Diffraction refers to various phenomena that occur when a wave
encounters an obstacle or opening. It is defined as the bending of waves around the corners of an obstacle or through an aperture
into the region of geometrical shadow
of the obstacle/aperture. The diffracting object or aperture effectively becomes a secondary source of the propagating
wave. Italian scientist Francesco Maria Grimaldi
coined the word ''diffraction'' and was the first to record accurate observations of the phenomenon in 1660.
In classical physics
, the diffraction phenomenon is described by the Huygens–Fresnel principle
that treats each point in a propagating wavefront
as a collection of individual spherical wavelet
s. The characteristic bending pattern is most pronounced when a wave from a coherent
source (such as a laser) encounters a slit/aperture that is comparable in size to its wavelength
, as shown in the inserted image. This is due to the addition, or interference
, of different points on the wavefront (or, equivalently, each wavelet) that travel by paths of different lengths to the registering surface. However, if there are multiple, closely spaced openings
, a complex pattern of varying intensity can result.
These effects also 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 wave
s, water waves
, and other electromagnetic waves
such as X-ray
s and radio waves
. Furthermore, quantum mechanics
also demonstrates that matter possesses wave-like properties
, and hence, undergoes diffraction (which is measurable at subatomic to molecular levels).
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. 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. Thomas Young
performed a celebrated experiment
in 1803 demonstrating interference from two closely spaced slits. Explaining his results by interference of the waves emanating from the two different slits, he deduced that light must propagate as waves. Augustin-Jean Fresnel
did more definitive studies and calculations of diffraction, made public in 1816 and 1818, and thereby gave great support to the wave theory of light that had been advanced by Christiaan Huygens
and reinvigorated by Young, against Newton's particle theory.
In classical physics
diffraction arises because of the way in which waves propagate; this is described by the Huygens–Fresnel principle
and the principle of superposition of waves
. The propagation of a wave can be visualized by considering every particle of the transmitted medium on a wavefront as a point source for a secondary spherical wave
. The wave displacement at any subsequent point is the sum of these secondary waves. When waves are added together, their sum is determined by the relative phases as well as the amplitudes of the individual waves so that the summed amplitude of the waves 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 the modern quantum mechanical understanding of light propagation through a slit (or slits) every photon has what is known as a wavefunction
. The wavefunction is determined by the physical surroundings such as slit geometry, screen distance and initial conditions when the photon is created. In important experiments (A low-intensity double-slit experiment was first performed by G. I. Taylor in 1909, see double-slit experiment
) the existence of the photon's wavefunction was demonstrated. In the quantum approach the diffraction pattern is created by the probability distribution, the observation of light and dark bands is the presence or absence of photons in these areas, where these particles were more or less likely to be detected. The quantum approach has some striking similarities to the Huygens-Fresnel principle
; based on that principle, as light travels through slits and boundaries, secondary, point light sources are created near or along these obstacles, and the resulting diffraction pattern is going to be the intensity profile based on the collective interference of all these lights sources that have different optical paths. That is similar to considering the limited regions around the slits and boundaries where photons are more likely to originate from, in the quantum formalism, and calculating the probability distribution. This distribution is directly proportional to the intensity, in the classical formalism.
There are various analytical models which allow the diffracted field to be calculated, including the Kirchhoff-Fresnel diffraction equation
which is derived from the wave equation
, the Fraunhofer diffraction
approximation of the Kirchhoff equation which applies to the far field
and the Fresnel diffraction
approximation which applies to the near field
. Most configurations cannot be solved analytically, but can yield numerical solutions through finite element
and boundary element
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.
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 will have to take into account the full three-dimensional nature of the problem.
File:Square diffraction.jpg|Computer generated intensity pattern formed on a screen by diffraction from a square aperture.
File:Two-Slit Diffraction.png|Generation of an interference pattern from two-slit diffraction.
File:Doubleslit.gif|Computational model of an interference pattern from two-slit diffraction.
File:Optical diffraction pattern ( laser), (analogous to X-ray crystallography).JPG|Optical diffraction pattern ( laser), (analogous to X-ray crystallography)
File:Diffraction pattern in spiderweb.JPG|Colors seen in a spider web are partially due to diffraction, according to some analyses.
from hot spring
s. A glory is an optical phenomenon produced by light backscatter
ed (a combination of diffraction, reflection
) towards its source by a cloud of uniformly sized water droplets.|thumb]]
The effects of diffraction are often seen in everyday life. The most striking examples of diffraction are those that involve light; for example, the closely spaced tracks on a CD or DVD 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 bright ring to be visible around a bright light source like the sun or the moon. A shadow of a solid object, using light from a compact source, shows small fringes near its edges. The speckle pattern
which is observed when laser light falls on an optically rough surface is also a diffraction phenomenon. When deli meat
appears to be iridescent
, that is diffraction off the meat fibers. All these effects are a consequence of the fact that light propagates as a wave
Diffraction can occur with any kind of wave. 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.
Diffraction can also be a concern in some technical applications; it sets a fundamental limit
to the resolution of a camera, telescope, or microscope.
Other examples of diffraction are considered below.
A long slit of infinitesimal width which is illuminated by light diffracts the light into a series of circular waves and the wavefront which emerges from the slit is a cylindrical wave of uniform intensity, in accordance with Huygens–Fresnel principle
A slit that is wider than a wavelength produces interference effects in the space downstream of the slit. These can be explained by assuming that the slit behaves as though it has a large number of point sources spaced evenly across the width of the slit. The analysis of this system is simplified if we consider light of a single wavelength. If the incident light is coherent
, these sources all have the same phase. Light incident at a given point in the space downstream of the slit is made up of contributions from each of these point sources and if the relative phases of these contributions vary by 2π or more, we may expect to find minima and maxima in the diffracted light. Such phase differences are caused by differences in the path lengths over which contributing rays reach the point from the slit.
We can find the angle at which a first minimum is obtained in the diffracted light by the following reasoning. The light from a source located at the top edge of the slit interferes destructively with a source located at the middle of the slit, when the path difference between them is equal to ''λ''/2. Similarly, the source just below the top of the slit will interfere destructively with the source located just below the middle of the slit at the same angle. We can continue this reasoning along the entire height of the slit to conclude that the condition for destructive interference for the entire slit is the same as the condition for destructive interference between two narrow slits a distance apart that is half the width of the slit. The path difference is approximately
so that the minimum intensity occurs at an angle ''θ''min
* ''d'' is the width of the slit,
is the angle of incidence at which the minimum intensity occurs, and
is the wavelength of the light
A similar argument can be used to show that if we imagine the slit to be divided into four, six, eight parts, etc., minima are obtained at angles ''θ''''n''
* ''n'' is an integer other than zero.
There is no such simple argument to enable us to find the maxima of the diffraction pattern. The intensity profile
can be calculated using the Fraunhofer diffraction
is the intensity at a given angle,
is the intensity at the central maximum (
), which is also a normalization factor of the intensity profile that can be determined by an integration from
and conservation of energy.
is the unnormalized sinc function
This analysis applies only to the far field
), that is, at a distance much larger than the width of the slit.
From the intensity profile
, the intensity will have little dependency on
, hence the wavefront emerging from the slit would resemble a cylindrical wave with azimuthal symmetry; If
would have appreciable intensity, hence the wavefront emerging from the slit would resemble that of geometrical optics
When the incident angle
of the light onto the slit is non-zero (which causes a change in the path length
), the intensity profile in the Fraunhofer regime (i.e. far field) becomes: