Airymönster

Airymønster, or Airy pattern, is the diffraction pattern produced when coherent light passes through a circular aperture. It consists of a central bright spot, the Airy disk, surrounded by concentric rings. This pattern arises in Fraunhofer, or far-field, diffraction and is a fundamental limit to the sharpness of optical imaging.

The intensity distribution of the Airymønster is described by a Bessel function. For an aperture with diameter D and light of wavelength λ, the on-axis angular intensity I(θ) is proportional to [2 J1(π D sin θ / λ) / (π D sin θ / λ)]^2, where J1 is the first-order Bessel function. On a screen at distance L, with small angles, r ≈ L θ, so I(r) ∝ [2 J1(π D r / (λ L)) / (π D r / (λ L))]^2. The first minimum occurs at sin θ ≈ 1.22 λ / D, which corresponds to a linear radius on the screen of r1 ≈ 1.22 λ L / D.

Significance and use: The Airy pattern sets the diffraction-limited angular resolution of optical systems. According to the Rayleigh criterion, two point sources are resolvable if their angular separation exceeds about 1.22 λ / D. The pattern scales with wavelength and aperture size: larger apertures yield a smaller Airy disk and higher potential resolution.

Variations and applications: Real-world patterns deviate due to aberrations, nonuniform illumination, and detector sampling. Airy patterns are used to characterize optical performance in telescopes, cameras, and microscopes, and to understand the fundamental limits of imaging systems.