RayleighSommerfeldin

Rayleigh-Sommerfeld diffraction theory is a scalar wave model that describes how waves propagate through and around an aperture in an opaque screen. It provides an integral representation for the diffracted field in terms of the field or its normal derivative on the aperture plane, addressing some limitations of the older Kirchhoff approach. The theory was developed from the work of Lord Rayleigh and Arnold Sommerfeld in the late 19th and early 20th centuries and is usually encountered as two formulations known as Rayleigh-Sommerfeld I (RS I) and Rayleigh-Sommerfeld II (RS II).

The two forms arise from applying Green's theorem to the Helmholtz equation with different boundary conditions on the aperture plane. RS I uses the field values on the aperture, while RS II uses the normal derivative of the field on the aperture. Both yield integral representations that are exact for monochromatic, scalar waves in homogeneous media and are widely used in optical and acoustic diffraction analyses.

In practice, RS diffraction integrals model both near-field (Fresnel) and far-field (Fraunhofer) diffraction from various apertures, including circular and rectangular shapes, as well as arbitrary openings. The formalism is valued for its accuracy near the aperture and its clear connection to boundary data, making it a staple in imaging, microscopy, and photonics research. It reduces to Kirchhoff diffraction in compatible limits, but often with more rigorous boundary-condition treatment.

See also: Kirchhoff diffraction, Huygens-Fresnel principle, Fourier optics.