Point group symmetry determination via observables revealed by polarized second-harmonic generation microscopy: (1) theory.

We present a methodology based on polarization-controlled second-harmonic generation microscopy that allows one to determine the point group symmetry of noncentrosymmetric structures in situ and in vivo in complex systems regardless of the occurrence of periodicity. Small, randomly oriented structures suffice for the analysis, which is based on simple recognition of observables in four tests. These can be performed in any standard SHG-microscope that allows polarization control of the incident and detected light. The method is resilient to birefringence and light dispersion.