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 polarimeterSchematics of the SOT polarimeter

Pupil image

HDM

Polarization modulator (PMU)

CTM-TM

OTA

M1M2

FG/NFI

SP

FG-CCD

SP-CCD left/right

SP- Polarization analyzer (polarizing beam splitter)

NFI- Polarization analyzer

Non-polarizing beam splitter

Collimator lens unit (CLU)

Tunable filter

Slit scan mirror

Mask wheelMech. shutter

Astigmatism collector lens (ACL)

Reimaging lens

Slit

3

Modulation and sampling schemeThe 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.

11111111

11111111

11111111

11111111

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:

Example of demodulation matrix for IQUV

16 frame continuous sampling

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)

4

1. Definition of polarimeter response matrix and its tolerance

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 : S” = S” - S = { Xr-1X- E } S

Statistical noise : S” = Xr-1S’ = Xr

-1

where X : true matrix (unknown)Xr : matrix used in calibration

Polarization modulation

Onboard demodulation

SOT product Incident Stokes vector

Modulated intensity on CCD

Ii SS’

ε

5

Requirement on the calibration accuracy

Solar-B, SOT = 0.001a = 0.05Pl = 0.15 （ max of Q,U ）Pv = 0.2 　（ max of V ）

0.0500.0070.0070.001

0.0050.0500.0070.001

0.0050.0070.0500.001

0.2500.3330.333

app

pap

ppa

papapa

ll

vl

vl

vll

//

//

//

///

XTolerance of X

1) for crosstalk among different elements of S (off diagonal of X)

S” < S” { X - Xr} S = X S <

2) for scale error (diagonal of X and QUVI crosstalk)

Q”/I” ) < a Q/I

6

Sheet polarizer

window

(I,Q,U,V)

mask

FPP

Heliostat

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 circul

ar) on OTA - Room T=20C, CLU T>25C

7

FPP

+Q

+U U

View from the top of SOT

Q

V

+V

View towards the sun

S/C +Y

S/C +X

W

N

S

E +Q

QU +U

V

+V

Definition of SOT polarization coordinate

8

RRlRRRlR

R

R

R

R

R

R

R

R

R

R

R

R

PsPc

V

c

s

V

s

c

V

c

s

V

s

c

2sin,2cos

1

,

1

,

1

,

1

135 90 45 0 RCP

FPP

0゜

45゜

90゜

135゜

HNCP37R

HN38

+Y

+X

View from top

0

0

1

,

0

0

1

,

0

0

1

,

0

0

1

135 90 45 0 LP

l

l

l

l

P

P

P

P

Created Stokes vectors

LLlLLLlL

L

L

L

L

L

L

L

L

L

L

L

L

PsPc

V

c

s

V

s

c

V

c

s

V

s

c

2sin,2cos

1

,

1

,

1

,

1

135 90 45 0 LCP

HNCP37L (only for 2005.6)

Configuration of sheet polarizer in SOT suntest 2004.8 / 2005.6

0゜

Pl ~ 1

9

Test cases

l 5172 5250 5896 6302 6563 dateFG shuttered IQUV (exp=90ms)

2048x1024 (2x2sum, OBS_ID = 3) - ○ ○ ○ ○ 2004.8.19/ 20512x1024 (2x2sum, OBS_ID = 3) (○ ) (○ ) (○ ) (○ ) (○ ) 2005.6.13 quality is poor (not used)

FG shutterless IQUV (exp=100ms)64x2048 (1x1sum, OBS_ID=33) - ○ ○ ○ ○ 2004.8.19/ 20 mask=8280x1024 (2x2sum) - ○ ○ ○ ○ 2004.8.19/ 20 mask=11272x1024 (2x2sum) ○ ○ ○ ○ ○ 2005.6.13/ 14 mask=112

