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SOT Polarization Calibration -- method and results for FG -- K.Ichimoto and SOT Team

This article discusses the method and results of the polarization calibration for the SOT polarimeter in the Solar Optical Telescope (SOT) on Solar-B. It covers the schematics of the polarimeter, the modulation and sampling scheme, and the polarization calibration test method. The article includes example demodulation matrices and fitting results for the polarimeter data.

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SOT Polarization Calibration -- method and results for FG -- K.Ichimoto and SOT Team

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  1. SOT Polarization Calibration -- method and results for FG -- K.Ichimoto and SOT Team SOT#17 2006.4.17-20

  2. 0. Descriptions of the SOT polarimeter Schematics of the SOT polarimeter Polarization modulator (PMU) OTA Collimator lens unit (CLU) HDM CTM-TM Pupil image Astigmatism collector lens (ACL) M2 M1 Mech. shutter NFI- Polarization analyzer Mask wheel Reimaging lens FG/NFI Tunable filter Non-polarizing beam splitter FG-CCD SP Slit scan mirror Slit SP- Polarization analyzer (polarizing beam splitter) SP-CCD left/right

  3. Modulation and sampling scheme The polarization modulator is a continuously rotating waveplate at the rate of 1rev./1.6sec. Retardation is optimized for equally modulating circular and linear polarization at 6302A and 5172A. Both SP and FG take multiple images in synchronous with PMU and appropriate demodulation is applied onboard to reduce the amount of telemetry data and to improve S/N. 16 frame continuous sampling SP takes 16 frames in every PMU revolution in both orthogonal states of polarization. FG has a variety of sampling scheme. In ‘shutter mode’, the mechanical shutter is used to take large area of CCD. In ‘shutterless mode’, continuous readout is performed for central area of CCD with masked outer parts of the CCD. Typical sampling schemes are as follow: • Shutter mode: • 8 exposures by 22.5deg step for IQUV • 4 exposures for IQUV • 2 exposures for IV • etc. (exposure time is flexible) • Shutterless mode: • 16 frames/rev. as SP for IQUV • 4 frames/half rev. for IV • 2 frames/half rev. for IV • etc. (accumulation number is flexible) Example of demodulation matrix for IQUV

  4. 1. Definition of polarimeter response matrix and its tolerance Onboard demodulation Polarization modulation S Ii S’ Modulated intensity on CCD Incident Stokes vector SOT product S’ = XS, X: SOT ‘polarimeter response matrix’ Incident Stokes vector is obtained by S” = X-1S’ ‘Polarization calibration’ is to determine the X for each SOT product. Calibration error : DS” = S” - S = { Xr-1X- E } S Statistical noise : dS” = Xr-1dS’ = Xr-1e where X : true matrix (unknown) Xr: matrix used in calibration

  5. Requirement on the calibration accuracy 1) for crosstalk among different elements of S (off diagonal of X) DS” < dS” { X - Xr} S =DX S < e 2) for scale error (diagonal of X and QUVI crosstalk) D(Q”/I” )< aQ/I Tolerance of X Solar-B, SOT e = 0.001 a = 0.05 Pl = 0.15 （max of Q,U） Pv = 0.2　（max of V）

  6. 2. Polarization calibration test method • Test configuration • Entire SOT is located under a heliostat in a clean room. • Sunlight fed by the heliostat • Sheet polarizers (linear, L/R circular) on OTA • Room T=20C, CLU T>25C Heliostat mask window (I,Q,U,V) Sheet polarizer FPP

  7. S/C +Y S/C +X Definition of SOT polarization coordinate -Q N -U -V +U -Q -U +U +V FPP +Q W +Q E -V +V S View from the top of SOT View towards the sun

  8. Configuration of sheet polarizer in SOT suntest 2004.8 / 2005.6 Created Stokes vectors HN38 0゜ Pl ~ 1 HNCP37R +Y 0゜ 45゜ HNCP37L (only for 2005.6) FPP +X 90゜ 135゜ View from top

