-
A polarizing filter cuts down thereflections (top) and made it
possibleto see the photographer through theglass at roughly
Brewster's anglealthough reflections off the backwindow of the car
are not cut becausethey are less-strongly polarized,according to
the Fresnel equations.
PolarizerFrom Wikipedia, the free encyclopedia
A polarizer or polariser is an optical filter that passes light
of a specificpolarization and blocks waves of other
polarizations.[1][2][3][4] It canconvert a beam of light of
undefined or mixed polarization into a beamwith well-defined
polarization, polarized light. The common types ofpolarizers are
linear polarizers and circular polarizers. Polarizers areused in
many optical techniques and instruments, and polarizing filtersfind
applications in photography and liquid crystal display
technology.Polarizers can also be made for other types of
electromagnetic wavesbesides light, such as radio waves,
microwaves, and X-rays.
Contents
1 Linear polarizers1.1 Wire-grid polarizer1.2 Absorptive
polarizers1.3 Beam-splitting polarizers
1.3.1 Polarization by reflection1.3.2 Birefringent
polarizers1.3.3 Thin film polarizers
1.4 Malus' law and other properties2 Circular polarizers
2.1 Creating circularly polarized light2.2 Absorbing and passing
circularly polarized light2.3 Homogenous circular polarizer2.4
Circular and Linear Types
3 See also4 References5 Further reading
Linear polarizers
Linear polarizers can be divided into two general categories:
absorptive polarizers, where the unwantedpolarization states are
absorbed by the device, and beam-splitting polarizers, where the
unpolarized beam issplit into two beams with opposite polarization
state.
Wire-grid polarizer
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A wire-grid polarizer converts an unpolarized beam into onewith
a single linear polarization. Coloured arrows depict theelectric
field vector. The diagonally polarized waves alsocontribute to the
transmitted polarization. Their verticalcomponents are transmitted,
while the horizontalcomponents are absorbed and reflected. (This is
not clearlyshown.)
The simplest linear polarizer in concept is thewire-grid
polarizer, which consists of a regulararray of fine parallel
metallic wires, placed in aplane perpendicular to the incident
beam.Electromagnetic waves which have a component oftheir electric
fields aligned parallel to the wiresinduce the movement of
electrons along the lengthof the wires. Since the electrons are
free to move inthis direction, the polarizer behaves in a
similarmanner to the surface of a metal when reflectinglight, and
the wave is reflected backwards along theincident beam (minus a
small amount of energy lostto joule heating of the wire).[5]
For waves with electric fields perpendicular to thewires, the
electrons cannot move very far across thewidth of each wire;
therefore, little energy isreflected, and the incident wave is able
to passthrough the grid. Since electric field componentsparallel to
the wires are reflected, the transmitted wave has an electric field
purely in the direction perpendicularto the wires, and is thus
linearly polarized. Note that the polarization direction is
perpendicular to the wires; thenotion that waves "slip through" the
gaps between the wires is wrong.[5]
For practical use, the separation distance between the wires
must be less than the wavelength of the radiation,and the wire
width should be a small fraction of this distance. This means that
wire-grid polarizers generallywork best for microwaves and for far-
and mid-infrared light. However, using advanced lithographic
techniques,very tight pitch metallic grids can be made which
polarize visible light to a useful degree. Since the degree
ofpolarization depends little on wavelength and angle of incidence,
they are used for broad-band applications suchas projection.
Absorptive polarizers
Certain crystals, due to the effects described by crystal
optics, show dichroism, preferential absorption of lightwhich is
polarized in particular directions. They can therefore be used as
linear polarizers. The best knowncrystal of this type is
tourmaline. However, this crystal is seldom used as a polarizer,
since the dichroic effect isstrongly wavelength dependent and the
crystal appears coloured. Herapathite is also dichroic, and is
notstrongly coloured, but is difficult to grow in large
crystals.
A Polaroid polarizing filter functions similarly on an atomic
scale to the wire-grid polarizer. It was originallymade of
microscopic herapathite crystals. Its current H-sheet form is made
from polyvinyl alcohol (PVA) plasticwith an iodine doping.
