Temporal and Spatial Modulation SOLIS VSM...

Lecture 10: Polarimeters

Outline

1 Temporal and Spatial Modulation2 Rotating Waveplate Polarimeters3 HARPS Polarimeter4 Liquid Crystal Polarimeters5 SOLIS VSM6 Piezoacoustic Modulator Polarimeters7 ZIMPOL8 Spectral Modulation Polarimeter: SPEX

Christoph U. Keller, Utrecht University, [email protected] Astronomical Telescopes and Instruments, Lecture 10: Polarimeters 1

Temporal and Spatial Modulation

General Polarimeters

Source Polarization

OpticsCalibrationPolarization

DetectorModulatorSpectro-meterTelescope

polarimeters: optical elements (e.g. retarders, polarizers) thatchange polarization state of incoming light in controlled waydetectors always measure only intensitiesintensity measurements combined to retrieve polarization state ofincoming lightpolarimeters vary by polarization modulation schemepolarimeter should also include polarization calibration optics


Spatial Polarization Modulation

DetectorBeamsplitterPolarizing

polarizing beam-splitter polarimetersimple linear polarimeter: polarizing beam-splitter producing 2beams corresponding to 2 orthogonal linear polarization statesfull linear polarization information from rotating assemblyspatial modulation: simultaneous measurements of two (or more)Stokes parameters


Temporal Polarization Modulation

Detector

rotating waveplate polarimeterrotating retarder, fixed linear polarizermeasured intensity as function of retardance δ, position angle θ

I′ =1

2

„I +

Q

2((1 + cos δ) + (1− cos δ) cos 4θ) +

U

2(1− cos δ) sin 4θ − V sin δ sin 2θ

«

only terms in θ lead to modulated signalequal modulation amplitudes in Q, U, and V for δ=127

temporal modulation: sequential measurements of I± one ormore Stokes parameters


Comparison of Temporal and Spatial Modulation Schemes

Modulation Advantages Disadvantagestemporal negligible effects of flat

field and optical aber-rations

influence of seeing ifmodulation is slow

potentially high polari-metric sensitivity

limited read-out rate ofarray detectors

spatial off-the-shelf array de-tectors

requires up to fourtimes larger sensor

high photon collectionefficiency

influence of flat field

allows post-facto re-construction

influence of differentialaberrations

schemes rather complementary⇒ modern, sensitive polarimeters useboth to combine advantages and minimize disadvantages


Rotating Waveplate Polarimeters

Fundamentals

I′ =1

2

„I +

Q

2((1 + cos δ) + (1− cos δ) cos 4θ) +

U

2(1− cos δ) sin 4θ − V sin δ sin 2θ

«

Q, U modulated at twice the frequency of Vphase shift in modulation between Q and U is 90⇒measurements at 8 angles to determine all 4 Stokes parameters


Double-Ratio Techniquecombination of spatial and temporal modulationdata reduction minimizes effects of many artifactsrotatable quarter-wave plate, polarizing beam-splitterconsider case of circularly polarized lightquarter-wave plate switches between +45 or -45 to polarizingbeam-splitterboth beams recorded simultaneouslyfour measurements are combined to obtain estimate ofStokes V/I ratio largely free of effects from seeing and gainvariations between different detector areasexcellent if polarization signal is smallfrequently used in stellar polarimetrycan be applied to any polarized Stokes parameterworks very well for solar applications where the spectrum in thefirst and the second exposures are different


Double-Ratio Technique (continued)measured intensities in two beams in first exposure

Sl1 = glα1(I1 + V1), Sr

1 = grα1(I1 − V1)

subscript 1: first exposuresubscripts l , r : left, right beamsS: measured signalg: gain in particular beamα: transmission of atmosphere, instrument

second exposure

Sl2 = glα2(I2 − V2), Sr

2 = grα2(I2 + V2)

incoming I and V in second exposure may be completely differentfrom first exposurealso includes beam-wobble induced by rotation of wave plate


Double-Ratio Technique (continued)combination of 4 measured intensities removes effect oftransmission changes and differential gain variations of differentdetector areas

14

(Sl

1

Sl2

Sr2

Sr1− 1

)=

12

I2V1 + I1V2

I1I2 − I2V1 − I1V2 + V1V2

if V I12

(V1

I1+

V2

I2

)obtain average V/I signal of two exposuresno spurious polarization signals are introduced


HARPS Polarimeter

IntroductionHARPS: Most successful exoplanet findermeasure magnetic fields of planet-hosting starsonly publicly accessible high-resolution spectropolarimeter in thesouthern hemisphere

RequirementsUse slider and volume of Iodine cellDo not compromise performance and operations of HARPSFull StokesPolarimetric sensitivity 10−4 for one night on a bright star380-690 nmMinimal instrumental polarizationMinimal (polarized) fringes


Liquid Crystal Polarimeters

Introductionno moving partsnematic liquid crystals

change retardance with applied electric fieldrelatively slow (<50 Hz)electrically tunable for different wavelengths

ferro-electric liquid crystalsflip fast axis orientation with applied electric field (2 states only)fast (<10 kHz)fixed retardation and optimum wavelength

often combinations of variable liquid crystal retarders and fixedretarders


SOLIS Vector-Spectromagnetograph (VSM)


