#### Transcript Polarization of Light - University of Hawaii

Polarization of Light: from Basics to Instruments (in less than 100 slides) N. Manset CFHT 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 N. Manset / CFHT Polarization of Light: Basics to Instruments 2 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 N. Manset / CFHT Polarization of Light: Basics to Instruments 3 Part I: Polarization states Light as an electromagnetic wave Light is a transverse wave, an electromagnetic wave N. Manset / CFHT Polarization of Light: Basics to Instruments 4 Part I: Polarization states Mathematical description of the EM wave Light wave that propagates in the z direction: E x ( z, t ) E 0x cos(kz - t) x E y ( z, t ) E 0y cos(kz - t ) y N. Manset / CFHT Polarization of Light: Basics to Instruments 5 Part I: Polarization states Graphical representation of the EM wave (I) One can go from: E x ( z, t ) E 0x cos(kz - t) x E y ( z, t ) E 0y cos(kz - t ) y to the equation of an ellipse (using trigonometric identities, squaring, adding): 2 Ey Ex Ey E x 2 cos sin 2 E0x E0y E0x E0y 2 N. Manset / CFHT Polarization of Light: Basics to Instruments 6 Part I: Polarization states Graphical representation of the EM wave (II) An ellipse can be represented by 4 quantities: 1. size of minor axis 2. size of major axis 3. orientation (angle) 4. sense (CW, CCW) Light can be represented by 4 quantities... N. Manset / CFHT Polarization of Light: Basics to Instruments 7 Part I: Polarization states, linear polarization Vertically polarized light E x ( z, t ) E 0x cos(kz - t) x E y ( z, t ) E 0y cos(kz - t ) y If there is no amplitude in x (E0x = 0), there is only one component, in y (vertical). N. Manset / CFHT Polarization of Light: Basics to Instruments 8 Part I: Polarization states, linear polarization Polarization at 45º (I) E x ( z, t ) E 0x cos(kz - t) x E y ( z, t ) E 0y cos(kz - t ) y If there is no phase difference (=0) and E0x = E0y, then Ex = Ey N. Manset / CFHT Polarization of Light: Basics to Instruments 9 Part I: Polarization states, linear polarization Polarization at 45º (II) N. Manset / CFHT Polarization of Light: Basics to Instruments 10 Part I: Polarization states, circular polarization Circular polarization (I) E x ( z, t ) E 0x cos(kz - t) x E y ( z, t ) E 0y cos(kz - t ) y If the phase difference is = 90º and E0x = E0y then: Ex / E0x = cos , Ey / E0y = sin and we get the equation of a circle: 2 Ex Ey cos2 sin 2 1 E E 0x 0y 2 N. Manset / CFHT Polarization of Light: Basics to Instruments 11 Part I: Polarization states, circular polarization Circular polarization (II) N. Manset / CFHT Polarization of Light: Basics to Instruments 12 Part I: Polarization states, circular polarization Circular polarization (III) N. Manset / CFHT Polarization of Light: Basics to Instruments 13 Part I: Polarization states, circular polarization... see it now? Circular polarization (IV) N. Manset / CFHT Polarization of Light: Basics to Instruments 14 Part I: Polarization states, elliptical polarization Elliptical polarization • Linear + circular polarization = elliptical polarization N. Manset / CFHT Polarization of Light: Basics to Instruments 15 Part I: Polarization states, unpolarized light Unpolarized light (natural light) N. Manset / CFHT Polarization of Light: Basics to Instruments 16 Part I: Polarization states A cool Applet Electromagnetic Wave Location: http://www.uno.edu/~jsulliva/java/EMWave.html N. Manset / CFHT Polarization of Light: Basics to Instruments 17 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 N. Manset / CFHT Polarization of Light: Basics to Instruments 18 Part II: Stokes parameters Stokes parameters A tiny itsy-bitsy little bit of history... • 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 N. Manset / CFHT Polarization of Light: Basics to Instruments 19 Part II: Stokes parameters Stokes parameters (I) The polarization ellipse is only valid at a given instant of time (function of time): 2 E y (t) E x (t) E y (t) E (t) x 2 cos εsin 2 ε E0x (t) E0y (t) E0x (t) E0y (t) 2 To get the Stokes parameters, do a time average (integral over time) and a little bit of algebra... N. Manset / CFHT Polarization of Light: Basics to Instruments 20 Part II: Stokes parameters Stokes parameters (II) described in terms of the electric field E 2 0x E E 2 2 0y 2 0x E 2E 2 2 0y The 4 Stokes parameters are: E0ycos ε 2 E0x E0ysin ε 2 0x 2 2 S0 I E0x E0y 2 2 S1 Q E0x E0y S2 U 2 E0x E0ycos ε S3 V 2 E0x E0ysin ε N. Manset / CFHT Polarization of Light: Basics to Instruments 21 2 Part II: Stokes parameters Stokes parameters (III) described in geometrical terms a2 I 2 Q a cos2 cos2 U a 2 cos2 sin 2 a 2 sin 2 V N. Manset / CFHT Polarization of Light: Basics to Instruments 22 Part II: Stokes parameters, Stokes vectors Stokes vector The Stokes parameters can be arranged in a Stokes vector: 2 2 E E I intensity 0x 0y 2 2 Q E0x E0y I0 I90 U 2 E E cos ε I45 I135 0x 0y 2 E E sin ε V 0x 0y IRCP ILCP • Linear polarization • Circular polarization • Fully polarized light • Partially polarized light • Unpolarized light N. Manset / CFHT Q 0, U 0, V 0 Q 0, U 0, V 0 I2 Q2 U 2 V2 I2 Q2 U 2 V 2 QUV0 Polarization of Light: Basics to Instruments 23 Part II: Stokes parameters Pictorial representation of the Stokes parameters N. Manset / CFHT Polarization of Light: Basics to Instruments 24 Part II: Stokes parameters, examples Stokes vectors for linearly polarized light LHP light LVP light +45º light -45º light 1 1 I0 0 0 1 1 I0 0 0 1 0 I0 1 0 1 0 I0 1 0 N. Manset / CFHT Polarization of Light: Basics to Instruments 25 Part II: Stokes parameters, examples Stokes vectors for circularly polarized light N. Manset / CFHT RCP light LCP light 1 0 I0 0 1 1 0 I0 0 1 Polarization of Light: Basics to Instruments 26 Part II: Stokes parameters (Q,U) to (P,) In the case of linear polarization (V=0): Q2 U 2 P I Q P cos 2 N. Manset / CFHT 1 U arctan 2 Q U P sin 2 Polarization of Light: Basics to Instruments 27 Part II: Stokes parameters, Mueller matrices Mueller matrices If light is represented by Stokes vectors, optical components are then described with Mueller matrices: [output light] = [Muller matrix] [input light] I' m11 m12 Q' m21 m22 U' m m32 31 V' m41 m42 N. Manset / CFHT m13 m23 m33 m43 m14 I m24 Q m34 U m44 V Polarization of Light: Basics to Instruments 28 Part II: Stokes parameters, Mueller matrices Mueller calculus (I) Element 1 Element 2 Element 3 M1 M2 M3 I’ = M3 M2 M1 I N. Manset / CFHT Polarization of Light: Basics to Instruments 29 Part II: Stokes parameters, Mueller matrices Mueller calculus (II) Mueller matrix M’ of an optical component with Mueller matrix M rotated by an angle : M’ = R(- ) M R() with: 0 0 1 0 cos2 sin 2 R( ) 0 sin 2 cos2 0 0 0 N. Manset / CFHT 0 0 0 1 Polarization of Light: Basics to Instruments 30 Part II: Stokes parameters, Jones formalism, not that important here... Jones formalism Stokes vectors and Mueller matrices cannot describe interference effects. If the phase information is important (radioastronomy, masers...), one has to use the Jones formalism, with complex vectors and Jones matrices: • Jones vectors to describe the • Jones matrices to represent polarization of light: optical components: j11 j12 E x (t ) J J (t ) E (t ) j21 j22 y BUT: Jones formalism can only deal with 100% polarization... N. Manset / CFHT Polarization of Light: Basics to Instruments 31 Part III: Optical components for polarimetry • Complex index of refraction • Polarizers • Retarders N. Manset / CFHT Polarization of Light: Basics to Instruments 32 Part III: Optical components Complex index of refraction The index of refraction is actually a complex quantity: m n ik • real part • imaginary part • optical path length, refraction: speed of light depends on media • absorption, attenuation, extinction: depends on media • birefringence: speed of light also depends on P • dichroism/diattenuation: also depends on P N. Manset / CFHT Polarization of Light: Basics to Instruments 33 Part III: Optical components, polarizers 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. N. Manset / CFHT Polarization of Light: Basics to Instruments 34 Part III: Optical components, polarizers Wire-grid polarizers (I) [dichroism] • 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 N. Manset / CFHT Polarization of Light: Basics to Instruments 35 Part III: Optical components, polarizers Wide-grid polarizers (II) [dichroism] N. Manset / CFHT Polarization of Light: Basics to Instruments 36 Part III: Optical components, polarizers Dichroic crystals [dichroism] Dichroic crystals absorb one polarization state over the other one. Example: tourmaline. N. Manset / CFHT Polarization of Light: Basics to Instruments 37 Part III: Optical components, polarizers – Polaroids, like in sunglasses! Polaroids [dichroism] 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. N. Manset / CFHT Polarization of Light: Basics to Instruments 38 Part III: Optical components, polarizers Crystal polarizers (I) [birefringence] • 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 N. Manset / CFHT Polarization of Light: Basics to Instruments 39 Part III: Optical components, polarizers Crystal polarizers (II) [birefringence] isotropic crystal (sodium chloride) anisotropic crystal (calcite) The 2 output beams are polarized (orthogonally). N. Manset / CFHT Polarization of Light: Basics to Instruments 40 Part III: Optical components, polarizers Crystal polarizers (IV) [birefringence] • Crystal polarizers used as: • Beam displacers, • Beam splitters, • Polarizers, • Analyzers, ... • Examples: Nicol prism, GlanThomson polarizer, Glan or GlanFoucault prism, Wollaston prism, Thin-film polarizer, ... N. Manset / CFHT Polarization of Light: Basics to Instruments 41 Part III: Optical components, polarizers Mueller matrices of polarizers (I) • (Ideal) linear polarizer at angle : cos2χ sin 2χ 1 cos2 2χ sin 2χ cos2χ 1 cos2χ sin 2 2χ 2 sin 2χ sin 2χ cos2χ 0 0 0 N. Manset / CFHT Polarization of Light: Basics to Instruments 0 0 0 0 42 Part III: Optical components, polarizers Mueller matrices of polarizers (II) Linear (±Q) polarizer at 0º: 1 1 1 1 0 .5 0 0 0 0 N. Manset / CFHT 0 0 0 0 0 0 0 0 Linear (±U) polarizer at 0º : 1 0 0 .5 1 0 0 1 0 0 0 1 0 0 0 0 0 0 Circular (±V) polarizer at 0º : 1 0 0 .5 0 1 Polarization of Light: Basics to Instruments 0 0 0 0 0 1 0 0 0 0 0 1 43 Part III: Optical components, polarizers Mueller calculus with a polarizer Input light: unpolarized --- output light: polarized I' 1 Q' 0 U' 0.5 1 V' 0 0 1 0 0 0 1 0 0 0 I I 0 0 0 0.5 0 0 -I 0 0 0 Total output intensity: 0.5 I N. Manset / CFHT Polarization of Light: Basics to Instruments 44 Part III: Optical components, retarders 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. N. Manset / CFHT Polarization of Light: Basics to Instruments 45 Part III: Optical components, retarders Half-Wave plate (I) • Retardation of ½ wave or 180º for one of the polarizations. • Used to flip the linear polarization or change the handedness of circular polarization. N. Manset / CFHT Polarization of Light: Basics to Instruments 46 Part III: Optical components, retarders Half-Wave plate (II) N. Manset / CFHT Polarization of Light: Basics to Instruments 47 Part III: Optical components, retarders Quarter-Wave plate (I) • Retardation of ¼ wave or 90º for one of the polarizations • Used to convert linear polarization to elliptical. N. Manset / CFHT Polarization of Light: Basics to Instruments 48 Part III: Optical components, retarders Quarter-Wave plate (II) • Special case: incoming light polarized at 45º with respect to the retarder’s axis • Conversion from linear to circular polarization (vice versa) N. Manset / CFHT Polarization of Light: Basics to Instruments 49 Part III: Optical components, retarders Mueller matrix of retarders (I) • Retarder of retardance and position angle : 0 0 1 H sin4ψ 0 G H cos4ψ 0 H sin4ψ G H cos4ψ sinτ cos2ψ 0 sinτ sin2ψ 1 with : G 1 cosτ and H 2 N. Manset / CFHT sinτ sin2ψ sinτ cos2ψ cosτ 1 1 cosτ 2 Polarization of Light: Basics to Instruments 0 50 Part III: Optical components, retarders Mueller