Polarization of Light: from Basics to Instruments in less than 100 slides

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Polarization of Lightfrom Basics to
Instruments(in less than 100 slides)

• N. Manset
• CFHT

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Introduction

• Part I Different polarization states of light
• Part II Stokes parameters, Mueller matrices
• Part III Optical components for polarimetry
• Part IV Polarimeters
• Part V ESPaDOnS

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Part I Different polarization states of light

• Light as an electromagnetic wave
• Mathematical and graphical descriptions of
  polarization
• Linear, circular, elliptical light
• Polarized, unpolarized light

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Light as an electromagnetic wave
Part I Polarization states

• Light is a transverse wave,
• an electromagnetic wave

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Mathematical description of the EM wave
Part I Polarization states

• Light wave that propagates in the z direction

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Graphical representation of the EM wave (I)
Part I Polarization states

• One can go from
• to the equation of an ellipse (using
  trigonometric identities, squaring, adding)

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Graphical representation of the EM wave (II)
Part I Polarization states

• An ellipse can be represented by 4 quantities
• size of minor axis
• size of major axis
• orientation (angle)
• sense (CW, CCW)

Light can be represented by 4 quantities...
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Vertically polarized light
Part I Polarization states, linear polarization

• If there is no amplitude in x (E0x 0), there is
  only one component, in y (vertical).

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Polarization at 45º (I)
Part I Polarization states, linear polarization

• If there is no phase difference (?0) and
• E0x E0y, then Ex Ey

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Polarization at 45º (II)
Part I Polarization states, linear polarization
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Circular polarization (I)
Part I Polarization states, circular polarization

• If the phase difference is ? 90º and E0x E0y
• then Ex / E0x cos ? , Ey / E0y sin ?
• and we get the equation of a circle

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Circular polarization (II)
Part I Polarization states, circular polarization
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Circular polarization (III)
Part I Polarization states, circular polarization
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Circular polarization (IV)
Part I Polarization states, circular
polarization... see it now?
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Elliptical polarization
Part I Polarization states, elliptical
polarization

• Linear circular polarization elliptical
  polarization

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Unpolarized light(natural light)
Part I Polarization states, unpolarized light
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A cool Applet
Part I Polarization states
Electromagnetic Wave
Location http//www.uno.edu/jsulliva/java/EMWave
.html
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Part II Stokes parameters and Mueller matrices

• Stokes parameters, Stokes vector
• Stokes parameters for linear and circular
  polarization
• Stokes parameters and polarization P
• Mueller matrices, Mueller calculus
• Jones formalism

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Stokes parametersA tiny itsy-bitsy little bit of
history...
Part II Stokes parameters

• 1669 Bartholinus discovers double refraction in
  calcite
• 17th 19th centuries Huygens, Malus, Brewster,
  Biot, Fresnel and Arago, Nicol...
• 19th century unsuccessful attempts to describe
  unpolarized light in terms of amplitudes
• 1852 Sir George Gabriel Stokes took a very
  different approach and discovered that
  polarization can be described in terms of
  observables using an experimental definition

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Stokes parameters (I)
Part II Stokes parameters
The polarization ellipse is only valid at a given
instant of time (function of time)
To get the Stokes parameters, do a time average
(integral over time) and a little bit of
algebra...
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Stokes parameters (II)described in terms of the
electric field
Part II Stokes parameters
The 4 Stokes parameters are
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Stokes parameters (III)described in geometrical
terms
Part II Stokes parameters
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Stokes vector
Part II Stokes parameters, Stokes vectors
The Stokes parameters can be arranged in a Stokes
vector

• Linear polarization
• Circular polarization
• Fully polarized light
• Partially polarized light
• Unpolarized light

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Pictorial representation of the Stokes parameters
Part II Stokes parameters
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Stokes vectors for linearly polarized light
Part II Stokes parameters, examples
LHP light
LVP light
45º light
-45º light
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Stokes vectors for circularly polarized light
Part II Stokes parameters, examples
RCP light
LCP light
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(Q,U) to (P,?)
Part II Stokes parameters
In the case of linear polarization (V0)
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Mueller matrices
Part II Stokes parameters, Mueller matrices
If light is represented by Stokes vectors,
optical components are then described with
Mueller matrices output light
Muller matrix input light
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Mueller calculus (I)
Part II Stokes parameters, Mueller matrices
Element 1 Element 2 Element 3
I M3 M2 M1 I
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Mueller calculus (II)
Part II Stokes parameters, Mueller matrices
Mueller matrix M of an optical component with
Mueller matrix M rotated by an angle ?
M R(- ?) M R(?) with
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Jones formalism
Part II Stokes parameters, Jones formalism, not
that important here...
Stokes vectors and Mueller matrices cannot
describe interference effects. If the phase
information is important (radio-astronomy,
masers...), one has to use the Jones formalism,
with complex vectors and Jones matrices

