      4 June 2009, accepted 24 August 2009


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