Diffraction is the deviation of waves from straight-line propagation due to an obstacle or through an aperture, without any change in their energy. Diffraction is the same physical effect as interference, but interference is typically used for the superposition of a few waves, while the term diffraction is used when many waves are superposed. The term diffraction pattern is used to refer to an image or map of the different directions of the waves after they have been diffracted. Diffraction patterns are pronounced when a wave from a coherent source (such as a laser) encounters a slit/aperture as shown in the first image.
In classical physics, diffraction is described by the Huygens–Fresnel principle that treats each point in a propagating wavefront as a collection of individual spherical wavelets.Wireless Communications: Principles and Practice, Prentice Hall communications engineering and emerging technologies series, T. S. Rappaport, Prentice Hall, 2002 pg 126 The patterns are due to the summation over different points on the wavefront (or, equivalently, each wavelet) that travel by paths of different lengths to the registering surface. If there are multiple closely spaced openings, a complex pattern of varying intensity can result. Other types of apertures or obstacles lead to different patterns, some of which are described later on this page.
These effects occur when a light wave travels through a medium with a varying refractive index, or when a sound wave travels through a medium with varying acoustic impedance – all waves diffract, including gravitational waves, water waves, and other electromagnetic waves such as X-rays, radio waves as well as matter waves such as electrons and neutrons. It plays a role in many areas, ranging from security devices on credit cards to methods of determining the atomic structure of materials at the nanoscale.
Italian scientist Francesco Maria Grimaldi coined the word diffraction and was the first to record accurate observations of the phenomenon in 1660. After that various equivalent formulations were derived; mathematically, diffraction is explained by solving the wave equation for electromagnetic waves, or Schroedinger's equation for matter waves, in some cases with relativistic corrections.
History
The effects of diffraction of light were first carefully observed and characterized by Francesco Maria Grimaldi, who also coined the term diffraction, from the Latin diffringere, 'to break into pieces', referring to light breaking up into different directions. The results of Grimaldi's observations were published posthumously in 1665.Francesco Maria Grimaldi, Physico mathesis de lumine, coloribus, et iride, aliisque annexis libri duo (Bologna ("Bonomia"), Italy: Vittorio Bonati, 1665), page 2 : Original : Nobis alius quartus modus illuxit, quem nunc proponimus, vocamusque; diffractionem, quia advertimus lumen aliquando diffringi, hoc est partes eius multiplici dissectione separatas per idem tamen medium in diversa ulterius procedere, eo modo, quem mox declarabimus. Translation : It has illuminated for us another, fourth way, which we now make known and call "diffraction" [i.e., shattering], because we sometimes observe light break up; that is, that parts of the compound [i.e., the beam of light], separated by division, advance farther through the medium but in different [directions], as we will soon show.Cajori, Florian "A History of Physics in its Elementary Branches, including the evolution of physical laboratories." MacMillan Company, New York 1899 Isaac Newton studied these effects and attributed them to inflexion of light rays. James Gregory (1638–1675) observed the diffraction patterns caused by a bird feather, which was effectively the first diffraction grating to be discovered.Letter from James Gregory to John Collins, dated 13 May 1673. Reprinted in: Correspondence of Scientific Men of the Seventeenth Century …, ed. Stephen Jordan Rigaud (Oxford, England: Oxford University Press, 1841), vol. 2, pp. 251–255, especially p. 254 .
Thomas Young developed the first wave treatment of diffraction in 1800. In his model Young proposed that the fringes observed behind an illuminated sharp edge arose from interference between the direct transmitted plane wave and a cylindrical wave that appears to emitted from the edge.
Augustin-Jean Fresnel revisited the problem and devised an alternative wave theory based on Huygens' principle. In this model, point sources of light are distributed up to the diffraction edge but not in the barrier. These point sources are driven by the incoming plane wave and they interfere beyond the barrier. Fresnel developed a mathematical treatment from his approach and Young's model was initially considered incorrect. Later work showed that Young's more physical approach is equivalent to Fresnel's mathematical one.
In 1818, supporters of the corpuscular theory of light proposed that the Paris Academy prize question address diffraction, expecting to see the wave theory defeated. When Fresnel's presentation on his new theory based on wave propagation looked like it might take the prize, Siméon Denis Poisson challenged the Fresnel theory by showing that it predicted light in the shadow behind a circular obstruction. Dominique-François-Jean Arago proceeded to demonstrate experimentally that such light is visible, confirming Fresnel's diffraction model.
In 1859 Hermann von Helmholtz and later in 1882 Gustav Kirchhoff developed integral equations for diffraction based on the concepts proposed by Fresnel as well as approximations needed to apply them. In general, all these approaches require formulating the problem in terms of virtual sources. Cases like those with an absorbing barrier require methods developed in the 1940s based on transverse amplitude diffusion.
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),Baker, B.B. & Copson, E.T. (1939), The Mathematical Theory of Huygens' Principle, Oxford, pp.36–40. 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, as are the colors of a spider web; there are many other cases for light colors.
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. A studied archaeoacoustic example is the Mayan pyramid of El Castillo (); a handclap made in front of the pyramid returns as a descending frequency sweep because its tall staircase, whose regularly spaced steps form an approximately periodic structure, acts as an acoustic diffraction grating.
Other examples of diffraction are considered in more detail below.
Different cases