Microscope optical resolution calculator
Lateral and axial resolution of an objective by the Abbe, Rayleigh or confocal conventions, with the Airy disk.
Result
| 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 |
226.6 nm
- Airy disk diameter
- 453.1 nm
- Airy disk at sensor
- 27 190 nm
Note
To compare with the camera’s physical pixel size.
Calculation, assumptions and sources
Provisional · Physical model · 2 sources · reviewed on 1 August 2026
OverviewLateral and axial resolution by the three common conventions (Abbe, Rayleigh, confocal), and the radius and diameter of the Airy disk, from wavelength, numerical aperture and immersion medium.
Lateral and axial resolution by the three common conventions (Abbe, Rayleigh, confocal), and the radius and diameter of the Airy disk, from wavelength, numerical aperture and immersion medium.
Method & formulasAbbe: d = λ / (2 × NA)
Abbe (0.5) describes the smallest spatial period transmitted by the objective. Rayleigh (0.61) describes the separation of two point sources and coincides by construction with the Airy disk radius; its value is roughly 22% larger than Abbe’s. The confocal coefficient assumes a closed pinhole. A resolution value comes with its convention.
- Numerical aperture (NA)
- NA = n × sin θ, where n is the medium index and θ the half-angle of acceptance. It can never exceed n, hence immersion.
- Lateral resolution
- smallest separable distance in the slide plane (x, y).
- Axial resolution
- smallest separable distance along the optical axis (z), roughly three times worse than lateral.
- Airy disk
- diffraction pattern of a point source. Its radius is 0.61 λ / NA whatever the convention.
AssumptionsA perfect optical system, free of aberrations, and a self-luminous object.
- A perfect optical system, free of aberrations, and a self-luminous object.
- The confocal axial coefficient (1.4) assumes a closed pinhole; it approximates the formula 0.88·λ/(n−√(n²−NA²)).
Validity domain1 validity limit; the calculation refuses values outside 1 of them
Residual aberrations, an index mismatch between mounting medium and immersion, or a poor signal-to-noise ratio degrade the resolution achieved. In confocal mode, at 1 Airy unit, the common working setting, lateral resolution is 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).
Resolution, magnification and pixel sizeResolution depends only on wavelength and numerical aperture.
Resolution depends only on wavelength and numerical aperture. Enlarging an already resolved image gives so-called empty magnification. The sensor only determines whether the resolution is properly sampled (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.
Wilson, T. & Sheppard, C. J. R., Theory and Practice of Scanning Optical Microscopy, Academic Press, Londres, 1984.
Scientific validationProvisional, reviewed on 1 August 2026
Scope and limitations
- The first two coefficients come from Abbe (1873) and Rayleigh (1879); without verifiable open access to these texts, the cited source is a technical page (Nikon MicroscopyU).
Provisional · Sources and assumptions are provided; the documentary review is incomplete.
Physical model. The result follows the significant figures of the least precise input.
Revision log
Ajout des sources des coefficients (Nikon MicroscopyU pour Abbe/Rayleigh, Wilson & Sheppard 1984 pour le confocal) et du domaine de validité de NA.
Aucun changement de résultat, les coefficients (0,5 / 0,61 / 0,4 / 2 / 1,4) ne sont pas modifiés.