![Laser Interference](https://upload.wikimedia.org/wikipedia/commons/4/42/Laser_Interference.JPG)
Diffraction is defined as the interference or bending of waves around the corners of an obstacle or through an
aperture
In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture and focal length of an optical system determine the cone angle of a bundle of rays that come to a focus in the image plane.
An ...
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.
![Single Slit Diffraction](https://upload.wikimedia.org/wikipedia/commons/0/0d/Single_Slit_Diffraction.svg)
In
classical physics, the diffraction phenomenon is described by the
Huygens–Fresnel principle that treats each point in a propagating
wavefront
In physics, the wavefront of a time-varying '' wave field'' is the set ( locus) of all points having the same '' phase''. The term is generally meaningful only for fields that, at each point, vary sinusoidally in time with a single temporal fr ...
as a collection of individual spherical
wavelet
A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the num ...
s. The characteristic bending pattern is most pronounced when a wave from a
coherent
Coherence, coherency, or coherent may refer to the following:
Physics
* Coherence (physics), an ideal property of waves that enables stationary (i.e. temporally and spatially constant) interference
* Coherence (units of measurement), a deri ...
source (such as a laser) encounters a slit/aperture that is comparable in size to its
wavelength
In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, t ...
, as shown in the inserted image. This is due to the addition, or
interference
Interference is the act of interfering, invading, or poaching. Interference may also refer to:
Communications
* Interference (communication), anything which alters, modifies, or disrupts a message
* Adjacent-channel interference, caused by extr ...
, of 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 (e.g., a
diffraction grating
In optics, a diffraction grating is an optical component with a periodic structure that diffracts light into several beams travelling in different directions (i.e., different diffraction angles). The emerging coloration is a form of structur ...
), 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
In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.
The refractive index determines how much the path of light is bent, or ...
, or when a
sound wave travels through a medium with varying
acoustic impedance
Acoustic impedance and specific acoustic impedance are measures of the opposition that a system presents to the acoustic flow resulting from an acoustic pressure applied to the system. The SI unit of acoustic impedance is the pascal-second per cu ...
– all waves diffract, including
gravitational waves,
water waves
In fluid dynamics, a wind wave, water wave, or wind-generated water wave, is a surface wave that occurs on the free surface of bodies of water as a result from the wind blowing over the water surface. The contact distance in the direction of ...
, and other
electromagnetic waves such as
X-ray
An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10 picometers to 10 nanometers, corresponding to frequencies in the range 30&nb ...
s and
radio waves
Radio waves are a type of electromagnetic radiation with the longest wavelengths in the electromagnetic spectrum, typically with frequencies of 300 gigahertz ( GHz) and below. At 300 GHz, the corresponding wavelength is 1 mm (s ...
. Furthermore,
quantum mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistr ...
also demonstrates that matter possesses
wave-like properties, and hence, undergoes diffraction (which is measurable at subatomic to molecular levels).
The amount of diffraction depends on the size of the gap. Diffraction is greatest when the size of the gap is similar to the wavelength of the wave. In this case, when the waves pass through the gap they become
semi-circular.
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.
Isaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a " natural philosopher"), widely recognised as one of the grea ...
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
In optics, a diffraction grating is an optical component with a periodic structure that diffracts light into several beams travelling in different directions (i.e., different diffraction angles). The emerging coloration is a form of structur ...
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
Augustin-Jean Fresnel (10 May 1788 – 14 July 1827) was a French civil engineer and physicist whose research in optics led to the almost unanimous acceptance of the wave theory of light, excluding any remnant of Newton's corpuscular th ...
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.
Mechanism
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 (two-way) wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields — as they occur in classical physics — such as mechanical waves (e.g. water waves, sound waves and seis ...
. 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
A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements ...
. 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 (two-way) wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields — as they occur in classical physics — such as mechanical waves (e.g. water waves, sound waves and seism ...
, the
Fraunhofer diffraction
In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when plane waves are incident on a diffracting object, and the diffraction pattern is viewed at a sufficiently long distance (a distance satisfying Fraunhofer ...
approximation of the Kirchhoff equation which applies to the
far field
The near field and far field are regions of the electromagnetic (EM) field around an object, such as a transmitting antenna, or the result of radiation scattering off an object. Non-radiative ''near-field'' behaviors dominate close to the ante ...
