Three-dimensional polarization second harmonic generation (3D-PSHG) imaging: the effect of the tilted-off the plane SHG active structures

Polarization sensitive second harmonic generation (PSHG) provides additional information in intensity only SHG imaging. In particular, it offers the SHG effective orientation of the implicated SHG active structures. Assuming that those structures possess cylindrical symmetry, the supplementary contrast is based on the ratio of two non-vanishing, independent elements of the χ 2 tensor. This ratio is experimentally extracted by fitting pixel by pixel a theoretical model to the PSHG images and by finding the maximum frequency value or the mean of the consequent pixels' histogram. In the present study we show that the above χ 2 elements' ratio critically depends on the tilted-off the plane SHG active structures. We performed PSHG in different z-planes of a starch granule (presenting radially oriented amylopectin molecules, the SHG source in starch) and we found different pick values of the χ 2 elements' ratio histogram for each plane. By assuming a fixed value for the χ 2 elements' ratio, we present here a generalized three dimensional (3D) model that determines the 3D orientation of the SHG active structures.