Polarimetry Techniques. K. Sankarasubramanian ISRO Satellite Centre Bangalore India

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1 Polarimetry Techniques K. Sankarasubramanian ISRO Satellite Centre Bangalore

2 Outline Introduction Why Polarimetry? Requirements Polarization Basics Stokes Parameters & Mueller Matrices Optical Components Simple Polarization Measurements Use of Polarizer and Quarter-Waveplate Modulation and Demodulation Solar Polarimeters ASP-type and ZIMPOL-type Balanced Vs Unbalanced Modulation Future Directions C 3 PO Achromatic and Tunable Polarimeters 22-Dec-26 2

3 Remote Measurement For astronomical Sources: Source of Information is Photons. Energy content of the photons at UV, Visible, IR etc.. Photometry. Relative absorption of photons at a spectral line because of atoms and molecules present in the atmosphere Spectroscopy. State of polarization of the light Polarimetry. 22-Dec-26 3

4 Why Polarimetry? Polarimetry: Study of polarization nature of the source (Any Source of Interest..!) Few Examples of Applications: (i) Astronomy (ii) Imaging of Earth (Synthetic Aperture Radar Polarimetry in Geoscience) (iii) Non-destructive Optical testings (iv) Used in Food, Chemical, and Pharmaceutical industries (v) Medical (or bio-medical) applications (Eyes, Tissues, Birefraction which allows detection of small size cancers) (vi) Material characterisation (vii) VLSI designs (Silicon wafer designs and thicknesses) (viii) Much more.. 22-Dec-26 4

5 Do we have enough Photons? C. U. Keller, 22, SPIE, 4843 Hydrostatic Condition Pressure Scale Height = Photon Mean free path ~ 7km Required Aperture ~ 1.5m Sound Speed ~ 7km/sec Exp. Time ~ 22-Dec-26 5

6 SNR - Requirements C. U. Keller, 22, SPIE, 4843 Unobscured Aperture 1% Overall Efficiency Maximum horizontal motion of the features ~ 5km/sec Nyquist Sampling Spectral Resolution ~ 15, Effective integration time from the previous figure 22-Dec-26 6

7 Polarization: Basics Light is a transverse wave, an electromagnetic wave r E r E x y (z, t) (z, t) = = E E x y r cos(kz -ω t) x cos(kz -ω t + ε ) r y 22-Dec-26 7

8 Generalised State E E x x 2 + E E y y 2 2 E E x x E E y y cos ε = sin 2 ε An ellipse can be represented by 4 quantities: size of minor axis size of major axis orientation (angle) sense (CW, CCW) 22-Dec-26 8

9 Representations 22-Dec-26 9

10 Circular polarization 22-Dec-26 1

11 Unpolarized light (natural light) 22-Dec-26 11

12 Stokes parameters The polarization ellipse is only valid at a given instant of time (function of time): 2 2 E E (t) y Ey(t) x x 2 E x (t) (t) + E y (t) E 2 E x (t) (t) E y (t) cos ε = sin ε To get the Stokes parameters, do a time average (integral over time) 22-Dec-26 12

13 Stokes parameters ( 2 2 ) 2 ( 2 2 ) 2 ( ) 2 E + E E E 2E E cosε = ( 2E E sinε) 2 x y x y x y x y The 4 Stokes parameters are: S S 1 = = I Q = = E E 2 x 2 x + E E 2 y 2 y S S 2 3 = = U V = = 2E 2E x x E E y y cos sin ε ε 22-Dec-26 13

14 Pictorial Rep. of Polarization Schurcliff, Polarized Light 22-Dec-26 14

15 Example I represents the total Intensity (pol.+unpol.). Q & U represents the linear polarization. V represents the circular polarization. Stokes parameters completely specify the polarization state. 22-Dec-26 15

16 Optics: Polarizer Allows only the light vibrating along the axis of the polarizers (e.g. wire grid polarizers, Dichroic crystal polarizers, Dichroic sheet polarizers, crystal polarizers, and thin film polarizers) 22-Dec-26 16

17 Optics: Retarder Retards one polarization compared to the orthogonal polarization Quarter wave 9deg retardance Half wave 18deg retardance Materials used: Quartz, Mica, Calcite, and Polymers 22-Dec-26 17

