Understanding the Diffraction Limit

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What the limit means

The diffraction limit is the smallest detail a perfect lens can resolve, set by the wavelength of light and the size of the aperture. Because light spreads as it passes through an aperture, two closely spaced points cannot be fully separated if they are closer than a certain angle. This is a physical limit, not a manufacturing defect.

The Rayleigh criterion

A common way to define resolution is the Rayleigh criterion. Two point sources are just resolved when the centre of the Airy pattern of one falls on the first dark ring of the other. For a circular aperture of diameter D, the smallest resolvable angle is approximately 1.22 λ divided by D, in radians.

This criterion is a convention. Other criteria exist and give slightly different limits. The Rayleigh value is the one most often quoted in introductory treatments.

The same limit in the frequency domain

Designers often describe resolution in terms of spatial frequency: how many line pairs per millimetre a lens can transmit. For incoherent light, the diffraction cutoff frequency is 1 divided by the product of the wavelength and the f-number. At 550 nanometres and f/8, that is about 227 line pairs per millimetre.

This is the frequency beyond which a diffraction-limited lens transmits no detail at all. The MTF chart shows how a real lens falls away towards this cutoff.

Why it matters for choosing equipment

A sensor with very small pixels can record detail beyond what a lens can deliver at a given aperture. In that case, the image is limited by the lens, not by the sensor. Knowing the diffraction limit helps you judge whether more pixels will improve the result.

Assumptions

The limit assumes a diffraction-limited lens with no significant aberrations, and it applies to the lens as a whole, not to any single element. Real lenses fall short of it, and many modern lenses approach it only in their best aperture range.

Diffraction limit and telescopes

The same principle applies to telescopes. A larger aperture gives a smaller angular resolution, because the diffraction-limited angle depends on wavelength divided by aperture diameter. This is why larger telescopes resolve finer detail in the same conditions. Atmospheric turbulence often limits real telescopes before diffraction does, which is why many observatories use adaptive optics. The diffraction limit remains the ideal the telescope can approach.

Why wavelength matters

For a given aperture, shorter wavelengths give a smaller Airy disk and a higher diffraction cutoff. Blue light therefore supports finer detail than red light through the same lens, all else being equal. This is one reason that imaging systems are sometimes evaluated at several wavelengths, and why colour sensors and lenses are designed as a system rather than as separate parts.

A short calculation to try

Calculate the Rayleigh angle for a 0.1 metre aperture at 550 nanometres. The angle is 1.22 × 550 × 10 to the power of minus 9 metres, divided by 0.1 metre, which is about 6.7 micro-radians. At a distance of 1 kilometre, two points separated by about 6.7 millimetres would be just resolved. Repeating the calculation for other apertures and distances builds an intuition for how far a lens can see fine detail.

The Sparrow criterion

The Rayleigh criterion is not the only way to define resolution. The Sparrow criterion defines two points as just resolved when the combined intensity between them shows no dip. It gives a slightly smaller separation than the Rayleigh value. Both are conventions, and the choice depends on the application. In practice, the difference is small compared with the effect of aberrations and noise.

Resolution in the image plane

The Rayleigh angle can be converted into a separation on the image plane by multiplying by the focal length. For a lens of 50 millimetres focal length operating at 550 nanometres with a 6.25 millimetre entrance pupil (f/8), the image-plane separation is about 5.4 micrometres. That separation is comparable to a 4 micrometre pixel pitch, so the lens and the sensor both contribute to what can be resolved.

Limits set by the medium

Diffraction limits apply in air and in other media. In a medium of higher refractive index, the wavelength is shorter, so the diffraction limit is finer. Immersion microscopy uses this effect. For photography, the medium is air, so the standard wavelength and aperture relation applies directly.

Diffraction and the eye

The human eye is also a diffraction-limited optical system at its best. Its pupil size and the wavelength of visible light set a limit on the detail the retina can receive from an image. In bright light, when the pupil is small, diffraction plays a larger part in the eye's resolution than in dim light. The principle is the same as for a camera lens.

Using the limit to set expectations

Before buying a longer lens for fine detail, calculate the diffraction limit at the aperture you plan to use. If the sensor pixel pitch is already coarser than the lens limit, a sharper lens will not produce more detail. If the sensor is finer than the lens limit, a sharper lens or a wider aperture may help. The calculation turns a general claim into a decision you can check.

Diffraction and telescopes in practice

Telescope makers quote resolution in arcseconds, which is convenient because the diffraction-limited angle is small. The same formula applies, but the wavelength and aperture are often in different units, so conversion is part of the work. Atmospheric turbulence limits most ground-based telescopes long before diffraction does.

When the limit is not the bottleneck

In many handheld photographs, subject motion, camera shake, focus error and noise limit the image before diffraction does. The diffraction limit matters most in tripod work, in astrophotography and in high-resolution scanning, where the other errors have been reduced.

Going further

Many photographers meet the diffraction limit without naming it, when a stopped-down image looks soft. Knowing the limit turns that experience into a number, which can be checked against the pixel pitch of the sensor in use.

Summary

The key point of this article is the one stated at its start. Check the formula, use the stated assumptions, and confirm any result with a test before relying on it in practice.

Sources

Eugene Hecht, Optics, Pearson (any current edition).
Max Born and Emil Wolf, Principles of Optics, Cambridge University Press (any current edition).
ISO 12233: Photography, Electronic still picture imaging, Resolution and spatial frequency responses.

Next step

Return to the pillar guide or the Diffraction summary to read the related articles.

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General information only. This page explains optical principles and does not replace lens design work, lens testing or advice from a qualified optical engineer.