1-wire grid polarizer

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

Polarizer - Wikipedia, the free encyclopedia http://en.wikipedia.org/wiki/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.


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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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