Quantification of the NA dependent change of shape in the image formation of a z-polarised fluorescent molecule using vectorial diffraction simulations

Abstract

The point spread function of a fixed fluorophore with its dipole axis colinear to the optical axis appears donut-shaped when seen through a microscope, and its light distribution in the pupil plane is radially polarized. Yet other techniques, such as photolithography, report that this same light distribution in the pupil plane appears as a solid spot. How can this same distribution lead to a spot in one case but a donut in the other? Here, we show how the tube lens of the system plays a critical role in determining this shape. Using a vectorial treatment of image formation, we simulate the relative contributions of both longitudinal and radial components to the image of a dipole emitter and thus show how the donut (typically reported for z-polarized single molecule fluorescence microscopy) transforms into a solid spot (as commonly reported for photolithography) as the numerical aperture of the tube lens increases. We find that the transition point occurs around 0.7 NA, which is significantly higher than used for most microscopy systems and lower than for common photolithography systems, thus resolving the seeming paradox of dipole shape.