PALM/STORM Localization Calculator

Localization precision from photons, background and pixel size, and effective resolution with label density, for single-molecule localization microscopy (PALM/STORM).

Model: Textbook approximation

Emission wavelength (nm)Numerical apertureDetected photons per localization NBackground b² (photons per pixel)Pixel size in the sample (nm)

Fit

Camera

Label density counted in

Label density (µm⁻²)Number of framesFrame rate (frames/s)

Results

PSF σ = 0.21 λ/NA91.2 nm

Localization precision σ_loc4.29 nm

Shot-noise limit σ/√N2.88 nm

Localization FWHM 2.355 σ_loc10.1 nm

Mean label spacing20.0 nm

Nyquist resolution 2/ρ^(1/D)40.0 nm

Effective resolution41.3 nm

Diffraction limit λ/(2NA)217 nm

Acquisition time200 s

σ_a² = σ² + a²/12. Least squares: σ_loc² = σ_a²/N · (16/9 + 8π σ_a² b²/(N a²)) (Mortensen 2010, eq. 6).

Maximum likelihood: σ_loc² = σ_a²/N · [1 + ∫₀¹ ln t / (1 + N a² t/(2π σ_a² b²)) dt]⁻¹ (eq. 5). EMCCD: × 2.

Effective resolution = √((2.355 σ_loc)² + (2/ρ^(1/D))²) (Legant 2016). It assumes every label is localized once.

sCMOS pixel read noise is not modelled (Mortensen et al. cover EMCCD and CCD).

Localization precision vs photon count

Effective resolution vs label density

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

Gaussian fit to the PSF (σ = 0.21 λ/NA), with Mortensen's pixelation and background terms, one localization per label, and the effective resolution as the localization FWHM and the Nyquist term in quadrature. Lateral precision only; drift, label size, repeated blinking and sCMOS read noise are not included.

Mortensen K. I., Churchman L. S., Spudich J. A., Flyvbjerg H. (2010). Optimized localization analysis for single-molecule tracking and super-resolution microscopy. Nat. Methods 7, 377–381. Precision of maximum-likelihood (eq. 5) and least-squares (eq. 6) Gaussian fits; EMCCD excess noise doubles the variance. doi:10.1038/nmeth.1447
Shroff H., Galbraith C. G., Galbraith J. A., Betzig E. (2008). Live-cell photoactivated localization microscopy of nanoscale adhesion dynamics. Nat. Methods 5, 417–423. Nyquist resolution 2/ρ^(1/D). doi:10.1038/nmeth.1202
Legant W. R. et al. (2016). High-density three-dimensional localization microscopy across large volumes. Nat. Methods 13, 359–365. Localization FWHM and Nyquist resolution combined in quadrature. doi:10.1038/nmeth.3797

Report a problem