Super-Resolution Calculator
STED and PALM/STORM resolution limits beyond the diffraction barrier.
Results
STED: d = λ/(2NA√(1 + (I/I_sat)(λ/λ_STED)²)), Harke et al.'s law d = d_c/√(1 + d_c²a²I/I_sat) (Opt. Express 16, 4154, 2008, Eq. 7) with the confocal d_c = λ/(2NA) at the excitation and a doughnut steepness a = 2NA/λ_STED, chosen so that λ_STED = λ recovers Westphal & Hell's λ/(2NA√(1 + I/I_sat)) (Phys. Rev. Lett. 94, 143903, 2005) and high depletion gives Harke's Eq. 1, λ_STED/(2NA√(I/I_sat)). Harke's computed vortex pattern is 6 % less steep, so real spots at high depletion are about 6 % wider; the I_sat convention also shifts the ratio. 2D (vortex) STED narrows only the lateral spot; the axial FWHM stays 0.88λ/(n − √(n² − NA²)).
PALM/STORM: σ = s/√N, s = 0.21λ/NA, the Gaussian width of the PSF (Zhang et al., Appl. Opt. 46, 1819, 2007). This is the shot-noise limit (Thompson et al., Biophys. J. 82, 2775, 2002): pixelation, background and EMCCD excess noise (×√2) make it worse (Mortensen et al., Nat. Methods 7, 377, 2010).
2D localization gives no axial position. 3D methods (astigmatism, biplane) are typically about twice as coarse axially as laterally (Huang et al., Science 319, 810, 2008).
STED resolution vs depletion
Localization precision vs photons
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
STED resolution law with separate excitation and depletion wavelengths (Harke's generalized law, doughnut steepness 2NA/λ_STED) and the shot-noise limit of single-molecule localization. Pixelation, background and EMCCD excess noise (×√2) make real localization worse; 2D localization gives no axial position.
- Westphal V., Hell S. W. (2005). Nanoscale Resolution in the Focal Plane of an Optical Microscope. Phys. Rev. Lett. 94, 143903. STED resolution d = λ/(2NA√(1 + I/I_s)). doi:10.1103/physrevlett.94.143903
- Harke B., Keller J., Ullal C. K., Westphal V., Schönle A., Hell S. W. (2008). Resolution scaling in STED microscopy. Opt. Express 16, 4154. Generalized law d = d_c/√(1 + d_c²a²I/I_s). doi:10.1364/OE.16.004154
- Zhang B., Zerubia J., Olivo-Marin J.-C. (2007). Gaussian approximations of fluorescence microscope point-spread function models. Appl. Opt. 46, 1819. Gaussian width 0.21 λ/NA that best fits the Airy PSF. doi:10.1364/ao.46.001819
- Thompson R. E., Larson D. R., Webb W. W. (2002). Precise Nanometer Localization Analysis for Individual Fluorescent Probes. Biophys. J. 82, 2775–2783. Shot-noise limit of localization precision. doi:10.1016/s0006-3495(02)75618-x
- Mortensen K. I. et al. (2010). Optimized localization analysis for single-molecule tracking and super-resolution microscopy. Nat. Methods 7, 377–381. Pixelation and EMCCD excess noise (×√2) make localization worse. doi:10.1038/nmeth.1447