The transport-of-intensity equation (TIE) is a computational approach to reconstruct the phase of a complex wave in optical and electron microscopy.
[1] It describes the internal relationship between the intensity and phase distribution of a wave.
[4] Teague approximated the amplitude of the wave propagating nominally in the z-direction by a parabolic equation and then expressed it in terms of irradiance and phase: where
TIE-based approaches are applied in biomedical and technical applications, such as quantitative monitoring of cell growth in culture,[6] investigation of cellular dynamics and characterization of optical elements.
[7] The TIE method is also applied for phase retrieval in transmission electron microscopy.