matrix of retarders (II) • Half-wave oriented at 0º or 90º 1 0 k 0 0 0 0 0 1 0 0 0 1 0 0 0 1 N. Manset / CFHT • Half-wave oriented at ±45º 1 0 0 1 k 0 0 0 0 0 0 0 0 1 0 0 1 Polarization of Light: Basics to Instruments 51 Part III: Optical components, retarders Mueller matrix of retarders (III) • Quarter-wave oriented at 0º 1 0 k 0 0 0 0 1 0 0 0 0 1 N. Manset / CFHT 0 0 1 0 • Quarter-wave oriented at ±45º 1 0 0 0 k 0 0 0 1 0 0 0 1 1 0 0 0 Polarization of Light: Basics to Instruments 52 Part III: Optical components, retarders Mueller calculus with a retarder • Input light linear polarized (Q=1) • Quarter-wave at +45º • Output light circularly polarized (V=1) I' 1 0 Q' 0 0 k U' 0 0 V' 0 1 N. Manset / CFHT 0 0 1 1 0 1 1 0 k 0 1 0 0 0 0 0 1 Polarization of Light: Basics to Instruments 53 Part III: Optical components, polarizers (Back to polarizers, briefly) Circular 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. N. Manset / CFHT Polarization of Light: Basics to Instruments 54 Part III: Optical components, retarders Achromatic retarders (I) • 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 N. Manset / CFHT Polarization of Light: Basics to Instruments 55 Part III: Optical components, retarders Achromatic retarders (II) =140-220º not very achromatic! = 177-183º much better! N. Manset / CFHT Polarization of Light: Basics to Instruments 56 Part III: Optical components, retarders Retardation on total internal reflection • 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 N. Manset / CFHT Polarization of Light: Basics to Instruments 57 Part III: Optical components, retarders Fresnel rhombs • Quarter-wave and half-wave rhombs are achieved with 2 or 4 reflections N. Manset / CFHT Polarization of Light: Basics to Instruments 58 Part III: Optical components, retarders Other 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... N. Manset / CFHT Polarization of Light: Basics to Instruments 59 Part IV: Polarimeters • Polaroid-type polarimeters • Dual-beam polarimeters N. Manset / CFHT Polarization of Light: Basics to Instruments 60 Part IV: Polarimeters, polaroid-type Polaroid-type polarimeter for linear polarimetry (I) • Use a linear polarizer (polaroid) to measure linear polarization ... [another cool applet] Location: http://www.colorado.edu/physics/2000/applets/lens.html • Polarization percentage and position angle: I max I min P I max I min ( I I max ) N. Manset / CFHT Polarization of Light: Basics to Instruments 61 Part IV: Polarimeters, polaroid-type Polaroid-type polarimeter for linear polarimetry (II) • 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... N. Manset / CFHT Polarization of Light: Basics to Instruments 62 Part IV: Polarimeters, polaroid-type Polaroid-type polarimeter for circular polarimetry • 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 N. Manset / CFHT Polarization of Light: Basics to Instruments 63 Part IV: Polarimeters, dual-beam type Dual-beam polarimeters Principle • 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 N. Manset / CFHT Polarization of Light: Basics to Instruments 64 Part IV: Polarimeters, dual-beam type Dual-beam polarimeters Switching beams • Unpolarized light: two beams have identical intensities whatever the prism’s position if the 2 pixels have the same gain • To compensate different gains, switch the 2 beams and average the 2 measurements N. Manset / CFHT Polarization of Light: Basics to Instruments 65 Part IV: Polarimeters, dual-beam type Dual-beam polarimeters Switching beams by rotating the prism rotate by 180º N. Manset / CFHT Polarization of Light: Basics to Instruments 66 Part IV: Polarimeters, dual-beam type Dual-beam polarimeters Switching beams using a ½ wave plate Rotated by 45º N. Manset / CFHT Polarization of Light: Basics to Instruments 67 Part IV: Polarimeters, example of circular polarimeter A real circular polarimeter Semel, Donati, Rees (1993) Quarter-wave plate, rotated at -45º and +45º Analyser: double calcite crystal N. Manset / CFHT Polarization of Light: Basics to