Airy disk

Airy disk refers to the pattern of light observed when a point light source passes through a circular aperture. This phenomenon is named after the British astronomer George Biddell Airy, who first described it in 1835. The Airy disk is a central concept in the field of optics, particularly in understanding the limitations of the resolving power of telescopes, microscopes, and other imaging systems.

Formation

The Airy disk is formed due to the diffraction of light, a wave phenomenon, as it passes through a circular aperture. According to the principles of wave optics, when light waves encounter an obstacle, they spread out instead of moving in straight lines. In the case of a circular aperture, this spreading results in a distinctive pattern on a screen placed behind the aperture. The central bright spot, surrounded by concentric rings of decreasing intensity, is what is known as the Airy disk. The size of the Airy disk is inversely proportional to the diameter of the aperture through which the light is passing.

Mathematical Description

The intensity distribution of the Airy disk can be described mathematically by the square of the first kind of Bessel function of the first order, normalized to the total power of the light beam. The radius of the first dark ring surrounding the central bright spot, known as the first Airy ring, is given by the equation:

\[ r = 1.22 \lambda \frac{f}{D} \]

where \( \lambda \) is the wavelength of the light, \( f \) is the focal length of the lens, and \( D \) is the diameter of the aperture. This equation highlights the dependence of the Airy disk's size on the wavelength of light and the aperture's dimensions.

Significance in Imaging Systems

The concept of the Airy disk is crucial in understanding the resolution limit of optical imaging systems, known as the Rayleigh criterion. According to this criterion, two point sources are considered to be just resolvable when the center of the Airy disk of one image coincides with the first minimum of the other. This limitation is fundamental in optical systems and determines the maximum resolution that can be achieved.

Applications

The Airy disk has applications in various fields of science and technology. In astronomy, it defines the resolving power of telescopes, limiting the ability to distinguish between closely spaced celestial objects. In microscopy, it sets the limit on the smallest detail that can be resolved. Furthermore, understanding and manipulating the Airy disk is essential in the development of advanced optical systems, including adaptive optics and super-resolution microscopy.

See Also

• Diffraction
• Optics
• George Biddell Airy
• Rayleigh criterion