Quantitative Fresnel Lorentz microscopy and the transport of intensity equation

Imaging of the magnetic structure of thin films by the Fresnel mode of Lorentz microscopy has been re-evaluated in terms of the Ampérian current density within a sample. The conditions for which this imaging can be treated as linear are discussed for quantitative application. Additionally, the consequences for magnetic phase reconstruction using the transport of intensity equation for defocused images are considered. While the range of applicability may initially appear rather limited examples of objects containing different spatial frequency components are used to illustrate the possibilities where relatively large defocus values may be used.