Instruments 69 Part IV: Polarimeters, example of circular polarimeter A real circular polarimeter free from gain (g) and atmospheric transmission () variation effects • First measurement with quarter-wave plate at -45º, signal l r S , S in the (r)ight and (l)eft beams: 1 1 • Second measurement with quarter-wave plate at +45º, l r S , S signal in the (r)ight and (l)eft beams: 2 2 • Measurements of the signals: S1l g l1 ( I1 V1 ) S1r g r1 ( I1 V1 ) S g 2 ( I 2 V2 ) S g 2 ( I 2 V2 ) l 2 N. Manset / CFHT l r 2 r Polarization of Light: Basics to Instruments 70 Part IV: Polarimeters, example of circular polarimeter A real circular polarimeter free from gain and atmospheric transmission variation effects • Build a ratio of measured signals which is free of gain and variable atmospheric transmission effects: 1 1 S1l S2r I 2V1 I1V2 F l r 1 4 S2 S1 2 I1 I 2 I 2V1 I1V2 V1V2 1 V1 V2 F forV 1 2 I1 I 2 average of the 2 measurements N. Manset / CFHT Polarization of Light: Basics to Instruments 71 Part IV: Polarimeters, summary 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 2 positions minimum – analyzer + half-wave plate • Circular polarimetry: – analyzer + quarter-wave plate N. Manset / CFHT 1 position minimum Polarization of Light: Basics to Instruments 72 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 N. Manset / CFHT Polarization of Light: Basics to Instruments 73 Part V: ESPaDOnS, circular polarimetry mode ESPaDOnS: circular polarimetry • 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 N. Manset / CFHT Polarization of Light: Basics to Instruments 74 Part V: ESPaDOnS, circular polarimetry mode ESPaDOnS: circular polarimetry of circular polarization • analyzer N. Manset / CFHT • half-wave • 22.5º positions • flips polarization • gain, transmission • quarterwave • fixed • circular to linear Polarization of Light: Basics to Instruments 75 Part V: ESPaDOnS, circular polarimetry mode ESPaDOnS: circular polarimetry of (unwanted) linear polarization • analyzer • circular part • half-wave goes through not analyzed and adds same intensities to both beams • 22.5º positions • linear part is analyzed! N. Manset / CFHT • gain, transmission • quarterwave • fixed • linear to elliptical Polarization of Light: Basics to Instruments • Add a rotating half-wave to “spread out” the unwanted signal 76 Part V: ESPaDOnS, linear polarimetry ESPaDOnS: linear polarimetry • Half-Wave rhombs positioned at 22.5º increments • Quarter-Wave fixed N. Manset / CFHT Polarization of Light: Basics to Instruments 77 Part V: ESPaDOnS, linear polarimetry 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 N. Manset / CFHT Polarization of Light: Basics to Instruments 78 Part V: ESPaDOnS, summary 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 N. Manset / CFHT Polarization of Light: Basics to Instruments 79 N. Manset / CFHT Polarization of Light: Basics to Instruments 80 Credits for pictures and movies • Christoph Keller’s 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.arizona.edu/jcwyant/JoseDiaz/Polarization-Circular.htm • Unpolarized light movie http://www.colorado.edu/physics/2000/polarization/polarizationII.html • Reflection of wave http://www.physicsclassroom.com/mmedia/waves/fix.html • ESPaDOnS web page and documents N. Manset / CFHT Polarization of Light: Basics to Instruments 81 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/index.html N. Manset / CFHT Polarization of Light: Basics to Instruments 82 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 N. Manset / CFHT Polarization of Light: Basics to Instruments 83 References/Further reading Astronomy, 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-oriented N. Manset / CFHT Polarization of Light: Basics to Instruments 84 References/Further reading Astronomy, advanced • Introduction to Spectropolarimetry, J.C. del Toro Iniesta – radiative transfer – ouch! • Astrophysical Spectropolarimetry, Trujillo-Bueno et al. (eds) – applications to astronomy N. Manset / CFHT Polarization of Light: Basics to Instruments 85