Creating a spherical focal spot with spatially modulated radial polarization in 4Pi microscopy

We propose an approach to obtain a diffraction-limited spherical focal spot in 4Pi microscopy. By combining the dipole antenna radiation pattern and the Richards-Wolf vectorial diffraction method, an input field at a pupil plane of aplanatic objective lenses for generating a spherical spot can be found analytically by solving the inverse problem. The required field at the pupil plane is found to be a radial polarization with spatial amplitude modulation. With spatial phase modulation, two identical spherical spots with diffraction-limited size and variable distance along the optical axis can also be obtained.