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

TL;DR

This paper provides an analytical model linking STED power to resolution using vector optical theory for vortex phase modulation, enabling direct resolution estimation from experimental parameters.

Contribution

It offers the first strict analytical description of the relationship between STED power and resolution for high-aperture vortex phase modulation.

Findings

Derived an analytical expression for STED resolution based on vector optical theory.

Validated the inverse square root relationship between STED power and resolution.

Provided a method to estimate resolution from saturation power measurements.

Abstract

Stimulated emission depletion (STED) can achieve optical super-resolution, with the optical diffraction limit broken by the suppression on the periphery of the fluorescent focal spot. Previously, it is generally experimentally accepted that there exists an inverse square root relationship with the STED power and the resolution, yet without strict analytical description. In this paper, we have analytically verified the relationship between the STED power and the achievable resolution from vector optical theory for the widely used 0-2$\pi$ vortex phase modulation. Electromagnetic fields of the focal region of a high numerical aperture objective are calculated and approximated into polynomials, and analytical expression of resolution as a function of the STED intensity has been derived. As a result, the resolution can be estimated directly from the measurement of the saturation power of the dye and the STED power applied.