Microscope optical resolution calculator
Abbe: d = λ / (2 × NA)
Enter wavelength, numerical aperture and immersion medium: the tool shows lateral and axial resolution side by side for the three common conventions (Abbe, Rayleigh. Confocal), along with the radius and diameter of the Airy disk. Values differ between conventions without any being wrong: they do not answer the same question.
| Convention | Lateral resolution | Axial resolution |
|---|---|---|
| Abbe | 185.7 nm | 803.9 nm |
| Rayleigh | 226.6 nm | 803.9 nm |
| Confocal (closed pinhole) | 148.6 nm | 562.7 nm |
Compare this value with your camera’s physical pixel size: it tells you whether the sensor samples the diffraction pattern.
Scientific dossier
What the tool computes, what it assumes, where it stops being valid, and where its data comes from.
Method & formulasAbbe: d = λ / (2 × NA)
Abbe: d = λ / (2 × NA)
Rayleigh: d = 0.61 × λ / NA
Confocal (closed pinhole): d = 0.4 × λ / NA
Axial (widefield): d_z = 2 × λ × n / NA²
Abbe describes the smallest spatial period transmitted by the objective. Rayleigh describes the separation of two point sources, and coincides by construction with the Airy disk radius. The confocal coefficient assumes a closed pinhole.
- Numerical aperture (NA)
- · NA = n × sin θ, where n is the medium index and θ the half-angle of acceptance. It can never exceed the medium index, hence the point of immersion.
- Lateral resolution
- · smallest separable distance in the slide plane (x, y).
- Axial resolution
- · smallest separable distance along the optical axis (z). It is always markedly worse than lateral, by roughly a factor of three.
- Airy disk
- · diffraction pattern of a point source. Its radius is 0.61 λ / NA, independent of the resolution convention chosen.
AssumptionsA perfect optical system, free of aberrations.
- A perfect optical system, free of aberrations. With a self-luminous object, see "Limitations" above.
- The confocal axial coefficient (1.4) assumes a closed pinhole, an approximation of the more exact formula 0.88·λ/(n−√(n²−NA²)). See ADR-0024.
Validity domain1 bound declared, 1 blocking
These formulas describe a perfect, aberration-free system with a self-luminous object. In practice, residual aberrations, an index mismatch between mounting medium and immersion, or a poor signal-to-noise ratio degrade the resolution actually achieved. The confocal mode further assumes a closed pinhole: at 1 Airy unit, the common working setting, lateral resolution falls back to essentially the widefield value.
na ≥ 0physical · refusal
Numerical aperture cannot be negative or zero.
Instead · Check the entered numerical aperture value (NA = n × sin θ).
Why two calculators give different valuesBecause they do not apply the same convention.
Because they do not apply the same convention. Rayleigh (0.61) gives a value roughly 22% larger than Abbe (0.5) for the same configuration: the first requires distinguishing two points, the second transmitting a period. Neither is wrong. A calculator that does not state its convention simply implies a precision it never defines.
Resolution, magnification and pixel sizeResolution depends only on wavelength and numerical aperture.
Resolution depends only on wavelength and numerical aperture. Neither magnification nor the sensor improves it: enlarging an already resolved image further produces so-called empty magnification. The sensor only determines whether that resolution is properly recorded, the sampling question. Handled by the Nyquist calculator.
SourcesNikon Instruments Inc. · MicroscopyU (auteur : Michael W. Davidson, National High Magnetic Field Laboratory, Florida State University) · Wilson, T. & Sheppard, C. J. R.
Nikon Instruments Inc. · MicroscopyU (auteur : Michael W. Davidson, National High Magnetic Field Laboratory, Florida State University), Resolution, © 2025, consulté 2026-08-01.
Location : Formules « Resolution (r) = λ/(2NA) » et « Resolution (r) = 0,61λ/NA » · accessed 2026-08-01
Wilson, T. & Sheppard, C. J. R., Theory and Practice of Scanning Optical Microscopy, Academic Press, Londres, 1984.
Location : Coefficient axial confocal 1,4·λ·n/NA² (approximation à sténopé fermé, voir ADR-0024) · accessed 2026-08-01
Scientific validationProvisional · revision 1 · reviewed 2026-08-01
Scope and limitations
- Abbe (1873) and Rayleigh (1879) are the original publications for the first two coefficients; without verifiable open access, the cited source is a corroborating technical page (Nikon MicroscopyU), not the primary papers themselves.
Provisional · Sources and assumptions are declared; the full documentary review is still pending.
Physical model. The result follows the significant figures of the least precise input.
revision 1 · reviewed 2026-08-01
Revision log
revision 1 · 2026-08-01 · source update
Bloc scientifique renseigné : sources des coefficients (Nikon MicroscopyU pour Abbe/Rayleigh, Wilson & Sheppard 1984 pour le confocal), domaine de validité de NA.
Aucun changement de résultat, les coefficients (0,5 / 0,61 / 0,4 / 2 / 1,4) ne sont pas modifiés.