Fraunhofer vs Fresnel Diffraction

Fraunhofer vs Fresnel Diffraction. Fraunhofer diffraction, the far‑field regime, is characterized by a planar wavefront impinging on an aperture and a screen placed at a distance large compared to both the wavelength and the aperture size, effectively at infinity. In this limit the incident wave may be treated as perfectly planar, and the angular distribution of the diffracted field is given directly by the Fourier transform of the aperture’s transmittance function; the intensity pattern on the observation screen thus mirrors the squared magnitude of that transform. The derivation relies on simplifying the path‑length difference between secondary wavelets to a linear phase term, yielding a stationary‑phase approximation that neglects terms of order 1/R in the propagation kernel, where R is the distance to the screen. Classical evidence for Fraunhofer regimes includes the canonical Fraunhofer double‑slit experiment and the appearance of diffraction maxima at integer multiples of λ/D, where D is the slit separation, which are reproduced by the sinc‑squared envelope predicted by the Fourier analysis.

Theoretical Context

Fresnel diffraction occupies the intermediate regime, where the distance between aperture and observation plane is comparable to the aperture dimensions or to the square of those dimensions divided by the wavelength, so that curvature of the secondary wavefronts cannot be ignored. The Fresnel integral retains the quadratic phase terms in the free‑space propagator, leading to a more complex, non‑transform‑based expression for the field that must be evaluated numerically or via approximate analytical methods such as the Fresnel–Kirchhoff integral. The resulting intensity patterns exhibit gradual evolution of fringe spacing and contrast with distance, and are commonly observed in near‑field imaging of apertures, edges, and gratings. Empirical confirmation of Fresnel theory comes from observing the transition from a tightly focused “Poisson spot” in circular aperture experiments to the emergence of a clear central maximum as the observation point moves further away, a behavior that matches the quadratic‑phase dependence of the Fresnel integral. The distinction between the two regimes is therefore rooted in the relative magnitude of the diffraction distance to the optical wavelength and aperture dimensions, with Fraunhofer representing the asymptotic far‑field limit and Fresnel describing the curvature‑dominated near‑field behavior.