Stretching of the sheet during manufacture causes the PVA chains to
align in oneparticular direction. Valence electrons from the iodine
dopant are able to move linearly along the polymerchains, but not
transverse to them. So incident light polarized parallel to the
chains is absorbed by the sheet;light polarized perpendicularly to
the chains is transmitted. The durability and practicality of
Polaroid makes itthe most common type of polarizer in use, for
example for sunglasses, photographic filters, and liquid
crystaldisplays. It is also much cheaper than other types of
polarizer.
A modern type of absorptive polarizer is made of elongated
silver nanoparticles embedded in thin (0.5 mm)glass plates. These
polarizers are more durable, and can polarize light much better
than plastic Polaroid film,achieving polarization ratios as high as
100,000:1 and absorption of correctly polarized light as low as
1.5%.[6]
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A stack of plates at Brewster's angle to a beam reflects off
afraction of the s-polarized light at each surface, leaving
ap-polarized beam. Full polarization at Brewster's anglerequires
many more plates than shown. The arrows indicatethe direction of
the electrical field, not the magnetic field,which is perpendicular
to the electric field
Such glass polarizers perform best for short-wavelength infrared
light, and are widely used in optical fibercommunications.
Beam-splitting polarizers
Beam-splitting polarizers split the incident beam into two beams
of differing linear polarization. For an idealpolarizing
beamsplitter these would be fully polarized, with orthogonal
polarizations. For many commonbeam-splitting polarizers, however,
only one of the two output beams is fully polarized. The other
contains amixture of polarization states.
Unlike absorptive polarizers, beam splitting polarizers do not
need to absorb and dissipate the energy of therejected polarization
state, and so they are more suitable for use with high intensity
beams such as laser light.True polarizing beamsplitters are also
useful where the two polarization components are to be analyzed or
usedsimultaneously.
Polarization by reflection
When light reflects at an angle from an interfacebetween two
transparent materials, the reflectivity isdifferent for light
polarized in the plane of incidenceand light polarized
perpendicular to it. Lightpolarized in the plane is said to be
p-polarized,while that polarized perpendicular to it iss-polarized.
At a special angle known as Brewster'sangle, no p-polarized light
is reflected from thesurface, thus all reflected light must be
s-polarized,with an electric field perpendicular to the plane
ofincidence.
A simple linear polarizer can be made by tilting astack of glass
plates at Brewster's angle to the beam.Some of the s-polarized
light is reflected from eachsurface of each plate. For a stack of
plates, eachreflection depletes the incident beam of
s-polarizedlight, leaving a greater fraction of p-polarized light
in the transmitted beam at each stage. For visible light in airand
typical glass, Brewster's angle is about 57, and about 16% of the
s-polarized light present in the beam isreflected for each
air-to-glass or glass-to-air transition. It takes many plates to
achieve even mediocrepolarization of the transmitted beam with this
approach. For a stack of 10 plates (20 reflections), about 3%(=
(1-0.16)20) of the s-polarized light is transmitted. The reflected
beam, while fully polarized, is spread out andmay not be very
useful.
A more useful polarized beam can be obtained by tilting the pile
of plates at a steeper angle to the incidentbeam.
Counterintuitively, using incident angles greater than Brewster's
angle yields a higher degree ofpolarization of the transmitted
beam, at the expense of decreased overall transmission. For angles
of incidencesteeper than 80 the polarization of the transmitted
beam can approach 100% with as few as four plates,although the
transmitted intensity is very low in this case.[7] Adding more
plates and reducing the angle allowsa better compromise between
transmission and polarization to be achieved.
Birefringent polarizers
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A Nicol prism
A Wollaston prism
Other linear polarizers exploit the birefringent properties of
crystals such as quartz and calcite. In these crystals,a beam of
unpolarized light incident on their surface is split by refraction
into two rays. Snell's law holds forone of these rays, the ordinary
or o-ray, but not for the other, the extraordinary or e-ray. In
general the two rayswill be in different polarization states,
though not in linear polarization states except for certain
propagationdirections relative to the crystal axis. The two rays
also experience differing refractive indices in the crystal.
