/ˌænɪˈsɒtrəpi/, /ˌænaɪˈsɒtrəpi/ is the property
of being directionally dependent, which implies different properties
in different directions, as opposed to isotropy. It can be defined as
a difference, when measured along different axes, in a material's
physical or mechanical properties (absorbance, refractive index,
conductivity, tensile strength, etc.) An example of anisotropy is
light coming through a polarizer. Another is wood, which is easier to
split along its grain than across it.
1 Fields of interest
1.1 Computer graphics
1.3 Real-world imagery
1.5 Geophysics and geology
1.6 Medical acoustics
1.7 Material science and engineering
1.10 Atmospheric radiative transfer
2 See also
4 External links
Fields of interest
In the field of computer graphics, an anisotropic surface changes in
appearance as it rotates about its geometric normal, as is the case
Anisotropic filtering (AF) is a method of enhancing the image quality
of textures on surfaces that are far away and steeply angled with
respect to the point of view. Older techniques, such as bilinear and
trilinear filtering, do not take into account the angle a surface is
viewed from, which can result in aliasing or blurring of textures. By
reducing detail in one direction more than another, these effects can
A chemical anisotropic filter, as used to filter particles, is a
filter with increasingly smaller interstitial spaces in the direction
of filtration so that the proximal regions filter out larger particles
and distal regions increasingly remove smaller particles, resulting in
greater flow-through and more efficient filtration.
In NMR spectroscopy, the orientation of nuclei with respect to the
applied magnetic field determines their chemical shift. In this
context, anisotropic systems refer to the electron distribution of
molecules with abnormally high electron density, like the pi system of
benzene. This abnormal electron density affects the applied magnetic
field and causes the observed chemical shift to change.
In fluorescence spectroscopy, the fluorescence anisotropy, calculated
from the polarization properties of fluorescence from samples excited
with plane-polarized light, is used, e.g., to determine the shape of a
Anisotropy measurements reveal the average angular
displacement of the fluorophore that occurs between absorption and
subsequent emission of a photon.
Images of a gravity-bound or man-made environment are particularly
anisotropic in the orientation domain, with more image structure
located at orientations parallel with or orthogonal to the direction
of gravity (vertical and horizontal).
A plasma lamp displaying the nature of plasmas, in this case, the
phenomenon of "filamentation"
University of California, Berkeley
University of California, Berkeley reported about
their detection of the cosine anisotropy in cosmic microwave
background radiation in 1977. Their experiment demonstrated the
Doppler shift caused by the movement of the earth with respect to the
early Universe matter, the source of the radiation. Cosmic
anisotropy has also been seen in the alignment of galaxies' rotation
axes and polarisation angles of quasars.
Physicists use the term anisotropy to describe direction-dependent
properties of materials. Magnetic anisotropy, for example, may occur
in a plasma, so that its magnetic field is oriented in a preferred
direction. Plasmas may also show "filamentation" (such as that seen in
lightning or a plasma globe) that is directional.
An anisotropic liquid has the fluidity of a normal liquid, but has an
average structural order relative to each other along the molecular
axis, unlike water or chloroform, which contain no structural ordering
of the molecules.
Liquid crystals are examples of anisotropic liquids.
Some materials conduct heat in a way that is isotropic, that is
independent of spatial orientation around the heat source. Heat
conduction is more commonly anisotropic, which implies that detailed
geometric modeling of typically diverse materials being thermally
managed is required. The materials used to transfer and reject heat
from the heat source in electronics are often anisotropic.
Many crystals are anisotropic to light ("optical anisotropy"), and
exhibit properties such as birefringence.
Crystal optics describes
light propagation in these media. An "axis of anisotropy" is defined
as the axis along which isotropy is broken (or an axis of symmetry,
such as normal to crystalline layers). Some materials can have
multiple such optical axes.
Geophysics and geology
Seismic anisotropy is the variation of seismic wavespeed with
Seismic anisotropy is an indicator of long range order in a
material, where features smaller than the seismic wavelength (e.g.,
crystals, cracks, pores, layers or inclusions) have a dominant
alignment. This alignment leads to a directional variation of
elasticity wavespeed. Measuring the effects of anisotropy in seismic
data can provide important information about processes and mineralogy
in the Earth; indeed, significant seismic anisotropy has been detected
in the Earth's crust, mantle and inner core.
Geological formations with distinct layers of sedimentary material can
exhibit electrical anisotropy; electrical conductivity in one
direction (e.g. parallel to a layer), is different from that in
another (e.g. perpendicular to a layer). This property is used in the
gas and oil exploration industry to identify hydrocarbon-bearing sands
in sequences of sand and shale. Sand-bearing hydrocarbon assets have
high resistivity (low conductivity), whereas shales have lower
Formation evaluation instruments measure this
conductivity/resistivity and the results are used to help find oil and
gas in wells.
The hydraulic conductivity of aquifers is often anisotropic for the
same reason. When calculating groundwater flow to drains or to
wells, the difference between horizontal and vertical permeability
must be taken into account, otherwise the results may be subject to
Most common rock-forming minerals are anisotropic, including quartz
Anisotropy in minerals is most reliably seen in their
optical properties. An example of an isotropic mineral is garnet.
