I beleive fibre diffraction also works on parallel fibres (non-helical). For example, long chains of beta-sheet (look at beta keratin, which is one of the early non-helical structures analyzed by Astbury).
When I was studying spindle shaped viruses by electron microscopy we'd get beautiful fiber diffraction patterns in the fourier transform of the micrographs. I always wanted to try and solve the helical parameters but never got around to it.