Phase Measurement in Electron Microscopy Using the Transport of Intensity Equation

Introduction Although many samples in electron microscopy are phase objects, as in the case of optical microscopy, we cannot directly measure phase modulation by microscopy. Dennis Gabor proposed a technique called in-line holography to record both amplitude and phase information at the rather early stage of electron microscopy (in 1947). With the development of highly coherent field emission electron sources, another type of holography, off-axis holography, became available for electrons. However, holography cannot be applied to general cases, since there is a requirement for a vacuum region where the reference wave passes through. Realizing a Zernike-type phase plate, as used in optical microscopy, has also been difficult in electron microscopy. Therefore, imaging conditions proposed by Scherzer have been utilized in electron microscopy, where an approximate phase plate is realized by introducing a defocus in the presence of spherical aberration.