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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Diffraction | 2/5 | https://en.wikipedia.org/wiki/Diffraction | reference | science, encyclopedia | 2026-05-05T10:54:57.453682+00:00 | kb-cron |
== Basics == Diffraction is a general phenomenon of waves, occurring whenever a wave encounters some form of obstruction. The obstruction may be solidly blocking the wave, or transparent and shifting the phase of the wave without any change in energy (elastic scattering). The waves beyond the obstacle interfere leading to a diffraction pattern. The diffraction pattern cannot be predicted by the straight line trajectories of geometrical optics. For a simple example, a strong light source blocked by a solid object does not show a crisp dark shadow when examined carefully. The appropriate model for diffraction depends upon the character of the waves and the obstructions. The simplest model uses the Huygens–Fresnel principle. The Huygens part visualizes propagation of a wave by considering every point on a wavefront as a source for a secondary spherical wave, these being called Huygens wavelets. The Fresnel part is the superposition (linear sum) of these secondary waves and their consequent interference. In the absence of obstacles, the Huygens's principle alone predicts wavefront propagation. When some of the secondary waves are blocked by an obstacle, the remainder will create both wavefront propagation in the unblocked direction and waves behind the obstacle which form the diffraction pattern. It is possible to obtain a qualitative understanding of many diffraction phenomena by considering how the relative phases of the individual secondary wave sources vary, and, in particular, the conditions in which the phase difference equals half a cycle in which case waves will cancel one another out. When waves are added together, their sum is determined by their relative phases as well as the amplitudes of the individual waves, so that the summed amplitude can have any value between zero and the sum of the individual amplitudes. Hence, diffraction patterns usually have a series of maxima and minima. In quantum mechanics, diffraction is also described in terms of a wave, but the wavefunction represents a probability amplitude whose modulus squared is the probability of detection. The light and dark regions in diffraction patterns are then areas where the quanta are more or less likely to be detected. Quantitative models which allow the diffraction to be calculated include the Kirchhoff diffraction equation (derived from the wave equation), the Fraunhofer diffraction approximation of the Kirchhoff equation (applicable to the far field), and the Fresnel diffraction approximation (applicable to the near field). Most configurations cannot be solved analytically, but can yield numerical solutions through finite element and boundary element methods. In many cases it is assumed that there is only one scattering event, what is called kinematical diffraction, with an Ewald's sphere construction used to represent that there is no change in energy during the diffraction process. For matter waves a similar but slightly different approach is used based upon a relativistically corrected form of the Schrödinger equation, as first detailed by Hans Bethe. The Fraunhofer and Fresnel limits exist for these as well, although they correspond more to approximations for the matter wave Green's function (propagator) for the Schrödinger equation. Multiple scattering models are required in many types of electron diffraction; in some cases similar dynamical diffraction models are also used for X-rays. The simplest descriptions of diffraction are those in which the situation can be reduced to a two-dimensional problem. For water waves, this is already the case; water waves propagate only on the surface of the water. For light, we can often neglect one direction if the diffracting object extends in that direction over a distance far greater than the wavelength. In the case of light shining through small circular holes, we have to take into account the full three-dimensional nature of the problem.
== Occurrence == The effects of diffraction are often seen in everyday life. The most commonly encountered examples of diffraction are those that involve light; for example, the closely spaced tracks on a CD or DVD which act as a diffraction grating to form the familiar rainbow pattern seen when looking at a disc. This principle can be extended to engineer a grating with a structure such that it will produce any diffraction pattern desired; the hologram on a credit card is an example.
Diffraction in the atmosphere by small particles can cause a corona—a bright disc and rings around a light source such as the Sun or the Moon. At the opposite point, one may observe a glory—bright rings around the shadow of the observer. In contrast to the corona, glory requires the particles to be transparent spheres (like fog droplets), since the backscattering of the light that forms the glory involves refraction and internal reflection within the droplet.
Another frequently encountered example is diffraction spikes which are caused by a range of processes including a non‑circular aperture in a camera or by support struts in a telescope; in normal vision, diffraction through eyelashes may produce similar spikes. When deli meat appears iridescent, the effect is caused by diffraction from the meat fibres.
While diffraction by light is the most common case encountered, diffraction can occur with any kind of wave, for instance ocean waves diffract around jetties and other obstacles. Sound waves can diffract around objects, which is why one can still hear someone calling even when hiding behind a tree. Other examples of diffraction are considered in more detail below.
== Different cases == The diffraction patterns depend upon the nature of the obstacles the wave encounters, both their physical dimensions as well as how the change the phase and/or direction of the wave. The simplest types of obstacles are slits or apertures which block of part of the wave In the far-field / Fraunhofer region, Huygens' principle applied to the open region around such obstacles says that the far-field diffraction pattern is the spatial Fourier transform of the open region shape. This is a direct by-product of using the parallel-rays approximation, which is identical to doing a plane wave decomposition of the plane fields across the open region (see Fourier optics).
=== Single-slit diffraction ===