Fig. 5. Comparison of simulated 2d magnetic encoding signals for different types of density distributions.

a, b The original input spatial distributions ${\rho \left(x,y\right)}_{\mathrm{smooth}}$ and ${\rho \left(x,y\right)}_{\mathrm{sharp}}$ respectively. c, d The corresponding calculated signals $S\left(k_x,k_y\right)$ demonstrating how smooth/wide features in real space appear as signals concentrated near the origin of $k_x,k_y$, whereas sharp/narrow features in real space extend throughout the $k_x,k_y$ space. For clarity, just the real part of $S\left(k_x,k_y\right)$ is shown. e, f show the $S\left(k_x,k_y\right)$ plotted above them after adding random noise to mimic their appearance in the presence of shot noise in an experiment.