Separation of Polarization Modulation and PolarizerFLC and retarders located behind spectrograph entrance slitpolarizing beamsplitters located in front of camerasspectrograph and associated optics built to minimize instrumentalpolarization between modulators and polarizing beam splittersadvantages of VSM approach: no moving parts for polarizationanalysis, switching of polarization states can occur rapidly, andboth polarization states are detected simultaneously after havingpassed through the same optics


Piezo-Elastic Modulators (PEMs)stress-induced birefringence, also sometimes called piezo-opticalor photo-elastic effectblock of a few cm in side length of common BK7 glass can bestressed enough by hand such as to introduce a quarter-waveretardationstress-induced birefringence is proportional to stress σretardation (in waves)

δ =1λ

Kdσ

K stress optical constantd thickness of variable retarderλ wavelength

construct variable retarder by compressing optical glassrequires considerable mechanical power to modulate


Mechanical Resonancemechanically resonant oscillation reduces power requirement toone over the mechanical Q (103-104 for most glasses)slab of length L excited at fundamental mode⇒ standing acousticwave with wavelength 2L, frequency ω

ω =cs

2L

cs: sound speed in optical material57-mm-long fused silica slab⇒ resonance frequency is 50 kHz.resulting stress, retardance as function of position x and time tstress-induced birefringence δ(x , t) given by

δ(x , t) = A sinωt sin(πxL

)

A amplitude of oscillationx from 0 to L


PEM Driver

to make slab oscillate, quartz crystal with electrodes on itssurfaces is forced to oscillate by externally applied electrical fieldvia piezo effectquartz slab mechanically coupled to modulator slabelectrical field driven at mechanical resonance frequencyoscillation amplitude A regulated with electronic feedback circuit


PEM Power

oscillation dampened by friction losses within modulator materialenergy loss inversely proportional to mechanical QQ very large⇒ little energy loss in modulator small (0.1 to 1 W)material with high Q (fused silica, Q ≈ 104) desirabletypical glass has Q ∼ 103

required drive power does not depend on length of slab


PEM Birefringence

stress-induced birefringence

δ(x , t) = A sinωt sin(πxL

)

combine sin(πxL ), amplitude A into spatially varying amplitude A(x)

birefringence becomes δ(x , t) = A(x) sin(ωt)A small⇒ PEM is true zero-order retarderPEM Mueller matrix corresponds to retarder with time-dependentretardationretarder Mueller matrix contains elements with sin δ(x , t) andcos δ(x , t)expand sin(sin(·)) and cos(sin(·)) in terms of Bessel functions


Bessel Functions

Mueller matrix elements become

sin δ(x, t) = 2J1(A(x)) sinωt + · · · ,cos δ(x , t) = J0(A(x)) + 2J2(A(x)) cos 2ωt + · · · ,

J0,1,2: Bessel functions of order 0,1 and 2


PEM Advantages and DisadvantagesAdvantages:

PEMs are stable in operationshow no degrading at high intensity levels and/or UV irradiationhave good optical propertieslarge spatial and angular aperturerequire only low voltages at moderate driving powers (< 1 W)

Disadvantages:sinusoidal modulation (as compared to more efficientsquare-wave modulation possible with liquid crystals)very high modulation frequency (20 to 50 kHz), which requiresspecialized array detectors (ZIMPOL)


Zurich Imaging Polarimeters (ZIMPOL)

CCD Array as Fast Demodulator


CCD Array as Fast DemodulatorZIMPOL I polarization modulator consists of 2 PEMS and apolarizer (single beam)modulation according to

I′(t) =1

2

“I + Q

√2J2(A) cos(2Ω1t) + U

√2J2(A) cos(2Ω2t) + V

√2J1(A) sin(Ω1t)

”

frequencies of PEMs given by Ω1, Ω2

amplitudes of both PEMs, A, chosen such that J0(A) = 0for vector polarimetry: 3 synchronous demodulators, eachsensitive to one of 2Ω1, 2Ω2, Ω1

development of demodulating CCD by Povel and coworkers about20 years agofractional polarization free of flat-field effectsno seeing effects due to high modulation frequency


Spectral Modulation

Introduction

optically add modulation to intensity spectrum:modulation amplitude = degree of linear polarization (

√Q2 + U2/i)

modulation phase = orientation of linear polarization (arctanQ/U)Advantages of spectral modulation:

Fully passiveScalableOne-shot measurementNo differential effectsLow susceptibility to noise


SPEX: Spectropolarimeter for Planetary EXplorationMeasure size distribution and composition of planetaryatmospheresdust (storms) on Mars, atmosphere of Jupiter, aerosols in Earthatmosphereneeds to cover large wavelength range,Outlook

Venus-as-an-exoplanet (prototype)Earth from helicopter (prototype)Mars (ExoMars)Jupiter + moons (EJSM)Titan (TandEM)Earth from ISSEarth from microsatellites (FAST)Earth-as-an-exoplanet from the moon (ESA lunar lander)


Temporal and Spatial Modulation SOLIS VSM...

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