• Jones vectors to describe the polarization of
  light

• Jones matrices to represent optical components

BUT Jones formalism can only deal with 100
polarization...
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Part III Optical components for polarimetry

• Complex index of refraction
• Polarizers
• Retarders

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Complex index of refraction
Part III Optical components
The index of refraction is actually a complex
quantity

• real part
• optical path length, refraction speed of light
  depends on media
• birefringence speed of light also depends on P

• imaginary part
• absorption, attenuation, extinction depends on
  media
• dichroism/diattenuation also depends on P

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Polarizers
Part III Optical components, polarizers
Polarizers absorb one component of the
polarization but not the other. The input is
natural light, the output is polarized light
(linear, circular, elliptical). They work by
dichroism, birefringence, reflection, or
scattering.
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Wire-grid polarizers (I)dichroism
Part III Optical components, polarizers

• Mainly used in the IR and longer wavelengths
• Grid of parallel conducting wires with a spacing
  comparable to the wavelength of observation
• Electric field vector parallel to the wires is
  attenuated because of currents induced in the
  wires

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Wide-grid polarizers (II) dichroism
Part III Optical components, polarizers
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Dichroic crystals dichroism
Part III Optical components, polarizers
Dichroic crystals absorb one polarization state
over the other one. Example tourmaline.
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Polaroids dichroism
Part III Optical components, polarizers
Polaroids, like in sunglasses!
Made by heating and stretching a sheet of PVA
laminated to a supporting sheet of cellulose
acetate treated with iodine solution (H-type
polaroid). Invented in 1928.
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Crystal polarizers (I) birefringence
Part III Optical components, polarizers

• Optically anisotropic crystals
• Mechanical model
• the crystal is anisotropic, which means that the
  electrons are bound with different springs
  depending on the orientation
• different spring constants gives different
  propagation speeds, therefore different indices
  of refraction, therefore 2 output beams

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Crystal polarizers (II)birefringence
Part III Optical components, polarizers
The 2 output beams are polarized (orthogonally).
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Crystal polarizers (IV)birefringence
Part III Optical components, polarizers

• Crystal polarizers used as
• Beam displacers,
• Beam splitters,
• Polarizers,
• Analyzers, ...
• Examples Nicol prism, Glan-Thomson polarizer,
  Glan or Glan-Foucault prism, Wollaston prism,
  Thin-film polarizer, ...

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Mueller matrices of polarizers (I)
Part III Optical components, polarizers

• (Ideal) linear polarizer at angle ?

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Mueller matrices of polarizers (II)
Part III Optical components, polarizers
Linear (Q) polarizer at 0º
Linear (U) polarizer at 0º
Circular (V) polarizer at 0º
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Mueller calculus with a polarizer
Part III Optical components, polarizers
Input light unpolarized --- output light
polarized
Total output intensity 0.5 I
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Retarders
Part III Optical components, retarders

• In retarders, one polarization gets retarded,
  or delayed, with respect to the other one. There
  is a final phase difference between the 2
  components of the polarization. Therefore, the
  polarization is changed.
• Most retarders are based on birefringent
  materials (quartz, mica, polymers) that have
  different indices of refraction depending on the
  polarization of the incoming light.

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Half-Wave plate (I)
Part III Optical components, retarders

• Retardation of ½ wave or 180º for one of the
  polarizations.
• Used to flip the linear polarization or change
  the handedness of circular polarization.

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Half-Wave plate (II)
Part III Optical components, retarders
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Quarter-Wave plate (I)
Part III Optical components, retarders

• Retardation of ¼ wave or 90º for one of the
  polarizations
• Used to convert linear polarization to
  elliptical.

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Quarter-Wave plate (II)
Part III Optical components, retarders

• Special case incoming light polarized at 45º
  with respect to the retarders axis
• Conversion from linear to circular polarization
  (vice versa)

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Mueller matrix of retarders (I)
Part III Optical components, retarders

• Retarder of retardance ? and position angle ?

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Mueller matrix of retarders (II)
Part III Optical components, retarders

• Half-wave oriented at 45º

• Half-wave oriented at 0º or 90º

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Mueller matrix of retarders (III)
Part III Optical components, retarders

• Quarter-wave oriented at 45º

• Quarter-wave oriented at 0º

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Mueller calculus with a retarder
Part III Optical components, retarders

• Input light linear polarized (Q1)
• Quarter-wave at 45º
• Output light circularly polarized (V1)

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(Back to polarizers, briefly)Circular polarizers
Part III Optical components, polarizers

• Input light unpolarized --- Output light
  circularly polarized
• Made of a linear polarizer glued to a
  quarter-wave plate oriented at 45º with respect
  to one another.

