  The field of electron optics exploits the analogy between the movement of
electrons or charged quasiparticles, primarily in two-dimensional materials
subjected to electric and magnetic (EM) fields and the propagation of
electromagnetic waves in a dielectric medium with varied refractive index. We
significantly extend this analogy by introducing Fourier electron optics (FEO)
with massless Dirac fermions (MDF), namely the charge carriers of single-layer
graphene under ambient conditions, by considering their scattering from a
two-dimensional quantum dot lattice (TDQDL) treated within Lippmann-Schwinger
formalism. By considering the scattering of MDF from TDQDL with a cavity, as
well as the moir\'{e} pattern of twisted TDQDLs, we establish an electronic
analogue of Babinet's principle in optics. Exploiting the similarity of the
resulting differential scattering cross-section with the Fraunhofer diffraction
pattern, we construct a dictionary for such FEO. Subsequently, we evaluate the
resistivity of such scattered MDF using the Boltzmann approach as a function of
the angle made between the direction of propagation of these charge-carriers
and the symmetry axis of the dot-lattice, and Fourier analyze them to show that
the spatial frequency associated with the angle-resolved resistivity gets
filtered according to the structural changes in the dot lattice, indicating
wider applicability of FEO of MDF.
