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J Electron Microsc (Tokyo). 2010;59(1):33-41. doi: 10.1093/jmicro/dfp046. Epub 2009 Sep 19.

Quantitativeness of phase measurement by transport of intensity equation.

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  • 1National Institute for Materials Science, 1-1 Namiki Tsukuba Ibaraki, 305-0044, Japan. MITOME.Masanori@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.

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