18 Representation of Polarized Light Jones Calculus: For coherent source (Schurcliff, Polarized light, 1962) Mueller Calculus: For incoherent source (Gerrard and Burch, Matrix methods in optics,1975) Poincare Sphere: Pictorial representation (Ramachandran and Ramaseshan, Geometrical representation of polarization, 1962) 22-Dec-26 18

19 Mueller matrices If light is represented by Stokes vectors, optical components are then described with Mueller matrices: [output light] = [Muller matrix] [input light] I' Q' U' V' = m m m m m m m m m m m m m m m m I Q U V 22-Dec-26 19

20 Mueller Calculus I = [I, Q, U, V] I = [I,Q,U,V ] M 4X4 matrix For N optical elements: M =M M M M T T N N I Input M I = M.I I output 22-Dec-26 2

21 22-Dec Mueller Matrix ± ± ± ± ± m k Linear Polarizer o 45 o QWP at 45 o 2χ sin sin 2χ cos2χ sin 2χ sin 2χ cos2χ 2χ cos cos2χ sin 2χ cos2χ Linear Polarizer at an angle

22 Mueller matrix of retarders Retarder of retardance τ and position angle ψ: 1 with : G G + H cos4ψ H sin4ψ sinτ = sin2ψ 1 2 ( ) ( ) 1+ cosτ G H sin4ψ sinτ H cos4ψ and cos2ψ H = sinτ sin2ψ sinτ cos2ψ cosτ 1 1 cosτ 2 22-Dec-26 22

23 A simple polarimeter Use Polarizer to detect linear polarization Rotate the polarizer to four different positions (, 45, 9, and 135) - Modulation Difference in intensity between and 9 gives Q - Demodulation Difference in intensity between 45 and 135 gives U - Demodulation Introduce retarder at 45 degree to convert the circular to linear - Demodulation Use the polarizer at and 9 degrees to detect the linear polarization (converted from the circular polarization Note: Polarization measurements are differential intensity measurement 22-Dec-26 23

24 Relation between Magnetic field and polarization. Zeeman Effect: Splitting of spectral lines in the presence of magnetic field. Splitting is proportional to the field strength and square of the wavelength. Field strength should be greater than few hundred Gauss for complete splitting 22-Dec

25 Relationship between magnetic field and polarization Hanle effect: Due to coherence scattering in the presence of magnetic field. Plasma density should be low. Anisotropic incident beam. Larmor frequency be comparable to the spontaneous emission rate. 22-Dec

26 Basic Technique 22-Dec-26 26

27 Modifications of Polarization Source: Range of height for the spectral line formation. Atmosphere: Changes in the atmospheric condition within the measurement time. Telescope: Preferred symmetric optics. Reflecting telescope changes polarization. Polarimeter: Optical elements in the polarimeter. Spectrograph: Efficiency changes with the input polarization. Detector: Pixel to pixel gain variation. 22-Dec-26 27

28 Efficiency of the grating for different polarization input. 22-Dec-26 28

29 ASP-Type Polarimeter Rotating Modulator Modulate the polarization on to the intensity. Detect the modulated intensity. Find the intensity difference between two orthogonal measurement. Demodulate the difference intensity to get the Stokes parameters. 22-Dec-26 29

30 Instruments: ASP Advanced Stokes Polarimeter Two beam system to reduce the seeing contribution (spatial modulation). Retarder kept before the focus and in the collimated beam. Uses a polarizing beam splitter. 22-Dec-26 3

31 Instrument: ZIMPOL - I Fast temporal modulation using the PEM s. Good polarization accuracy. Specially made detectors in order to do fast measurements. 22-Dec-26 31

32 ZIMPOL - I Alternate detectors masked Possibility of long integration Sensitivity ~ few times 1-6 Low Efficiency since alternate pixels are masked Courtesy: C. U. Keller 22-Dec-26 32

