Motivated by the recent observation of periodic filter characteristics of an oval-shaped microcavity, we study the possible interference of multiple beams in the far field of a laser-illuminated quadrupolar glass fiber. From numerical ray-tracing simulations we obtain the interference-relevant length-difference spectrum and compare it with data extracted from the experimental filter results. Our analysis reveals that different polygonal cavity modes that are refractively output coupled in the high-curvature region of the fiber contribute to the observed far-field interference.