Image scanning microscopy: a vectorial physical optics analysis

Image scanning microscopy (ISM) achieves resolution beyond the diffraction limit by a factor of 2. However, prior ISM research predominantly employs scalar diffraction theory, neglecting critical physical effects such as polarization, aberrations, and Stokes shift. This paper presents a comprehensive vectorial ISM point spread function (PSF) model that accounts for these phenomena. By considering the effect of polarization in emission and excitation paths, as well as aberrations and Stokes shift, our model provides a more accurate representation of ISM. We analyze the differences between scalar and vectorial theories in ISM and investigate the impact of pinhole size and aberration strength on resolution. At a numerical aperture of 1.2, the full width half maximum (FWHM) discrepancy between scalar and vectorial ISM PSFs can reach 45 nm, representing a 30% deviation from the vectorial model. Additionally, we explore multiphoton excitation in ISM and observe increased FWHM for 2-photon and 3-photon excitation compared to 1-photon excitation. The FWHM of the 2-photon excitation ISM PSF increases by 20% and the FWHM of the 3-photon excitation ISM PSF increases by 28% compared to the 1-photon excitation ISM. In addition, we found that the optimal sweep factor for 2-photon ISM is 1.22, and the optimal sweep factor of 3-photon ISM is 1.12 instead of the 2 predicted by the one-photon scalar ISM theory. Our work improves the understanding of ISM and contributes to its advancement as a high-resolution imaging technique.