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Stimulated emission depletion (STED) can achieve optical super-resolution,with the optical diffraction limit broken by the suppression on the peripheryof the fluorescent focal spot. Previously, it is generally experimentallyaccepted that there exists an inverse square root relationship with the STEDpower and the resolution, yet without strict analytical description. In thispaper, we have analytically verified the relationship between the STED powerand the achievable resolution from vector optical theory for the widely used0-2$\pi$ vortex phase modulation. Electromagnetic fields of the focal region ofa high numerical aperture objective are calculated and approximated intopolynomials, and analytical expression of resolution as a function of the STEDintensity has been derived. As a result, the resolution can be estimateddirectly from the measurement of the saturation power of the dye and the STEDpower applied.

Analytical description of high-aperture STED resolution with 0-2$\pi$ vortex phase modulation