SP224x1024 (1x1sum) △ 2004.8.19/ 20 SP was after thisｍｏｄｉｆｉｅｄ " ○ 2005.6.13/ 14

10

3. Derivation of X matrix: (FG/NFI)

k

k

k

kkkk

k

k

kk

kk

kk

v

u

q

vxuxqx

xxxx

xxxx

xxxx

v

u

q

IV

IU

IQ1

1'

'

'

'/'

'/'

'/'

302010

33231303

32221202

31211101

# of unknowns: xij 15 = 15 (with x00 = 1) PlR, PlL, R, L (linear polarization and offset angle of RCP,LCP) are

determined from average over the CCD and then fixed in fitting for each pixel assume PcR

2 + PlR2 = 1, PcL

2 + PlL2 = 1

# of equations : 3x12 = 36

k

k

kk

k

k

k

k

kkkk

v

u

q

xxxx

xxxx

xxxx

xxx

I

V

U

Q

I

I

11

'

'

'

'

'

33231303

32221202

31211101

302010

xsXSS

Sk’ : polarimeter productsk : incident Stokes vector with I=1.k stands for polarizer config. 0,1,~ ,11

Relation between FG products and incident Stokes vector

Fitting equation; normalized by I’k to eliminate the sky fluctuation

Incident Stokes vectors determined by sheet polarizersSOT products

11

4. Fitting results for polari. cal. data (an example)

NFI shutterless: 630nm, CCD center

Q

V

U

I

Symbols: observedLines: fitting

12

5. SP X matrix

Be presented by B.Lites

13

6. FG X matrices6303, Shutter 2048x1024 (2x2sum, OBS_ID=3)

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

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

Mean X matrices for left and right halves of CCD

Horizontal lines show the tolerance of each element.

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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

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

Horizontal position

All points of CCD plottedDot lines are tolerance

Mean X matrices for left and right halves of CCD

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.

6302, Shutterless 80x1024 (2x2sum)

spxmat_0506p.pro

15

0.0500.0070.0070.001

0.0050.0500.0070.001

0.0050.0070.0500.001

0.2500.3330.333

Left: d= 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

Repeatability, shutterless 6302

Difference 6/14 – 6/13

Repeatability is good enough compared with the tolerance matrix.

right : d= 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

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

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

2005/6/13

2005/6/14

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

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

16

7. Summary of representative X matricesrepresentative X- matrix (experiment, average for each CCD left and right)

FGSIQUV 2005.6.13 80x1024, (sum2x2)l

th_left= - 0.2410 th_right= - 3.1110 2.8701.0000 0.8824 0.0547 - 0.0319 1.0000 0.8804 0.0510 - 0.03240.0000 0.0729 0.0003 - 0.0001 0.0000 0.0714 - 0.0070 0.00010.0001 - 0.0015 - 0.0728 0.0003 0.0001 - 0.0088 - 0.0730 0.00030.0029 - 0.0111 - 0.0016 - 0.4016 0.0032 - 0.0114 - 0.0007 - 0.3998

6303 th_left= - 1.0020 th_right= - 3.8520 2.8501.0000 0.2185 0.0215 0.0178 1.0000 0.2182 0.0216 0.0174

- 0.0001 0.5026 - 0.0103 0.0033 - 0.0001 0.4970 - 0.0601 0.0038- 0.0002 - 0.0249 - 0.5029 0.0051 - 0.0001 - 0.0747 - 0.4990 0.00490.0046 - 0.0217 - 0.0047 - 0.5260 0.0048 - 0.0218 - 0.0034 - 0.5236

5896 th_left= - 1.8780 th_right= - 4.6920 2.8141.0000 0.5364 0.0748 - 0.0083 1.0000 0.5361 0.0745 - 0.0079

- 0.0008 0.2967 - 0.0153 0.0018 - 0.0007 0.2928 - 0.0449 0.0020- 0.0002 - 0.0237 - 0.2967 0.0039 0.0000 - 0.0520 - 0.2938 0.0036- 0.0071 - 0.0065 0.0055 0.6326 - 0.0070 - 0.0066 0.0056 0.6281

5250 th_left= - 2.3520 th_right= - 5.1660 2.8141.0000 0.0492 0.0058 - 0.0571 1.0000 0.0503 0.0063 - 0.05690.0012 0.6085 - 0.0449 0.0053 0.0011 0.5991 - 0.1037 0.0059

- 0.0015 - 0.0550 - 0.6058 0.0086 - 0.0016 - 0.1144 - 0.5972 0.0080- 0.0041 - 0.0142 0.0049 0.2660 - 0.0039 - 0.0141 0.0055 0.2638

5172 th_left= - 1.5740 th_right= - 4.4400 2.8661.0000 0.2992 0.0333 - 0.0436 1.0000 0.2863 0.0305 - 0.04360.0009 0.4546 - 0.0208 0.0046 - 0.0004 0.4472 - 0.0653 0.0037

- 0.0009 - 0.0288 - 0.4474 0.0068 - 0.0007 - 0.0739 - 0.4434 0.0061- 0.0084 - 0.0319 0.0134 0.5772 - 0.0077 - 0.0312 0.0151 0.5715

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

17

representative X- matrix (experiment, average for each CCD left and right)FGIQUV 2004.8.20 2048x1024, (sum2x2)

l th_left= 3.7050 th_right= 3.9890 - 0.284

1.0000 0.9005 0.0887 0.0000 1.0000 0.9132 0.0825 0.00000.0018 0.0697 0.0104 - 0.0016 0.0019 0.0694 0.0112 - 0.0015

- 0.0015 0.0076 - 0.0689 0.0039 - 0.0003 0.0086 - 0.0719 0.00240.0014 - 0.0109 - 0.0059 - 0.4137 0.0016 - 0.0125 - 0.0070 - 0.4208

6303 th_left= 3.6480 th_right= 3.5550 0.0931.0000 0.2258 0.0304 0.0000 1.0000 0.2371 0.0362 0.00000.0043 0.5072 0.0723 0.0030 0.0048 0.5206 0.0725 0.0027

- 0.0003 0.0571 - 0.5029 0.0092 0.0002 0.0569 - 0.5169 0.01060.0022 - 0.0268 - 0.0059 - 0.5249 0.0009 - 0.0281 - 0.0061 - 0.5368

5896 th_left= 2.4410 th_right= 2.5680 - 0.1271.0000 0.5460 0.0724 0.0000 1.0000 0.5605 0.0800 0.00000.0027 0.3024 0.0322 0.0002 0.0030 0.3053 0.0342 0.00000.0034 0.0195 - 0.3025 0.0035 0.0031 0.0209 - 0.3079 0.0035

- 0.0081 - 0.0125 0.0063 0.6447 - 0.0082 - 0.0191 0.0068 0.6526

5250 th_left= 2.4540 th_right= 2.4350 0.0191.0000 0.0508 0.0023 0.0000 1.0000 0.0609 0.0087 0.00000.0102 0.6151 0.0627 - 0.0032 0.0113 0.6299 0.0644 - 0.00470.0082 0.0440 - 0.6299 0.0012 0.0080 0.0443 - 0.6489 0.0028

- 0.0069 - 0.0101 - 0.0012 0.2862 - 0.0071 - 0.0093 - 0.0016 0.2945

SP 2005.6.136303 th_left= 3.4670 th_right= 2.8500 0.617

1.0000 - 0.2232 - 0.0142 - 0.0063 1.0000 0.2077 0.0199 - 0.00790.0028 - 0.4819 - 0.0642 0.0007 - 0.0039 0.4886 0.0551 0.00050.0022 - 0.0529 0.4814 - 0.0030 - 0.0021 0.0427 - 0.4918 0.0034

- 0.0034 - 0.0026 0.0043 0.5249 0.0035 0.0013 - 0.0044 - 0.5304

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.

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.