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Achromatic retarders (I)
Part III Optical components, retarders

• Retardation depends on wavelength
• Achromatic retarders made of 2 different
  materials with opposite variations of index of
  refraction as a function of wavelength
• Pancharatnam achromatic retarders made of 3
  identical plates rotated w/r one another
• Superachromatic retarders 3 pairs of quartz and
  MgF2 plates

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Achromatic retarders (II)
Part III Optical components, retarders

• ?140-220º
• not very achromatic!

• ? 177-183º
• much better!

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Retardation on total internal reflection
Part III Optical components, retarders

• Total internal reflection produces retardation
  (phase shift)

• In this case, retardation is very achromatic
  since it only depends on the refractive index
• Application Fresnel rhombs

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Fresnel rhombs
Part III Optical components, retarders

• Quarter-wave and half-wave rhombs are achieved
  with 2 or 4 reflections

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Other retarders
Part III Optical components, retarders

• Soleil-Babinet variable retardation to better
  than 0.01 waves
• Nematic liquid crystals... Liquid crystal
  variable retarders... Ferroelectric liquid
  crystals... Piezo-elastic modulators... Pockels
  and Kerr cells...

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Part IV Polarimeters

• Polaroid-type polarimeters
• Dual-beam polarimeters

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Polaroid-type polarimeterfor linear polarimetry
(I)
Part IV Polarimeters, polaroid-type

• Use a linear polarizer (polaroid) to measure
  linear polarization ... another cool applet
  Location http//www.colorado.edu/physics/2000/app
  lets/lens.html
• Polarization percentage and position angle

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Polaroid-type polarimeterfor linear polarimetry
(II)
Part IV Polarimeters, polaroid-type

• Move the polaroid to 2 positions, 0º and 45º (to
  measure Q, then U)

• Advantage very simple to make
• Disadvantage half of the light is cut out
• Other disadvantages non-simultaneous
  measurements, cross-talk...

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Polaroid-type polarimeterfor circular polarimetry
Part IV Polarimeters, polaroid-type

• Polaroids are not sensitive to circular
  polarization, so convert circular polarization to
  linear first, by using a quarter-wave plate
• Polarimeter now uses a quarter-wave plate and a
  polaroid
• Same disadvantages as before

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Dual-beam polarimetersPrinciple
Part IV Polarimeters, dual-beam type

• Instead of cutting out one polarization and
  keeping the other one (polaroid), split the 2
  polarization states and keep them both
• Use a Wollaston prism as an analyzer
• Disadvantages need 2 detectors (PMTs, APDs) or
  an array end up with 2 pixels with different
  gain
• Solution rotate the Wollaston or keep it fixed
  and use a half-wave plate to switch the 2 beams

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Dual-beam polarimetersSwitching beams
Part IV Polarimeters, dual-beam type

• Unpolarized light two beams have identical
  intensities whatever the prisms position if the
  2 pixels have the same gain
• To compensate different gains, switch the 2
  beams and average the 2 measurements

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Dual-beam polarimetersSwitching beams by
rotating the prism
Part IV Polarimeters, dual-beam type
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Dual-beam polarimetersSwitching beams using a ½
wave plate
Part IV Polarimeters, dual-beam type
Rotated by 45º
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Dual-beam polarimeter for circular polarization -
Wollaston and quarter-wave plate
Part IV Polarimeters, dual-beam type

• The measurements V/I is
• Switch the beams to compensate the gain effects

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A real circular polarimeterSemel, Donati, Rees
(1993)
Part IV Polarimeters, example of circular
polarimeter
Quarter-wave plate, rotated at -45º and 45º
Analyser double calcite crystal
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A real circular polarimeterfree from gain (g)
and atmospheric transmission (?) variation effects
Part IV Polarimeters, example of circular
polarimeter

• First measurement with quarter-wave plate at
  -45º, signal in the (r)ight and (l)eft beams
• Second measurement with quarter-wave plate at
  45º, signal in the (r)ight and (l)eft beams
• Measurements of the signals

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A real circular polarimeterfree from gain and
atmospheric transmission variation effects
Part IV Polarimeters, example of circular
polarimeter

• Build a ratio of measured signals which is free
  of gain and variable atmospheric transmission
  effects

average of the 2 measurements
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Polarimeters - Summary
Part IV Polarimeters, summary