Anisotropy is also a well-known property in medical ultrasound imaging
describing a different resulting echogenicity of soft tissues, such as
tendons, when the angle of the transducer is changed. Tendon fibers
appear hyperechoic (bright) when the transducer is perpendicular to
the tendon, but can appear hypoechoic (darker) when the transducer is
angled obliquely. This can be a source of interpretation error for
Material science and engineering
Anisotropy, in Material Science, is a material's directional
dependence of a physical property. Most materials exhibit anisotropic
behavior. An example would be the dependence of
Young's modulus on the
direction of load.
Anisotropy in polycrystalline materials can also
be due to certain texture patterns often produced during manufacturing
of the material. In the case of rolling, "stringers" of texture are
produced in the direction of rolling, which can lead to vastly
different properties in the rolling and transverse directions. Some
materials, such as wood and fibre-reinforced composites are very
anisotropic, being much stronger along the grain/fibre than across it.
Metals and alloys tend to be more isotropic, though they can sometimes
exhibit significant anisotropic behaviour. This is especially
important in processes such as deep-drawing.
Wood is a naturally anisotropic (but often simplified to be
transversely isotropic) material. Its properties vary widely when
measured with or against the growth grain. For example, wood's
strength and hardness is different for the same sample measured in
In the Mechanics of Continuum Materials isotropy and anisotropy are
rigorously described through the symmetry group of the constitutive
Anisotropic etching techniques (such as deep reactive ion etching) are
used in microfabrication processes to create well defined microscopic
features with a high aspect ratio. These features are commonly used in
MEMS and microfluidic devices, where the anisotropy of the features is
needed to impart desired optical, electrical, or physical properties
to the device. Anisotropic etching can also refer to certain chemical
etchants used to etch a certain material preferentially over certain
crystallographic planes (e.g., KOH etching of silicon  produces
Diffusion tensor imaging
Diffusion tensor imaging is an MRI technique that involves measuring
the fractional anisotropy of the random motion (Brownian motion) of
water molecules in the brain. Water molecules located in fiber tracts
are more likely to be anisotropic, since they are restricted in their
movement (they move more in the dimension parallel to the fiber tract
rather than in the two dimensions orthogonal to it), whereas water
molecules dispersed in the rest of the brain have less restricted
movement and therefore display more isotropy. This difference in
fractional anisotropy is exploited to create a map of the fiber tracts
in the brains of the individual.
Atmospheric radiative transfer
Radiance fields (see BRDF) from a reflective surface are often not
isotropic in nature. This makes calculations of the total energy being
reflected from any scene a difficult quantity to calculate. In remote
sensing applications, anisotropy functions can be derived for specific
scenes, immensely simplifying the calculation of the net reflectance
or (thereby) the net irradiance of a scene. For example, let the BRDF
displaystyle gamma (Omega _ i ,Omega _ v )
where 'i' denotes incident direction and 'v' denotes viewing
direction (as if from a satellite or other instrument). And let P be
the Planar Albedo, which represents the total reflectance from the
displaystyle P(Omega _ i )=int _ Omega _ v gamma (Omega _ i
,Omega _ v ) hat n cdot d hat Omega _ v
displaystyle A(Omega _ i ,Omega _ v )= frac gamma (Omega _ i
,Omega _ v ) P(Omega _ i )
It is of interest because, with knowledge of the anisotropy function
as defined, a measurement of the
BRDF from a single viewing direction
displaystyle Omega _ v
) yields a measure of the total scene reflectance (Planar Albedo) for
that specific incident geometry (say,
displaystyle Omega _ i
^ Smoot G. F.; Gorenstein M. V. & Muller R. A. (5 October 1977).
Anisotropy in the Cosmic Blackbody Radiation" (PDF).
Lawrence Berkeley Laboratory
Lawrence Berkeley Laboratory and Space Sciences Laboratory, University
of California, Berkeley. Retrieved 15 September 2013.
^ Tian, Xiaojuan; Itkis, Mikhail E; Bekyarova, Elena B; Haddon, Robert
C (8 April 2013). "Anisotropic Thermal and Electrical Properties of
Thin Thermal Interface Layers of Graphite Nanoplatelet-Based
Composites". Nature.com. Archived from the original on 11 August 2016.
Retrieved 11 August 2016.
^ R.J.Oosterbaan, 1997, The energy balance of groundwater flow applied
to subsurface drainage in anisotropic soils by pipes or ditches with
entrance resistance. On line: . The corresponding free EnDrain
program can be downloaded from: .
^ R.J.Oosterbaan, 2002, Subsurface drainage by (tube)wells, 9 pp. On
line: . The corresponding free WellDrain program can be downloaded
^ Kocks, U.F. (2000). Texture and Anisotropy: Preferred Orientations
in Polycrystals and their effect on Materials Properties. Cambridge.
^ Truesdell, Clifford; Noll, Walter. The Non-Linear Field Theories of
Mechanics - Springer. doi:10.1007/978-3-662-10388-3.
Look up anisotropy in Wiktionary, the free dictionary.
"Gauge, and knitted fabric generally, is an anisotropic phenomenon"
"Overview of Anisotropy"
DoITPoMS Teaching and Learning Package: "Introduction to Anisotropy"