Simulation of stimulated emission depletion intensity distribution by scalar integral

Stimulated emission depletion (STED) optical nanoscopy can achieve super-resolution fluorescence imaging, by suppressing fluorescence on the peripheral of excitation center with a 0-2pi spiral phase plate. Previously, the STED intensity distribution at the focal plane and the derived expression of resolution are generally analytical described by vectorial integral. To overcome the complex and multifarious of the vectorial calculation, we proposed scalar integral method and used the Collins-Huygens integral to analytically describe the peak intensity, the central intensity of the doughnut spot and the resolution of STED nanoscopy. We verified our method by comparing our results with vector theory. And we found it agreed well with vectorial theory under the high STED power, which was commonly used experimental condition for high resolution. Our method provides a fast and convenient way to evaluate the performance of STED with spiral phase modulation.