Sum frequency generation image reconstruction: Aliphatic membrane under spherical cap geometry

The article explores an opportunity to approach structural properties of phospholipid membranes using Sum Frequency Generation microscopy. To establish the principles of sum frequency generation image reconstruction in such systems, at first approach, we may adopt an idealistic spherical cap uniform assembly of hydrocarbon molecules. Quantum mechanical studies for decanoic acid (used here as a representative molecular system) provide necessary information on transition dipole moments and Raman tensors of the normal modes specific to methyl terminal – a typical moiety in aliphatic (and phospholipid) membranes. Relative degree of localization and frequencies of the normal modes of methyl terminals make nonlinearities of this moiety to be promising in structural analysis using Sum Frequency Generation imaging. Accordingly, the article describes derivations of relevant macroscopic nonlinearities and suggests a mapping procedure to translate amplitudes of the nonlinearities onto microscopy image plane according to geometry of spherical assembly, local molecular orientation, and optical geometry. Reconstructed images indicate a possibility to extract local curvature of bilayer envelopes of spherical character. This may have practical implications for structural extractions in membrane systems of practical relevance