SSOT = D W T Sin , X = D W T

D : demodulation matrix

W(k,*) = (1,1,0,0) P(l, k , t, dt) : polarization modulation matrix

T : ‘telescope’ matrix l: retardation of the waveplate

k : phase angles of PMU at each exposuret : exposure timedt : delay of exposure timing

19

inV

U

Q

I

tttt

tttt

tttt

tttt

w

w

w

w

w

w

w

w

w

w

w

wwwww

wwww

wwww

wwww

wwww

V

U

Q

I

33323130

23222120

13121110

03020100

73

63

53

72

62

52

71

61

51

70

60

50

43424140

33323130

23222120

13121110

03020100

SOT11111111

11111111

11111111

11111111

Example of DWT matrix: OBS_ID=3, FGIQUV (shutter mode) 8 exposures at k = 12.25+22.5*[0,1,2,3,4,5,6,7]

DW TDemodulation matrix

Modulation matrix ‘Telescope’ matrix

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Least square fitting to the experimental X matricesXexperiment Xfit = D W( k, t, dt, l) Least square fitting dt, l

T (l) = Xfit,-1

Xex

Wavelength 6302 5250, ….

mode shutterless shuttered

Data set Data-1 Data-2 …. Data-1 Data-2,,, ….

Xex

left

Xex

right

Xex

left

Xex

right

Xex

left

Xex

right

Xex

left

Xex

right

Xex

Fitting parameters

l l …. l l ….

dt dt dt dt …. dt dt dt dt ….

T T T T …. T T T T ….

Average for SOT model

l

dt_left, dt_right dt

T

k and t are specified for each data setXex are averaged over the each CCD-left and right

Standard deviation of the fitting residual X = Xex(i) Xmode is compared with the tolerance matrix.

ll TWDX ),,,(model dttk SOT polarization model is given by

l,dt, T(l) are determined for each data set, and then averaged over the wavelength or mdoes

21

More about the ‘exposure’ in FG shutterless mode

xp+ 1024

mask

Geometrical sketch

In shutterless mode of FG, each pixel experiences ‘smearing periods’ during the frame transfer.

xm

t0 t2

t = t1+ t2+t3

‘exposure’ cycle (typ. =100ms)

time

Time sketch illuminated period

t3

Start of exposure: ts

Start at CCD center: t0

End of exposureStart of transfer: te

t2+t3

= 1024

2048

t1

CCD

CCD center x=0

pixel position xp

t1 : exposure at the pixel positiont0, t2: smearing periodt3 : transfer time under maskteff = t0 + t1 + t2 : illuminated period

22

In polarization calibration test:

Sin0 = Sin2 = Sin1

SSOT = D [ W(t0) + W(t1) + W(t2)] T Sin1

Xex = X(t0) + X(t1) + X(t2)

In real observation:

Sin0 = Sin2 = (I,0,0,0)t (assume that smear regions have mixed polarity to give Q,U,V =0)

SSOT = (I, 0, 0, 0)t + X(t1) Sin1 (assume T ~ 1)

I = I (t0 + t2) / (t0 + t1 + t2 ) -- bias intensity due to smearing

X(t1) is what we need for polarization calibration for NFI/shutterless mode.

- Xex depends on both mask size and pixel position on the CCD.

- X(t1) is independent on the mask size nor pixel position.

The SOT polarization model takes this point into account and can provide ethe

r X(t1) or Xex.

SOT product is summation of the contributions from three periods t0 , t1 , t2

SSOT = D [ W(t0) T Sin0 + W(t1) T Sin1 + W(t2) T Sin2 ]

Modification of X matrix due to smearing

23

9. Results of model fitting

Average l, dtleft, dtright

Wavelength (nm)

Retardation

(wave)

Modulation amplitude

(Diagonal element of X)

Time delay of tc (ms)

shutterless shuttered

design measured QU V left right left right

517.3 6.650 6.6822 0.45 0.58 -0.24 6.16 - -

525.0 6.558 6.5720 0.61 0.27 0.80 7.09 -5.52 -5.55

589.6 5.816 5.7624 0.30 0.63 0.28 6.63 -5.47 -6.05

630.2 5.350 5.3442 0.50 0.53 -1.47 4.93 -7.99 -7.52

656.3 5.050 5.1095 0.07 0.40 -4.23 3.02 -9.87 -9.35

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

24

Data points refer to t

c, independant on mask nor pix.pos.

