Rayleigh Resolution Calculator
The Rayleigh criterion gives the minimum angular separation at which two point sources can be distinguished through a circular aperture: theta = 1.22 lambda / D, where lambda is the wavelength and D is the aperture diameter. This is the diffraction limit of optical resolution. For a telescope with a 200 mm diameter aperture and 550 nm wavelength, theta = 1.22 x 550e-9 / 0.200 = 3.36e-6 rad = 0.69 arcseconds. You can also specify a focal length to get the linear resolution at the focal plane (minimum resolvable distance between two image points). Enter wavelength and aperture in consistent units.
Rayleigh resolution formula
theta = 1.22 lambda / D (radians)
Linear resolution = theta x focal length
Where lambda is the wavelength and D is the aperture diameter, both in the same units. Convert radians to arcseconds: multiply by (180 / pi) x 3600.
Resolution limits for common instruments
- Human eye (pupil ~5 mm, lambda = 550 nm): theta approximately 1.34e-4 rad = 27 arcseconds, or about 1 arcminute resolution limit.
- 200 mm telescope at 550 nm: theta approximately 0.69 arcseconds.
- Hubble Space Telescope (2.4 m mirror, 500 nm): theta approximately 0.050 arcseconds.
- Oil immersion microscope (NA = 1.40, 550 nm): linear resolution approximately 0.24 micrometers.
Rayleigh resolution: frequently asked questions
What is the Rayleigh criterion?
The Rayleigh criterion states that two point sources are just resolved when the central diffraction maximum of one coincides with the first minimum of the other. For a circular aperture of diameter D, the minimum resolvable angular separation is theta = 1.22 lambda / D radians, where lambda is the wavelength.
How do I find the minimum resolvable distance?
Minimum linear resolution = 1.22 lambda x (image distance or focal length) / D. For a telescope or camera: resolution = 1.22 lambda f / D = 1.22 lambda / (2 NA). For a microscope objective at 550 nm and NA = 1.25: resolution approximately 0.27 micrometers.
What is the difference between Rayleigh and Abbe resolution limits?
The Rayleigh criterion (1.22 lambda/D) applies to incoherent imaging of point sources through circular apertures. The Abbe resolution limit (lambda / (2 NA)) applies to coherent or partially coherent imaging of periodic structures (gratings) and is used more commonly in microscopy. For incoherent illumination, the Abbe limit effectively becomes 0.61 lambda / NA, which equals the Rayleigh criterion.
Why does the Hubble Space Telescope have such good resolution?
Hubble has a 2.4 m primary mirror. At 500 nm (visible), its Rayleigh limit is 1.22 x 500e-9 / 2.4 = approximately 2.5e-7 radians = 0.05 arcseconds. This is diffraction-limited resolution impossible from Earth due to atmospheric seeing, which limits ground-based telescopes to about 0.5 to 2 arcseconds without adaptive optics.
Does the Rayleigh criterion apply to radio telescopes?
Yes. The formula is the same. A single radio dish of 100 m diameter at 21 cm wavelength (neutral hydrogen line) has theta = 1.22 x 0.21 / 100 = approximately 2.6 mrad = 0.15 degrees. Radio telescope arrays (VLBI) use interferometry to achieve arcsecond or sub-arcsecond resolution using baselines of thousands of kilometers.
Official sources
- OpenStax University Physics Volume 3, Chapter 4: Diffraction. openstax.org.
- NIST, Physical Measurement Laboratory. physics.nist.gov.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.