  The ability to map electro- and magneto-static fields in transmission
electron microscopy (TEM) has been critical to fundamental research into
materials and their applications. Here, we outline the parallel mode of
differential phase contrast (TEM-DPC), which uses real-space distortion of
Fresnel images to quantify the phase gradient of samples with some degree of
structural contrast. Through numerical simulations, we compare the technique to
the widely used transport-of-intensity (TIE) method for phase recovery, and
discuss the relative advantages and limitations of each. The TEM-DPC technique
is particularly suitable for \textit{in-situ} studies of samples with
significant structural contrast and, as such, complements the TIE method since
this property usually hinders the former, but is an essential feature that
enables the latter. We use the TEM-DPC technique on cryo-TEM images of a thin
lamella of a low temperature two-dimensional (2-D) ferromagnetic material,
K$_2$CuF$_4$. By tracking the induction as the sample is driven through a phase
transition by heating, we extract estimates for the critical temperature and
critical exponent of the ordering parameter that are consistent with the 2-D XY
class.
