diffraction limit calculator

What this diffraction limit calculator tells you

This tool estimates the best-case optical resolution imposed by wave physics. Even with perfect glass, perfect focus, and no atmospheric turbulence, a finite aperture spreads a point source into an Airy pattern. That sets a hard limit on sharpness called the diffraction limit.

The calculator provides:

• Angular resolution in radians, degrees, and arcseconds
• f-number from your focal length and aperture
• Airy disk diameter at the focal plane (useful for camera pixels and sampling)
• Approximate diffraction-limited cutoff frequency in cycles/mm (when focal length is provided)

Core equations used

1) Rayleigh criterion (circular aperture)

Where θ is the minimum resolvable angular separation (radians), λ is wavelength, and D is aperture diameter.

2) Airy disk diameter at image plane

Here, N is f-number, and f is focal length. This gives the central spot diameter and helps compare optical blur size to sensor pixel pitch.

How to use the calculator

1. Set wavelength in nanometers (e.g., 550 nm for green light).
2. Enter aperture diameter in millimeters.
3. Enter focal length for focal-plane metrics (Airy size and cutoff frequency).
4. Use refractive index if working in media other than air.

If your system uses broad-spectrum light, run the calculation at several wavelengths (for example 450 nm, 550 nm, 650 nm) to see how diffraction changes across color.

Practical interpretation

Telescopes

Bigger aperture means smaller diffraction angle and better resolving power. In practice, atmospheric seeing often dominates before you reach the theoretical limit.

Microscopes and imaging optics

Shorter wavelength and larger numerical aperture improve detail. For sensors, compare the Airy disk diameter to pixel size: if pixels are much larger than the Airy disk, sampling is coarse; if much smaller, you may oversample.

Cameras stopped down to high f-number

As f-number increases, Airy disks grow. This is why very small apertures can reduce sharpness despite deeper depth of field.

Quick example

At 550 nm and 100 mm aperture, the Rayleigh limit is about 1.38 arcseconds. If focal length is 1000 mm (f/10), the Airy disk diameter is approximately 13.4 µm.

Important limitations

• Assumes a perfect, diffraction-limited circular aperture.
• Does not include aberrations, alignment error, vibration, detector noise, or seeing.
• Central obstructions and non-circular pupils modify the point spread function.

Use this result as a physical baseline: real systems are usually equal or worse, never better, than the diffraction limit.