, the
Fresnel diffraction
In optics, the Fresnel diffraction equation for near-field diffraction is an approximation of the Kirchhoff–Fresnel diffraction that can be applied to the propagation of waves in the near field. It is used to calculate the diffraction pattern ...
approximation which applies to the
near field and the Feynman path integral formulation. Most configurations cannot be solved analytically, but can yield numerical solutions through
finite element
The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat t ...
and
boundary element methods.
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
A spider web, spiderweb, spider's web, or cobweb (from the archaic word '' coppe'', meaning "spider") is a structure created by a spider out of proteinaceous spider silk extruded from its spinnerets, generally meant to catch its prey.
Spi ...
are partially due to diffraction, according to some analyses.
Examples
![Night London Panorama with Full Moon](https://upload.wikimedia.org/wikipedia/commons/0/06/Night_London_Panorama_with_Full_Moon.jpg)
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
In optics, a diffraction grating is an optical component with a periodic structure that diffracts light into several beams travelling in different directions (i.e., different diffraction angles). The emerging coloration is a form of structur ...
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
Holography is a technique that enables a wavefront to be recorded and later re-constructed. Holography is best known as a method of generating real three-dimensional images, but it also has a wide range of other applications. In principle, i ...
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
Speckle, speckle pattern, or speckle noise is a granular noise texture degrading the quality as a consequence of interference among wavefronts in coherent imaging systems, such as radar, synthetic aperture radar (SAR), medical ultrasound and o ...
which is observed when laser light falls on an optically rough surface is also a diffraction phenomenon. When
deli meat
Lunch meats—also known as cold cuts, luncheon meats, cooked meats, sliced meats, cold meats, sandwich meats, and deli meats—are precooked or cured meats that are sliced and served cold or hot. They are typically served in sandwiches or on ...
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
In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (re ...
.
Diffraction can occur with any kind of wave. Ocean waves diffract around
jetties
A jetty is a structure that projects from land out into water. A jetty may serve as a breakwater, as a walkway, or both; or, in pairs, as a means of constricting a channel. The term derives from the French word ', "thrown", signifying somet ...
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.
Single-slit diffraction
![DiffractionSingleSlit Anim](https://upload.wikimedia.org/wikipedia/commons/8/82/DiffractionSingleSlit_Anim.gif)
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.
An illuminated slit that is wider than a wavelength produces interference effects in the space downstream of the slit. Assuming that the slit behaves as though it has a large number of point sources spaced evenly across the width of the slit interference effects can be calculated. The analysis of this system is simplified if we consider light of a single wavelength. If the incident light is
coherent
Coherence, coherency, or coherent may refer to the following:
Physics
* Coherence (physics), an ideal property of waves that enables stationary (i.e. temporally and spatially constant) interference
* Coherence (units of measurement), a deri ...
, 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
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
given by
:
where
*
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
given by
:
where
*
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
In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when plane waves are incident on a diffracting object, and the diffraction pattern is viewed at a sufficiently long distance (a distance satisfying Fraunhofer ...
equation as
:
where
*
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
to
and conservation of energy.
*
is the
unnormalized sinc function
In mathematics, physics and engineering, the sinc function, denoted by , has two forms, normalized and unnormalized..
In mathematics, the historical unnormalized sinc function is defined for by
\operatornamex = \frac.
Alternatively, the ...
.
This analysis applies only to the
far field
The near field and far field are regions of the electromagnetic (EM) field around an object, such as a transmitting antenna, or the result of radiation scattering off an object. Non-radiative ''near-field'' behaviors dominate close to the ante ...
(
Fraunhofer diffraction
In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when plane waves are incident on a diffracting object, and the diffraction pattern is viewed at a sufficiently long distance (a distance satisfying Fraunhofer ...
), that is, at a distance much larger than the width of the slit.
From the
intensity profile above, if
, the intensity will have little dependency on
, hence the wavefront emerging from the slit would resemble a cylindrical wave with azimuthal symmetry; If
, only
would have appreciable intensity, hence the wavefront emerging from the slit would resemble that of
geometrical optics
Geometrical optics, or ray optics, is a model of optics that describes light propagation in terms of '' rays''. The ray in geometrical optics is an abstraction useful for approximating the paths along which light propagates under certain circumstan ...
.
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:
: