Transport of intensity equation method and its applications

A phase retrieval technique based on a transport of intensity equation (TIE) is one of the defocus series reconstruction techniques in microscopy. Since it does not require any dedicated devices like a biprism, and only three defocus images are enough to retrieve phase information, it has been applied to observe magnetic fields, magnetic domains, electrostatic potentials, and strains. It is also used to improve image resolution by correcting spherical aberration. This technique is simple and easy to use, but some artifacts often appear in the retrieved phase map. One should pay careful attention to the experimental conditions, and the algorithms and boundary conditions used to solve the TIE. This paper reviews the principle of the TIE method, the algorithms used to solve it, and application results in materials science.