  9. Test cases

  10. 3. Derivation of X matrix: (FG/NFI) Relation between FG products and incident Stokes vector Sk’ : polarimeter product sk : incident Stokes vector with I=1. k stands for polarizer config. 0,1,~ ,11 Incident Stokes vectors determined by sheet polarizers SOT products Fitting equation; normalized by I’kto eliminate the sky fluctuation # of unknowns:xij 15 = 15 (with x00 = 1) PlR, PlL, qR, qL (linear polarization and offset angle of RCP,LCP) are determined from average over the CCD and then fixed in fitting for each pixel assume PcR2 + PlR2 = 1, PcL2 + PlL2 = 1 # of equations : 3x12 = 36

  11. 4. Fitting results for polari. cal. data (an example) NFI shutterless: 630nm, CCD center Symbols: observed Lines: fitting I U Q V

  12. 5. SP X matrix Be presented by B.Lites

  13. 6. FG X matrices 6303, Shutter 2048x1024 (2x2sum, OBS_ID=3) Horizontal lines show the tolerance of each element. Mean X matrices for left and right halves of CCD left: theta= 3.648deg. 1.0000 0.2258 0.0304 0.0000 0.0043 0.5072 0.0723 0.0030 -0.0003 0.0571 -0.5029 0.0092 0.0022 -0.0268 -0.0059 -0.5249 right: theta= 3.555deg. 1.0000 0.2371 0.0362 0.0000 0.0048 0.5206 0.0725 0.0027 0.0002 0.0569 -0.5169 0.0106 0.0009 -0.0281 -0.0061 -0.5368

  14. 6302, Shutterless 80x1024 (2x2sum) All points of CCD plotted Dot lines are tolerance Rotation of Q-U frame between left and right halves of CCD caused by the delay of exposure. Cause a rotation of B azimuth by about 3 deg. Horizontal position Mean X matrices for left and right halves of CCD left: theta= -1.009deg. 1.0000 0.2184 0.0216 0.0178 -0.0001 0.5026 -0.0104 0.0033 -0.0002 -0.0250 -0.5029 0.0052 0.0046 -0.0216 -0.0048 -0.5260 right: theta= -3.857deg. 1.0000 0.2182 0.0216 0.0174 -0.0001 0.4970 -0.0602 0.0038 -0.0000 -0.0748 -0.4990 0.0049 0.0048 -0.0218 -0.0035 -0.5236 spxmat_0506p.pro

  15. Repeatability, shutterless 6302 2005/6/13 left: theta= -1.009deg. 1.0000 0.2184 0.0216 0.0178 -0.0001 0.5026 -0.0104 0.0033 -0.0002 -0.0250 -0.5029 0.0052 0.0046 -0.0216 -0.0048 -0.5260 right: theta= -3.857deg. 1.0000 0.2182 0.0216 0.0174 -0.0001 0.4970 -0.0602 0.0038 -0.0000 -0.0748 -0.4990 0.0049 0.0048 -0.0218 -0.0035 -0.5236 2005/6/14 left: theta= -1.285deg. 1.0000 0.2191 0.0193 0.0155 0.0002 0.5071 -0.0167 0.0032 0.0002 -0.0289 -0.5078 0.0049 0.0050 -0.0211 -0.0037 -0.5290 right: theta= -4.094deg. 1.0000 0.2207 0.0198 0.0151 0.0005 0.5002 -0.0661 0.0037 -0.0002 -0.0784 -0.5035 0.0043 0.0049 -0.0210 -0.0027 -0.5257 Difference 6/14 – 6/13 Left: dq = 0.276 0.0000 0.0007 -0.0023 -0.0023 0.0003 0.0045 -0.0063 -0.0001 0.0004 -0.0038 -0.0048 -0.0003 0.0004 0.0005 0.0011 -0.0030 right : dq = 0.237 0.0000 0.0025 -0.0018 -0.0023 0.0006 0.0032 -0.0059 -0.0001 -0.0001 -0.0036 -0.0045 -0.0006 0.0001 0.0008 0.0008 -0.0021 Repeatability is good enough compared with the tolerance matrix.

  16. 7. Summary of representative X matrices Delay between left and right CCD in PMU angle (deg.)

