Rigorous modelling of second harmonic generation imaging through stratified media focused by radially polarized beams

For second harmonic generation (SHG) imaging, the specimen is often observed through an immersion medium and a cover glass whose refractive indices are usually different from that of the specimen. However, the currently used theoretical models are based on the assumption that the specimen is situated in a homogeneous medium. The limitation of these models is that they ignore the effects of the refractive index mismatches and the imaging depth. In this paper, we have demonstrated, for the first time to our knowledge, a rigorous model of SHG imaging through stratified media focused by radially polarized beams. Based on the proposed model, the detected SHG intensity patterns excited in a refractive index perfectly matched, aberration-free medium and in mismatched stratified media are compared. The effects of the imaging depth and effective numerical aperture (NA) on the performance of SHG imaging with oil immersion objectives are investigated by the stratified media model. It is found that the full width at half maximum (FWHM) in the axial direction at imaging depth of 80 µm is ~3.1 times as large as that of 10 µm imaging depth. While for the transverse FWHM, the increment is only about 23%. The quality of the SHG intensity distribution can be increased by reducing the NA appropriately at the expense of the detected signal strength. The proposed model is helpful to provide guidelines for the adaptive aberration correction in SHG imaging and can be used to optimize the experimental configuration.