A Nicol prism was an early type of birefringent polarizer,
thatconsists of a crystal of calcite which has been split and
rejoinedwith Canada balsam. The crystal is cut such that the o- and
e-raysare in orthogonal linear polarization states. Total internal
reflectionof the o-ray occurs at the balsam interface, since it
experiences alarger refractive index in calcite than in the balsam,
and the ray isdeflected to the side of the crystal. The e-ray,
which sees a smallerrefractive index in the calcite, is transmitted
through the interfacewithout deflection. Nicol prisms produce a
very high purity of polarized light, and were extensively used
inmicroscopy, though in modern use they have been mostly replaced
with alternatives such as theGlanThompson prism, GlanFoucault
prism, and GlanTaylor prism. These prisms are not true
polarizingbeamsplitters since only the transmitted beam is fully
polarized.
A Wollaston prism is another birefringent polarizer consisting
of twotriangular calcite prisms with orthogonal crystal axes that
are cementedtogether. At the internal interface, an unpolarized
beam splits into twolinearly polarized rays which leave the prism
at a divergence angle of1545. The Rochon and Snarmont prisms are
similar, but usedifferent optical axis orientations in the two
prisms. The Snarmontprism is air spaced, unlike the Wollaston and
Rochon prisms. Theseprisms truly split the beam into two fully
polarized beams withperpendicular polarizations. The Nomarski prism
is a variant of theWollaston prism, which is widely used in
differential interferencecontrast microscopy.
Thin film polarizers
Thin-film linear polarizers are glass substrates on which a
special optical coating is applied. Either Brewster'sangle
reflections or interference effects in the film cause them to act
as beam-splitting polarizers. The substratefor the film can either
be a plate, which is inserted into the beam at a particular angle,
or a wedge of glass that iscemented to a second wedge to form a
cube with the film cutting diagonally across the center (one form
of thisis the very common MacNeille cube[8]). Thin-film polarizers
generally do not perform as well as Glan-typepolarizers, but they
are inexpensive and provide two beams that are about equally well
polarized. The cube-typepolarizers generally perform better than
the plate polarizers. The former are easily confused with
Glan-typebirefringent polarizers.
Malus' law and other properties
Malus' law, which is named after tienne-Louis Malus, says that
when a perfect polarizer is placed in apolarized beam of light, the
intensity, I, of the light that passes through is given by
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Polarization of light.In this picture, 1 0 = i.
where I0 is the initial intensity, and i is the anglebetween the
light's initial polarization direction andthe axis of the
polarizer.
A beam of unpolarized light can be thought of ascontaining a
uniform mixture of linear polarizationsat all possible angles.
Since the average value of
is 1/2, the transmission coefficient becomes
In practice, some light is lost in the polarizer and theactual
transmission of unpolarized light will besomewhat lower than this,
around 38% forPolaroid-type polarizers but considerably
higher(>49.9%) for some birefringent prism types.
If two polarizers are placed one after another (the second
polarizer is generally called an analyzer), the mutualangle between
their polarizing axes gives the value of in Malus' law. If the two
axes are orthogonal, thepolarizers are crossed and in theory no
light is transmitted, though again practically speaking no
polarizer isperfect and the transmission is not exactly zero (for
example, crossed Polaroid sheets appear slightly blue incolour). If
a transparent object is placed between the crossed polarizers, any
polarization effects present in thesample (such as birefringence)
will be shown as an increase in transmission. This effect is used
in polarimetryto measure the optical activity of a sample.
Real polarizers are also not perfect blockers of the
polarization orthogonal to their polarization axis; the ratio ofthe
transmission of the unwanted component to the wanted component is
called the extinction ratio, and variesfrom around 1:500 for
Polaroid to about 1:106 for GlanTaylor prism polarizers.
