Diffraction Limit Calculator
Calculate the smallest resolvable spot or feature that an optical system can distinguish, based on wavelength and aperture. Use it when designing cameras, telescopes, or microscopes where resolution is critical.
About this calculator
Diffraction prevents any lens from focusing light to a perfect point. The Rayleigh criterion states that two point sources are just resolved when the central maximum of one falls on the first minimum of the other, giving a minimum resolvable spot radius r = 1.22 · λ · f / D, where λ is the wavelength, f is the focal length, and D is the aperture diameter. The Sparrow criterion is slightly tighter: r = 1.03 · λ · f / D, representing the separation at which the combined intensity profile shows no dip between the two peaks. Both formulas assume a circular aperture and monochromatic illumination. The ratio f/D is the familiar f-number (f/#) used in photography, so r = 1.22 · λ · (f/#) for the Rayleigh case.
How to use
Example using the Rayleigh criterion: wavelength λ = 550 nm = 550 × 10⁻⁶ mm, aperture D = 100 mm, focal length f = 500 mm. Step 1: r = 1.22 × (550 × 10⁻⁶) × 500 / 100. Step 2: r = 1.22 × 0.00055 × 5 = 1.22 × 0.00275 ≈ 0.003355 mm ≈ 3.36 µm. This is the minimum resolvable feature at the focal plane. Using Sparrow: r = 1.03 × 0.00275 ≈ 2.83 µm, about 16% smaller.
Frequently asked questions
What is the difference between the Rayleigh and Sparrow diffraction criteria?
The Rayleigh criterion (factor 1.22) defines resolution as the point where the central maximum of one Airy disk falls on the first zero of the adjacent one, producing a just-visible dip of about 26% in combined intensity. The Sparrow criterion (factor 1.03) is more aggressive: it is the separation at which the combined profile becomes flat at the midpoint, with no dip at all. The Sparrow limit is used in contexts where image processing or interferometry can extract information below the Rayleigh limit, while Rayleigh is the standard in classical visual astronomy.
How does aperture diameter affect the diffraction-limited resolution of a telescope?
Resolution improves (smaller r) linearly as aperture increases, because a larger aperture collects a wider wavefront and produces a narrower Airy disk. Doubling the aperture halves the minimum resolvable spot size. This is why large observatory mirrors can resolve fine planetary detail and faint double stars that small amateur telescopes cannot. Atmospheric turbulence (seeing) often limits ground-based telescopes before diffraction does, which is why space telescopes and adaptive optics systems are so valuable.
Why does shorter wavelength light give better optical resolution?
The diffraction spot radius r = 1.22 · λ · f / D is directly proportional to wavelength. Ultraviolet light (λ ≈ 200 nm) produces spots roughly 2.75× smaller than green light (λ ≈ 550 nm), which is why UV lithography and electron microscopy (effectively λ < 1 nm) can resolve nanometre-scale features. In fluorescence microscopy, selecting shorter-wavelength excitation improves resolution. This principle also drives the use of blue lasers in Blu-ray discs compared with the red lasers in DVDs.