The Rayleigh criterion defines the minimum angular separation at which two point light sources can be distinctly resolved by an optical instrument, such as a microscope or telescope. It stems from the wave nature of light, which causes diffraction when light passes through an aperture like a lens.
The Concept:
When light from two close objects enters a circular aperture (e.g., a lens), each point source forms a diffraction pattern called an Airy disk — a bright central spot surrounded by rings. As the objects get closer together, their Airy disks begin to overlap.
According to the Rayleigh criterion, two sources are just resolvable when the central maximum of one Airy disk coincides with the first minimum of the other. If they are closer than this, their images blur into each other and cannot be distinguished.
Implications:
- The angular resolution limit (θ) depends on the wavelength (λ) of light and the diameter (D) of the aperture:
θ ≈ 1.22 × (λ / D) - Larger apertures and shorter wavelengths improve resolution.
Applications:
- Astronomy: Limits the detail visible in distant stars or planets.
- Microscopy: Determines the smallest structures that can be seen clearly.
- Photography and optical engineering: Sets practical limits on camera resolution.
The Rayleigh criterion emphasizes that diffraction is a fundamental barrier to optical resolution, and overcoming it requires innovative technologies like adaptive optics or super-resolution microscopy.