In X-ray the Malus law (relativistic form):
where - frequency of the polarized radiation falling on the
polarizer, - frequency of the radiation passesthrough polarizer, -
Compton wavelength of electron, - speed of light in vacuum.[9]
Circular polarizers
Circular polarizers, also referred to as circular polarizing
filters, can be used to create circularly polarizedlight or
alternatively to selectively absorb or pass clockwise and
counter-clockwise circularly polarized light.They are used as
polarizing filters in photography to reduce oblique reflections
from non-metallic surfaces, andare the lenses of the 3D glasses
worn for the viewing some stereoscopic movies (notably, the RealD
3D variety),where the polarization of light is used to
differentiate which image should be seen by the left and right
eye.
Creating circularly polarized light
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Circular polarizer creating left-handed circularly polarized
light. It is considered left-handed as viewed from thereceiver and
right-handed as viewed from the source.[10]
There are several ways to create circularly polarized light, the
cheapest and most common involves placing aquarter-wave plate after
a linear polarizer and directing unpolarized light through the
linear polarizer. Thelinearly polarized light leaving the linear
polarizer is transformed into circularly polarized light by the
quarterwave plate. The transmission axis of the linear polarizer
needs to be half way (45) between the fast and slowaxes of the
quarter-wave plate.In the arrangement above, the transmission axis
of the linear polarizer is at a positive 45 angle relative to
theright horizontal and is represented with an orange line. The
quarter-wave plate has a horizontal slow axis and avertical fast
axis and they are also represented using orange lines. In this
instance the unpolarized light enteringthe linear polarizer is
displayed as a single wave whose amplitude and angle of linear
polarization are suddenlychanging.When one attempts to pass
unpolarized light through the linear polarizer, only light that has
its electric field atthe positive 45 angle leaves the linear
polarizer and enters the quarter-wave plate. In the illustration,
the threewavelengths of unpolarized light represented would be
transformed into the three wavelengths of linearlypolarized light
on the other side of the linear polarizer.
In the illustration toward the right is the electric field of
the linearly polarized light just before it enters thequarter-wave
plate. The red line and associated field vectors represent how the
magnitude and direction of theelectric field varies along the
direction of travel. For this plane electromagnetic wave, each
vector represents themagnitude and direction of the electric field
for an entire plane that is perpendicular to the direction of
travel.Refer to these two images in the plane wave article to
better appreciate this.Light and all other electromagnetic waves
have a magnetic field which is in phase with, and perpendicular
to,the electric field being displayed in these illustrations.To
understand the effect the quarter-wave plate has on the linearly
polarized light it is useful think of the light asbeing divided
into two components which are at right angles (orthogonal) to each
other. Towards this end, theblue and green lines are projections of
the red line onto the vertical and horizontal planes respectively
andrepresent how the electric field changes in the direction of
those two planes. The two components have the sameamplitude and are
in phase.Because the quarter-wave plate is made of a birefringent
material, when in the wave plate, the light travels atdifferent
speeds depending on the direction of its electric field. This means
that the horizontal component whichis along the slow axis of the
wave plate will travel at a slower speed than the component that is
directed along
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Linearly polarized light, represented using components, entering
aquarter-wave plate. The blue and green curves are projections of
the redline on the vertical and horizontal planes respectively.
the vertical fast axis. Initially the twocomponents are in
phase, but as the twocomponents travel through the waveplate the
horizontal component of thelight drifts farther behind that of
thevertical. By adjusting the thickness ofthe wave plate one can
control howmuch the horizontal component isdelayed relative to
vertical componentbefore the light leaves the wave plateand they
begin again to travel at thesame speed. When the light leaves
thequarter-wave plate the rightwardhorizontal component will be
exactlyone quarter of a wavelength behind thevertical component
making the lightleft-hand circularly polarized whenviewed from the
receiver.[10]
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The top image is left-handed/counter-clockwise circularly
polarized, asviewed from the receiver.[10] The bottom image is that
of linearlypolarized light. The blue and green curves are
projections of the red lineson the vertical and horizontal planes
respectively.
