Choose Rayleigh, Abbe, or Airy modes for your setup and parameter presets. Enter wavelength and aperture, then get resolution in arcseconds, microns, plus exports.
| Scenario | λ | D / NA / f/# | Typical result | Notes |
|---|---|---|---|---|
| Telescope (visible) | 550 nm | D = 100 mm | θ ≈ 1.38 arcsec | Rayleigh angular criterion for a circular aperture. |
| Microscope (oil) | 550 nm | NA = 1.30 | d ≈ 0.26 µm | Rayleigh lateral resolution, high-NA objective. |
| Camera lens | 550 nm | f/# = 8 | Airy diameter ≈ 10.7 µm | Useful when comparing pixel pitch to spot size. |
Values are approximate and assume ideal circular pupils.
These relations assume diffraction-limited performance, a circular pupil, and monochromatic light. Aberrations, misalignment, and atmospheric turbulence can enlarge real-world spots.
Any finite pupil spreads light into an Airy pattern. Even a perfect lens cannot focus a point into an infinitely small dot. The practical consequence is a minimum angular or spatial separation needed to distinguish two features, regardless of magnification.
For a circular aperture, the first minimum occurs at θ = 1.22·λ/D. At λ = 550 nm and D = 100 mm, θ ≈ 6.7×10-6 rad, which is about 1.38 arcseconds. Larger D improves resolution linearly, while longer wavelengths reduce it.
For distant targets, the small-angle approximation converts angular resolution into a linear distance: s ≈ θ·L. For the same 100 mm aperture at 1 km, the limit is roughly 6.7 mm. This is useful for inspection optics, ranging systems, and field tests.
In microscopy, the limiting factor is the collection cone rather than a simple diameter. The numerical aperture is NA = n·sin(α), with typical air objectives around 0.95 and oil immersion commonly 1.30–1.40. Higher NA increases detail without requiring shorter wavelengths.
Two common lateral-resolution estimates are Abbe d = λ/(2·NA) and Rayleigh d = 0.61·λ/NA. With λ = 550 nm and NA = 1.30, Abbe gives ~0.21 µm and Rayleigh ~0.26 µm. Use consistent criteria when comparing objectives or publications.
At the focal plane, the Airy diameter is 2.44·λ·(f/#). At λ = 550 nm and f/8, the diameter is ~10.7 µm. If pixel pitch is 3.9 µm, the diffraction blur spans ~2.7 pixels, so stopping down may reduce sharpness even when depth of field improves.
Diffraction is only one part of image quality. Aberrations, focus error, vibration, atmospheric seeing, and scattering can dominate. A common engineering approach is to compare the predicted diffraction spot with measured point spread data and track the ratio as a performance indicator.
Start by selecting the mode that matches your hardware. Enter wavelength bands you care about, then sweep aperture, NA, or f-number to see how limits scale. Export results for documentation, and keep criteria consistent across comparisons and tests.
A system is diffraction-limited when aberrations are small enough that the Airy pattern sets the dominant blur, so resolution follows the wavelength and aperture-based formulas rather than lens imperfections.
Use the band that matters for your detector or filter. For visible imaging, 550 nm is a common reference. For RGB sensors, evaluate each channel or a weighted average for your application.
For a circular pupil, diffraction produces an Airy pattern whose first zero occurs at 1.22·λ/D in angle. That constant comes from the first root of the Bessel function describing the pattern.
Yes. In immersion microscopy, the medium refractive index n exceeds 1, so NA = n·sin(α) can exceed 1. Air objectives typically stay below 1 because n≈1 for air.
Either is acceptable, but be consistent. Abbe is slightly more optimistic than Rayleigh. Rayleigh often matches two-point distinguishability, while Abbe is popular for periodic structures and teaching contexts.
F-number is f/D, the focal length divided by the entrance pupil diameter. Smaller f/# means a larger aperture, smaller diffraction spots, and higher light throughput, but may increase aberrations in real lenses.
Magnification enlarges the image but does not change the diffraction blur already formed by the optics. To resolve finer detail, you need a larger aperture, higher NA, or a shorter wavelength.
Accurate diffraction estimates help you choose better optical systems.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.