  17. Delay between left and right CCD in PMU angle (deg.)

  18. 8. Modeling of SOT polarization (for NFI) FG has a variety of observing sequence with different exposure, on-chip summing and polarization sampling scheme, and we do not have the experimental X matrix for all of them. To extend our knowledge of the X matrix of the tested cases, a simple SOT polarization model is created with which one can obtain the X matrix for arbitrary observing scheme. SSOT= D W T Sin , X =D W T D :demodulation matrix W(k,*) = (1,1,0,0) P(dl , fk ,Dt, dt) : polarization modulation matrix T : ‘telescope’ matrix dl: retardation of the waveplate fk : phase angles of PMU at each exposure Dt : exposure time dt : delay of exposure timing • Assumptions in the model: • Ideal PMU retarder and polarization analyzer, • Exposure length and mutual separation of exposure are as specified by the command, while a constant delay of exposure is incorporated, • Residual deviations of X from the theoretical matrix are attributed to the ‘telescope’ matrix.

  19. Example of DWT matrix: OBS_ID=3, FGIQUV (shutter mode) 8 exposures at fk = 12.25+22.5*[0,1,2,3,4,5,6,7] D T W Demodulation matrix Modulation matrix ‘Telescope’ matrix

  20. Least square fitting to the experimental X matrices Xexperiment Xfit = D W( fk, Dt, dt,dl ) Least square fitting  dt, dl T(l) = Xfit,-1Xex fk and Dt are specified for each data set Xex are averaged over the each CCD-left and right dl,dt,T(l) are determined for each data set, and then averaged over the wavelength or mdoes SOT polarization model is given by Standard deviation of the fitting residual DX = Xex(i) - Xmode is compared with the tolerance matrix.

  21. More about the ‘exposure’ in FG shutterless mode In shutterless mode of FG, each pixel experiences ‘smearing periods’ during the frame transfer. Geometrical sketch pixel position xp mask CCD center x=0 xp+ 1024 2048 xm CCD Start at CCD center: t0 Time sketch illuminated period time Dt1 Dt0 Dt3 Dt2 Dt2+Dt3 =1024t Dt = Dt1+ Dt2+Dt3 ‘exposure’ cycle (typ. =100ms) Start of exposure: ts End of exposure Start of transfer: te Dt1 : exposure at the pixel position Dt0, Dt2: smearing period Dt3 : transfer time under mask Dteff = Dt0+ Dt1+ Dt2: illuminated period

  22. Modification of X matrix due to smearing SOT product is summation of the contributions from three periods Dt0 , Dt1 , Dt2 SSOT= D [ W(Dt0) T Sin0 + W(Dt1) T Sin1+ W(Dt2) T Sin2 ] In polarization calibration test: Sin0 = Sin2 = Sin1 SSOT= D[ W(Dt0)+ W(Dt1)+ W(Dt2)] T Sin1  Xex = X(Dt0)+ X(Dt1)+ X(Dt2) In real observation: Sin0 = Sin2 = (I,0,0,0)t(assume that smear regions have mixed polarity to give Q,U,V =0) SSOT= (DI, 0, 0, 0)t + X(Dt1) Sin1 (assume T ~ 1) DI = I (Dt0+ Dt2) / (Dt0+ Dt1 + Dt2 ) -- bias intensity due to smearing X(Dt1) is what we need for polarization calibration for NFI/shutterless mode. - Xex depends on both mask size and pixel position on the CCD. - X(Dt1) is independent on the mask size nor pixel position. The SOT polarization model takes this point into account and can provide ether X(Dt1) or Xex.

  23. 9. Results of model fitting Average dl, dtleft,dtright Averaged retardation of the waveplate (dl) and exposure delay (dtleft,dtright) obtained by the model fitting are given below for each wavelength and for shuttered or shutterless modes.

  24. Exposure timing wrt PMU phase, tc: center of readout cycle Data points refer to tc, independant on mask nor pix.pos. ~10ms Shutterless mode Tolerance of exposure timing ~ 2ms

  25. SOT modulation profiles with obtained PMU retardance 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Q V U

  26. Fitting residual DX = Xobs-Xmodel Red elements are larger than tolerance T-matrix is sometimes unphysical. This may be due to incomplete modeling of the SOT polarization. SOT polarization model well reproduces the experimental X matrix except the first column.