At the top of the illustration toward theright, is the
circularly polarized lightafter it leaves the wave plate, and
againdirectly below it, for comparisonpurposes, the linearly
polarized lightthat entered the quarter-wave plate. Inthe upper
image, because this is a planewave, each vector leading from the
axisto the helix represents the magnitudeand direction of the
electric field for anentire plane that is perpendicular to
thedirection of travel. All the electric fieldvectors have the same
magnitudeindicating that the strength of theelectric field does not
change. Thedirection of the electric field howeversteadily
rotates.The blue and green lines are projectionsof the helix onto
the vertical andhorizontal planes respectively andrepresent how the
electric field changesin the direction of those two planes.Notice
how the rightward horizontalcomponent is now one quarter of
awavelength behind the verticalcomponent. It is this quarter of
awavelength phase shift that results inthe rotational nature of the
electric field.It is significant to note that when themagnitude of
one component is at amaximum the magnitude of the othercomponent is
always zero. This is thereason that there are helix vectorswhich
exactly correspond to themaxima of the two components.
In the instance just cited, using the handedness convention used
in many optics textbooks, the light isconsidered
left-handed/counter-clockwise circularly polarized. Referring to
the accompanying animation, it isconsidered left-handed because if
one points ones left thumb against the direction of travel, ones
fingers curl inthe direction the electric field rotates as the wave
passes a given point in space. The helix also forms aleft-handed
helix in space. Similarly this light is considered
counter-clockwise circularly polarized because if astationary
observer faces against the direction of travel, the person will
observe its electric field rotate in thecounter-clockwise direction
as the wave passes a given point in space.[10]
To create right-handed, clockwise circularly polarized light one
simply rotates the axis of the quarter-wave plate90 relative to the
linear polarizer. This reverses the fast and slow axes of the wave
plate relative to thetransmission axis of the linear polarizer
reversing which component leads and which component lags.
In trying to appreciate how the quarter-wave plate transforms
the linearly polarized light, it is important torealize that the
two components discussed are not entities in and of themselves but
are merely mental constructs
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Animation of left-handed/counter-clockwisecircularly polarized
light. (Left-handed as viewedfrom the receiver.[10])
one uses to help appreciate what is happening. In the caseof
linearly and circularly polarized light, at each point inspace,
there is always a single electric field with a distinctvector
direction, the quarter-wave plate merely has theeffect of
transforming this single electric field.
Absorbing and passing circularly polarized light
Circular polarizers can also be used to selectively absorb or
pass right-handed or left-handed circularlypolarized light. It is
this feature which is utilized by the 3D glasses in stereoscopic
cinemas such as RealDCinema. A given polarizer which creates one of
the two polarizations of light will pass that same polarization
oflight when that light is sent through it in the other direction.
In contrast it will block light of the oppositepolarization.
Circular polarizer passing left-handed, counter-clockwise
circularly polarized light. (Left-handed as viewed fromthe
receiver.)[10]
The illustration above is identical to the previous similar one
with the exception that the left-handed circularlypolarized light
is now approaching the polarizer from the opposite direction and
linearly polarized light isexiting the polarizer toward the
right.First note that a quarter-wave plate always transforms
circularly polarized light into linearly polarized light. It isonly
the resulting angle of polarization of the linearly polarized light
that is determined by the orientation of the
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Left-handed/Counter-Clockwise circularly polarized light
displayed abovelinearly polarized light.[10] The blue and green
curves are projections ofthe helix on the vertical and horizontal
planes respectively.
fast and slow axes of the quarter-wave plate and the handedness
of the circularly polarized light. In theillustration, the
left-handed circularly polarized light entering the polarizer is
transformed into linearly polarizedlight which has its direction of
polarization along the transmission axis of the linear polarizer
and it thereforepasses. In contrast right-handed circularly
polarized light would have been transformed into linearly
polarizedlight that had its direction of polarization along the
absorbing axis of the linear polarizer, which is at rightangles to
the transmission axis, and it would have therefore been
blocked.
