Top: Cross section of a steady-state FDM filament with FDM mass m = 2 × 10⁻²² eV at redshift z = 4. The interference is constructed as a post-processing step for an interference-free background density which may be provided by an analytical model (this work) or DM simulations (future work). Bottom: Volume rendering of a toy filament obtained by extruding above cross section along a straight filament spine. Section 2 models FDM filaments as infinitely long versions of such extrusions. In Sect. 3 we find a physically-sound extrusion length for our 2D model via ellipsoidal collapse considerations.