• 2 types
• polaroid-type easy to make but ½ light is lost,
  and affected by variable atmospheric transmission
• dual-beam type no light lost but affected by
  gain differences and variable transmission
  problems
• Linear polarimetry
• analyzer, rotatable
• analyzer half-wave plate
• Circular polarimetry
• analyzer quarter-wave plate

• 2 positions minimum

• 1 position minimum

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Part V ESPaDOnS

• Optical components of the polarimeter part
• Wollaston prism analyses the polarization and
  separates the 2 (linear!) orthogonal polarization
  states
• Retarders, 3 Fresnel rhombs
• Two half-wave plates to switch the beams around
• Quarter-wave plate to do circular polarimetry

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ESPaDOnS circular polarimetry
Part V ESPaDOnS, circular polarimetry mode

• Fixed quarter-wave rhomb
• Rotating bottom half-wave, at 22.5º increments
• Top half-wave rotates continuously at about 1Hz
  to average out linear polarization when measuring
  circular polarization

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ESPaDOnS circular polarimetry of circular
polarization
Part V ESPaDOnS, circular polarimetry mode

• half-wave
• 22.5º positions
• flips polarization
• gain, transmission

• quarter-wave
• fixed
• circular to linear

• analyzer

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ESPaDOnS circular polarimetry of (unwanted)
linear polarization
Part V ESPaDOnS, circular polarimetry mode

• analyzer

• half-wave
• 22.5º positions
• gain, transmission

• quarter-wave
• fixed
• linear to elliptical

• circular part goes through not analyzed and adds
  same intensities to both beams
• linear part is analyzed!

• Add a rotating half-wave to spread out the
  unwanted signal

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ESPaDOnS linear polarimetry
Part V ESPaDOnS, linear polarimetry

• Half-Wave rhombs positioned at 22.5º increments
• Quarter-Wave fixed

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ESPaDOnS linear polarimetry
Part V ESPaDOnS, linear polarimetry

• Half-Wave rhombs positioned as 22.5º increments
• First position gives Q
• Second position gives U
• Switch beams for gain and atmosphere effects
• Quarter-Wave fixed

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ESPaDOnS - Summary
Part V ESPaDOnS, summary

• ESPaDOnS can do linear and circular polarimetry
  (quarter-wave plate)
• Beams are switched around to do the measurements,
  compensate for gain and atmospheric effects
• Fesnel rhombs are very achromatic

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Credits for pictures and movies

• Christoph Kellers home page his 5 lectures
  http//www.noao.edu/noao/staff/keller/
• Basic Polarisation techniques and devices,
  Meadowlark Optics Inc. http//www.meadowlark.com/
• Optics, E. Hecht and Astronomical Polarimetry,
  J. Tinbergen
• Planets, Stars and Nebulae Studied With
  Photopolarimetry, T. Gehrels
• Circular polarization movie http//www.optics.ariz
  ona.edu/jcwyant/JoseDiaz/Polarization-Circular.htm
  
• Unpolarized light movie http//www.colorado.edu/ph
  ysics/2000/polarization/polarizationII.html
• Reflection of wave http//www.physicsclassroom.com
  /mmedia/waves/fix.html
• ESPaDOnS web page and documents

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References/Further reading On the Web

• Very short and quick introduction, no equation
  http//www.cfht.hawaii.edu/manset/PolarIntro_eng.
  html
• Easy fun page with Applets, on polarizing filters
  http//www.colorado.edu/physics/2000/polarization/
  polarizationI.html
• Polarization short course http//www.glenbrook.k12
  .il.us/gbssci/phys/Class/light/u12l1e.html
• Instrumentation for Astrophysical
  Spectropolarimetry, a series of 5 lectures given
  at the IAC Winter School on Astrophysical
  Spectropolarimetry, November 2000
  http//www.noao.edu/noao/staff/keller/lectures/in
  dex.html

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References/Further reading Polarization basics

• Polarized Light, D. Goldstein excellent book,
  easy read, gives a lot of insight, highly
  recommended
• Undergraduate textbooks, either will do
• Optics, E. Hecht
• Waves, F. S. Crawford, Berkeley Physics Course
  vol. 3

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References/Further readingAstronomy,
easy/intermediate

• Astronomical Polarimetry, J. Tinbergen
  instrumentation-oriented
• La polarisation de la lumière et l'observation
  astronomique, J.-L. Leroy astronomy-oriented
• Planets, Stars and Nebulae Studied With
  Photopolarimetry, T. Gehrels old but classic
• 3 papers by K. Serkowski instrumentation-oriente
  d

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References/Further readingAstronomy, advanced

• Introduction to Spectropolarimetry, J.C. del Toro
  Iniesta radiative transfer ouch!
• Astrophysical Spectropolarimetry, Trujillo-Bueno
  et al. (eds) applications to astronomy