To understand this process, refer to theillustration on the
right. It is absolutelyidentical to the earlier illustration
eventhough the circularly polarized light atthe top is now
considered to beapproaching the polarizer from the left.One can
observe from the illustrationthat the leftward horizontal (as
observedlooking along the direction of travel)component is leading
the verticalcomponent and that when the horizontalcomponent is
retarded by one quarter ofa wavelength it will be transformed
intothe linearly polarized light illustrated atthe bottom and it
will pass through thelinear polarizer.
There is a relatively straightforwardway to appreciate why a
polarizerwhich creates a given handedness ofcircularly polarized
light also passesthat same handedness of polarized light.First,
given the dual usefulness of thisimage, begin by imagining
thecircularly polarized light displayed atthe top as still leaving
the quarter-waveplate and traveling toward the left.Observe that
had the horizontalcomponent of the linearly polarizedlight been
retarded by a quarter ofwavelength twice, which would amountto a
full half wavelength, the resultwould have been linearly polarized
lightthat was at a right angle to the light thatentered. If such
orthogonally polarizedlight were rotated on the horizontal plane
and directed back through the linear polarizer section of the
circularpolarizer it would clearly pass through given its
orientation. Now imagine the circularly polarized light whichhas
already passed through the quarter-wave plate once, turned around
and directed back toward the circularpolarizer again. Let the
circularly polarized light illustrated at the top now represent
that light. Such light isgoing to travel through the quarter-wave
plate a second time before reaching the linear polarizer and in
theprocess, its horizontal component is going to be retarded a
second time by one quarter of a wavelength. Whetherthat horizontal
component is retarded by one quarter of a wavelength in two
distinct steps or retarded a full halfwavelength all at once, the
orientation of the resulting linearly polarized light will be such
that it passes through
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the linear polarizer.
Had it been right-handed, clockwise circularly polarized light
approaching the circular polarizer from the left,its horizontal
component would have also been retarded, however the resulting
linearly polarized light wouldhave been polarized along the
absorbing axis of the linear polarizer and it would not have
passed.
To create a circular polarizer that instead passes right-handed
polarized light and absorbs left-handed light, oneagain rotates the
wave plate and linear polarizer 90 relative to each another. It is
easy to appreciate that byreversing the positions of the
transmitting and absorbing axes of the linear polarizer relative to
the quarter-waveplate, one changes which handedness of polarized
light gets transmitted and which gets absorbed.
Homogenous circular polarizer
Homogeneous circular polarizer passing left-handed,
counter-clockwise circularly polarized light. (Left-handed asviewed
from the receiver.)[10]
A homogenous circular polarizer passes one handedness of
circular polarization unaltered and blocks the otherhandedness.
This is similar to the way that a linear polarizer would fully pass
one angle of linearly polarizedlight unaltered, but would fully
block any linearly polarized light that was orthogonal to it.
A homogenous circular polarizer can be created by sandwiching a
linear polarizer between two quarter-waveplates.[11] Specifically
we take the circular polarizer described previously, which
transforms circularly polarizedlight into linear polarized light,
and add to it a second quarter-wave plate rotated 90 relative to
the first one.
Generally speaking, and not making direct reference to the above
illustration, when either of the twopolarizations of circularly
polarized light enters the first quarter-wave plate, one of a pair
of orthogonalcomponents is retarded by one quarter of a wavelength
relative to the other. This creates one of two linearpolarizations
depending on the handedness the circularly polarized light. The
linear polarizer sandwichedbetween the quarter wave plates is
oriented so that it will pass one linear polarization and block the
other. Thesecond quarter-wave plate then takes the linearly
polarized light that passes and retards the orthogonalcomponent
that was not retarded by the previous quarter-wave plate. This
brings the two components back into
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Wikimedia Commons hasmedia related toPolarization.
their initial phase relationship, reestablishing the selected
circular polarization.Note that it does not matter in which
direction one passes the circularly polarized light.
