  Super-resolution mapping of the 3D orientation of fluorophores reveals the
alignment of biological structures where the fluorophores are tightly attached,
and thus plays a vital role in studying the organization and dynamics of
bio-complexes. However, current super-resolution imaging techniques are either
limited to 2D orientation mapping or suffer from slow speed and the requirement
of special labels in 3D orientation mapping. Here, we propose a novel polarized
virtual spatial-frequency-shift effect to overcome these restrictions to
achieve a universal 3D orientation super-resolution mapping capability. To
demonstrate the mechanism, we simulate the imaging process and reconstruct the
spatial-angular information for sparsely distributed dipoles with random 3D
orientations and microfilament-like structures decorated with fluorophores
oriented parallel to them. The 3D orientation distribution can be recovered
with a doubled spatial resolution and an average angular precision of up to
2.39 degrees. The performance of the approach with noise has also been analyzed
considering real implementation.
