Calculate angular resolution using the Rayleigh criterion, Dawes' limit, and Sparrow limit. Compare apertures and find minimum resolvable features.
Angular resolution defines the smallest angular separation between two point sources that an optical system can distinguish. It is fundamentally limited by diffraction — as light passes through a circular aperture, it forms an Airy disk pattern rather than a perfect point. Two sources are considered resolved when their Airy disks are sufficiently separated.
The Rayleigh criterion, the most widely used standard, states that two sources are just resolved when the central maximum of one Airy disk falls on the first minimum of the other. This gives the resolution angle θ = 1.22 λ/D, where λ is the wavelength and D is the aperture diameter. Two alternative criteria — the Dawes' limit (empirical, for visual double stars) and the Sparrow limit (theoretical minimum for any detectable dip) — provide slightly different thresholds.
This calculator computes all three resolution limits, converts between angular units (arcseconds, microradians, milliradians), and calculates the minimum resolvable feature size at a given observation distance. The comparison table lets you evaluate how different aperture sizes affect resolution at your chosen wavelength, making it invaluable for telescope selection, camera lens evaluation, and remote sensing system design.
This calculator helps astronomers choose telescopes, photographers evaluate lens sharpness, and engineers design optical sensing systems. By comparing Rayleigh, Dawes, and Sparrow limits across apertures, you can make informed decisions about optical equipment.
This tool is designed for quick, accurate results without manual computation. Whether you are a student working through coursework, a professional verifying a result, or an educator preparing examples, accurate answers are always just a few keystrokes away.
Rayleigh Criterion: θ = 1.22 λ / D (radians). Dawes' Limit: θ = 116 / D_mm (arcseconds). Sparrow Limit: θ ≈ 0.84 × Rayleigh. Minimum resolvable feature: s = d × θ, where d is the observation distance.
Result: 0.6824 arcsec
An 8-inch (203 mm) telescope at 550 nm wavelength has a Rayleigh resolution of 1.22 × 550e-9 / 0.203 = 3.31 µrad ≈ 0.68 arcseconds.
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It is the standard diffraction-limited resolution criterion: two point sources are just resolved when the central peak of one Airy pattern falls on the first dark ring of the other. Use this as a practical reminder before finalizing the result.
Dawes' limit is empirical, based on visual observations of double stars by 19th-century astronomers. It is slightly sharper than Rayleigh because trained observers can detect separation even when the dip is small.
Yes. Earth's atmosphere typically limits ground-based telescopes to about 1-2 arcseconds regardless of aperture. Adaptive optics or space-based telescopes overcome this.
Techniques like interferometry, super-resolution microscopy (STED, PALM), and computational methods can achieve sub-diffraction resolution in specific contexts. Keep this note short and outcome-focused for reuse.
For visible light, 550 nm (green) is standard. For infrared, radio, or UV observations, use the actual wavelength. Shorter wavelengths give better resolution.
A camera lens has an effective aperture of focal_length / f-number. For a 50mm f/1.8 lens, the aperture is about 27.8 mm, limiting pixel-level sharpness at high resolution.