Circular and Linear Types
Linear polarizing filters were the first types to be used in
photography and can still be used for non-reflex andolder SLR
cameras. However, cameras with through-the-lens metering and
autofocusing systems - that is, allmodern SLR and DSLR - rely on
optical elements that pass linearly polarized light. If light
entering the camerais already linearly polarized, it can upset the
exposure or autofocus systems. Circular polarizing filters cut
outlinearly polarized light and so can be used to darken skies or
remove reflections, but the circular polarized lightit passes does
not impair through-the-lens systems.[12]
See also
Related to circular polarizers
PolarizationCircular polarizationLinear polarizationLinear
polarizerWave platePhotoelastic modulator - a wave plate that can
rapidly switch fast and slow axes, and thus produce
rapidlyalternating left and right circular polarization. They
commonly operate in the ultrasonic range.Electromagnetic waves3D
GlassesRealD cinemaPolarizing filter (photography)Fresnel rhomb -
another way of producing circularly polarized light; it does not
use a wave plate
Other
Extinction crossPhotographic filterPoincar sphereEdwin
LandPolariscopePolarized light microscope
References
^ Wolf, Mark J. P. (2008). The Video Game Explosion: A History
from PONG to Playstation and
Beyond(http://books.google.com/books?id=XiM0nthMybNwC&pg=PA315&dq=%22polarizer+filter).
ABC-CLIO. p. 315.
1.
Polarizer - Wikipedia, the free encyclopedia
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ISBN 031333868X.^ Johnsen, Snke (2012). The Optics of Life: A
Biologist's Guide to Light in Nature
(http://books.google.com/books?id=Q8zWqiKA7JMC&pg=PA208&dq=polarizer+filter).
Princeton Univ. Press. pp. 207208.ISBN 0691139911.
2.
^ Basu, Dipak (2000). Dictionary of Pure and Applied Physics
(http://books.google.com/books?id=-QhAkBSk7IUC&pg=PA144&dq=polarizer+%22polarizing+filter).
CRC Press. pp. 142143. ISBN 1420050222.
3.
^ Gsvik, Kjell J. (2003). Optical Metrology
(http://books.google.com/books?id=u15atbXzADUC&pg=PA219&dq=polarizing+filter%22polarizer)
(3 ed.). John Wiley and Sons. pp. 219221. ISBN 0470846704.
4.
^ a b Hecht, Eugene. Optics, 2nd ed., Addison Wesley (1990) ISBN
0-201-11609-X. Chapter 8.5.^ "Polarcor glass polarizers: Product
information"
(http://www.corning.com/docs/specialtymaterials/pisheets/Pi201.pdf)
(pdf). Corning.com. December 2006. Retrieved 2008-08-08.
6.
^ Collett, Edward. Field Guide to Polarization, SPIE Field
Guides vol. FG05, SPIE (2005) ISBN 0-8194-5868-6.7.^ US patent
2,403,731
(http://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=US2,403,731),
Stephen M.MacNeille, "Beam splitter", issued 1946-June-4
8.
^ A. N. Volobuev (2013). Interaction of the Electromagnetic
Field with Substance. Nova Science Publishers, Inc.New York. ISBN
978-1-62618-348-3.
9.
^ a b c d e f g h Refer to well referenced section in Circular
Polarization article for a discussion of handedness.Left/Right
Handedness
10.
^ Bass M (1995) Handbook of Optics
(http://cdn.preterhuman.net/texts/science_and_technology/physics/Optics/Handbook%20of%20Optics%20%20second%20edition%20vol.%202%20-%20Bass%20M.pdf),
Second edition,Vol. 2, Ch. 22.19, McGraw-Hill, ISBN
0-07-047974-7
11.
^ Ang, Tom (2008).Fundamentals of Modern Photography. Octopus
Publishing Group Limited. p168. ISBN978-1-84533-2310.
12.
Further reading
Kliger, David S. Polarized Light in Optics and Spectroscopy,
Academic Press (1990) ISBN0-12-414975-8Mann, James "Austine Wood
Comarow: Paintings in Polarized Light", Wasabi Publishing (2005)
ISBN978-0976819806
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