  27. I’ = x00x10x20x30I V’x03x13x23x33Q U V 10. Other observing schemes 10-1. NFI IV observation (shutter mode) NFI can takes IV information with only 2 exposures centered at the PMU phases of +45 deg. (see figure below) . The exposure time is selectable. Shuttered IV (Obs_ID = 2) exposure = 100, 150, 200, 300, 400ms 2 intensities are given by. I+ = I + cQQ + cV V I- = I + cQQ-cV V where cQ :Q I crosstalk cV : Efficiency of V measurement In this case the X matrix is a 4x2 matrix. demodulation 1 1 -1 1 Dt The X matrices for this mode with different exposures were not measured with real SOT and the verification test was performed with FPP+PMU(backup) on 2006.1.22. For details, ‘polarization t-cal.ppt’

  28. Theoretical cQ, cV vs. exposure time 6302 solid: sensitivity to V, cV 6563 304ms 265ms dash: QI crosstalk, cQ 380ms 5250 5172 5986

  29. 11. Critical components – CLU – In the development of SOT, the polarization properties of all optical elements were verified by theoretical prediction and experiments. Critical components in polarizational point of view were identified as PMU, CLU and astigmatism corrector lens (ACL) since they are located in upstream of the optics and their thermal environment is not well controled as in the FPP. Special attention was paid on their opto-thermal characteristics. It was turned out that the PMU and ACL are stable enough against the possible temperature excursion in orbit, while the CLU is quite sensitive to temperature; especially in the cold case, the mechanical stress on the glasses induced from the metal housing cause a significant retardation, and this drove us to set the lowest ‘operational temperature range’ of CLU as 25C. Extensive tests was made by using the ‘Component Polarization Analyzer’ of HAO for the CLU flight model mounted in a thermal shroud.

  30. CLU Mueller matrix image at different temperatures (example) T=15C (from 20C) T=30C (from 40C) Rectangular shows the SOT field of view. Interval of contours indicates the tolerance of each Mueller matrix element.

  31. after 4th cold cycle after vibration after 2nd /3rd cold cycle after 1st cold cycle initial Hysteresis of (3,4) element (=linear retardation) of the CLU Mueller matrix against temperature torelance

  32. Summary of the CLU polarization-thermal properties : • The only significant polarization property of CLU is the linear retardation. • The CLU retardation can be regarded as uniform over the SOT field of view and constant against T if temperature is higher than 25C (=lower limit of operational temp.). • The experimental X matrices of SOT include the CLU retardation, but the CLU may have a small retardation offset after the launch vibration and the initial low-T cycle. • Signature of circular to linear crosstalk needs to be checked after launch using sunspots.

  33. Summary • Polarimeter response matrices (X) were obtained experimentally using entire SOT for representative products of NFI as functions of position in FOV. • The accuracy of measurements inferred from the repeatability meets the required accuracy of X except for the first column. • The X-matrices can be regarded as uniform over the field of view except the NFI shutterless mode, in which the left and right halves of CCD have a non negligible difference due to the relative delay of exposures. • The ‘SOT polarization model’ reproduces experimental X matrices of NFI with the required accuracy, and can be used to get the X matrices of other observing sequences for which the experimental X matrix was not obtained. IDL procedure ‘nfi_modelx’ is prepared (Appendix). • The first columns of X matrices will be determined more exactly after launch using the continuum of the sun light. • The SOT polarization characteristics is expected to be fairly stable in orbit, while the linear retardation of CLU might have a small offset after experiencing the launch environment. This will be checked in real sun data.

  34. IDL procedure to obtain NFI X X = nfi_modelx(wav, obs_id=obs_id, expo=expo) or X = nfi_modelx(wav, pmupos=pmupos, Dmat=Dmat, expo=expo, delay=delay, , $ Tmat=Tmat,,mask=mask, ix=ix) ; wav - wavelength, [nm] ; obs_id - if set, pmupos and Dmat are taken from fpp_obsid.pro ; expo - exposure, [ms] ; pmupos(*) - PMU angles at the center of exposure, [deg]. ; Dmat(*,4) - demodulation matrix ; delay(1 or 2) - delay of exposure for (left/right) CCD, [ms], if not set, use cal.data ; Tmat(4,4) - Telescope matrix, if not set, use cal.data, Tmat =1 for unit matrix ; mask - mask# for shutterless mode ; ix - pixel position from CCD center ; if mask and ix are set, return experimental X If ‘delay’ and ‘Tmat’ are not specified, experimental data are used, thus X is the most probable X(Dt1) for use of real sun data.

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