- A diffraction-limited system refers to an optical system whose resolution is restricted solely by the fundamental effects of diffraction, rather than by imperfections in the lenses, mirrors, or detectors. In such systems, the ability to distinguish two closely spaced points is governed by the wave nature of light, which causes it to spread when passing through an aperture. This spreading results in a characteristic diffraction pattern known as the Airy disk, with a bright central maximum surrounded by concentric rings of decreasing intensity. The finite size of this diffraction pattern sets a physical limit on how close two objects can be before their images blur together.
- The classical definition of the diffraction limit comes from the Rayleigh criterion, which states that two point sources are resolvable when the central maximum of one Airy disk coincides with the first minimum of the other. According to this criterion, the minimum resolvable distance d depends on the wavelength of light λ and the numerical aperture (NA) of the imaging system:
- d ≈ 0.61 λ / NA
- Here, the numerical aperture is defined as NA = n sin θ, where n is the refractive index of the medium between the objective lens and the sample, and θ (theta) is the half-angle of light collection. This relationship highlights that higher resolution can be achieved either by using shorter wavelengths of light or by increasing the NA, for instance, with immersion lenses.
- In practice, no optical system is completely perfect, and aberrations such as spherical or chromatic distortions, alignment errors, or lens imperfections can degrade performance below the diffraction limit. However, with high-quality optics, precise alignment, and appropriate corrections, modern microscopes and telescopes can closely approach diffraction-limited performance. Achieving this state ensures that the full resolving power dictated by physics is utilized, enabling the sharpest possible images.
- The concept of diffraction-limited systems is central to both microscopy and astronomy. In microscopy, it defines the fundamental resolution barrier of conventional optical instruments, historically around 200 nanometers for visible light. In astronomy, it sets the theoretical sharpness of images formed by telescopes, where atmospheric turbulence often prevents diffraction-limited resolution unless corrected by adaptive optics. This fundamental understanding of the diffraction limit has also driven the development of super-resolution techniques such as STED, PALM, and STORM, which cleverly circumvent the diffraction-imposed boundary, opening new frontiers in nanoscale imaging.