33 ZIMPOL - I Courtesy: C. U. Keller 22-Dec-26 33

34 ZIMPOL - II 22-Dec-26 Courtesy: C. U. Keller 34

35 Comparison Modulation Scheme Advantages Disadvantages Temporal modulation (ZIMPOL) Spatial (ASP) Negligible flat-field effect. High polarization accuracy. Off-the-shelf array detector can be used. High photon collecting efficiency. Influence of seeing if modulation is slow. Regular array detector limits modulation frequency. Expensive with fast modulation. Requires up to 4-times large array detector. Influence of flat-field Influence of differential aberration. 22-Dec-26 35

36 Dual-beam polarimeters Switching beams Semel s Technique 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 Courtesy: Manset, CFHT 22-Dec-26 36

37 Dual-beam polarimeters Switching beams by rotating the prism rotate by 18º 22-Dec-26 37

38 Future Directions: C 3 PO Geometric fill factor Peak quantum efficiency Wavelengt h coverage Full-well depth ZIMPOL II <25% <35% 2-11 nm 25, C 3 Po 1% >85% 2-1, nm >5, Courtesy: C. U. Keller 22-Dec-26 38

39 C 3 PO Courtesy: C. U. Keller 22-Dec-26 39

40 Requirement for C 3 PO Item Format Pixel pitch Number of image states Full well depth per image state Geometric fill factor Frame rate Dynamic range Readout noise Quantum efficiency Dark current Dark current stability Flatness Image lag Specification 124 by 124 pixels 18 micrometers square 4 >5, e 1% >= 1 frames per second >1 <3 e rms per pixel 63 nm 854 nm nm <5 e per sec per -15C Better than 3 e/s/pixel rms over 12 hours <1 micrometer peak-peak <.2% Comments 248 by 248 would be great Larger pixels would hold more charges 2 is the absolute minimum More would be better, but would require larger pixels No incident photons blocked goal of 25 frames/s Full well / readout noise goal of <15 e at operating temperature Signal remaining from previous frame Courtesy: C. U. Keller 22-Dec-26 4

41 Observed Stokes profiles Observed in the penumbral region of a sunspot. Stokes profiles are corrected for the instrumental polarization. 22-Dec-26 41

42 Stokes parameter map of a sunspot. Taken with the ASP and the AO. Maps are produced using few wavelength positions in the wing of the spectral line The whole spectrograph is moved to scan the region. Seeing was excellent. 22-Dec-26 42

43 Calculation of vector field. Need to know the physical processes which are happening in the line forming region. Radiative transfer processes. Good imagination with supportive physics. 22-Dec-26 43

44 ASP inversion code. Input Calibrated I, Q, U, V; and a model file. Output Fitted parameters with associated errors. 1 fitted parameters Vector field (3), Doppler broadening, line depth, fill fraction, velocity, damping factor, source fn. (2), scattered light. Assumption: The atmosphere is a Milne-Eddington (ME) atmosphere. The parameters are constant with depth. 22-Dec-26 44

45 Forward Vs. Inverse Forward Reverse Compares the values of the observed Stokes parameters with that of a calculated one by solving the RTE using assumed model parameters. Time consuming once the number of model parameters are large and also with large number of observed profiles. Infer the unknown model parameters using the observed Stokes profiles. In doing so use a minimization technique. Large computation time Simple to use and can be used for large number of profiles and for large number of model parameters. 22-Dec-26 45

46 Polarimetry at Other wavelengths Gamma Ray Polarimetry Not so important for solar but for GRBs X Ray Polarimetry Detected in solar flares VUV Polarimetry Not yet tried Visible Instrumentation well understood and fine tuning is going on EUV and UV polarimetry Still in the infant stage IR and Far-IR Detector development is the major hurdle but progress has been made Microwave Have produced some interesting results Radio wave Well established and under development for solar observations 22-Dec-26 46

Lecture 8: Polarimetry 2. Polarizers and Retarders. Polarimeters. Scattering Polarization. Zeeman Effect. Outline

Lecture 8: Polarimetry 2. Polarizers and Retarders. Polarimeters. Scattering Polarization. Zeeman Effect. Outline Lecture 8: Polarimetry 2 Outline 1 Polarizers and Retarders 2 Polarimeters 3 Scattering Polarization 4 Zeeman Effect Christoph U. Keller, Utrecht University, C.U.Keller@uu.nl Observational Astrophysics