Exposure timing wrt PMU phase, tc: center of readout cycle

~10msShutterless mode

Tolerance of exposure timing ~ 2ms

25

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Q

U

V

SOT modulation profiles with obtained PMU retardance

Wavelength (nm)

Retardation (wave)

517.3 6.682

525.0 6.572

589.6 5.762

630.2 5.344

656.3 5.110

26

Red elements are larger than toleranceT-matrix is sometimes unphysical. This may be due to incomplete modeling of the SOT polarization.

X = Xobs Xmodel

SOT polarization model well reproduces the experimental X matrix except the first column.

Fitting residualaverage T matrix STD deviation of fitting residual

0.9893 - 0.0420 - 0.0491 0.0018 0.0000 0.0117 0.0296 0.0113- 0.0121 0.9541 0.0190 0.0072 0.0006 0.0025 0.0005 0.0009- 0.0052 0.0088 0.9764 0.0205 0.0010 0.0011 0.0015 0.0013- 0.0049 - 0.0285 - 0.0135 1.0070 0.0008 0.0010 0.0019 0.0067

6303 0.9976 0.0101 0.0276 0.0031 0.0000 0.0069 0.0087 0.00620.0108 0.9990 0.0145 - 0.0025 0.0028 0.0080 0.0022 0.00360.0030 0.0131 0.9983 - 0.0157 0.0012 0.0021 0.0079 0.0017

- 0.0050 0.0437 0.0099 0.9763 0.0015 0.0020 0.0010 0.0086

5896 0.9951 0.0008 0.0730 - 0.0006 0.0000 0.0075 0.0107 0.00280.0091 0.9970 0.0144 - 0.0010 0.0018 0.0046 0.0018 0.00130.0013 0.0147 1.0021 - 0.0143 0.0018 0.0016 0.0049 0.0019

- 0.0099 - 0.0178 0.0111 0.9927 0.0010 0.0031 0.0009 0.0103

5250 0.9994 0.0061 0.0141 - 0.0082 0.0000 0.0040 0.0148 0.01990.0113 0.9996 0.0131 0.0011 0.0032 0.0083 0.0046 0.00270.0030 0.0136 1.0031 - 0.0169 0.0043 0.0033 0.0137 0.0042

- 0.0169 - 0.0459 0.0025 0.9931 0.0011 0.0015 0.0020 0.0074

5172 0.9998 0.0007 - 0.0296 - 0.0458 0.0000 0.0064 0.0014 0.0000- 0.0007 1.0003 0.0077 - 0.0077 0.0006 0.0011 0.0004 0.0007- 0.0018 0.0093 0.9863 0.0149 0.0002 0.0004 0.0002 0.0002- 0.0139 0.0543 - 0.0246 0.9901 0.0003 0.0003 0.0009 0.0021

27

10. Other observing schemes10-1. NFI IV observation (shutter mode)

Shuttered IV (Obs_ID = 2)exposure = 100, 150, 200, 300, 400ms

demodulation 1 1 -1 1

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.

t

2 intensities are given by. I+ = I + cQQ + cV V I = I + cQQ cV Vwhere cQ : Q I crosstalk cV : Efficiency of V measurement

I’ = x00 x10 x20 x30 I

V’ x03 x13 x23 x33 Q

U V

In this case the X matrix is a 4x2 matrix.

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

dash: QI crosstalk, cQ

5986

5172

5250

6563

6302

265ms 304ms

380ms

Theoretical cQ, cV vs. exposure time

solid: sensitivity to V, cV

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

T=15C (from 20C) T=30C (from 40C)

CLU Mueller matrix image at different temperatures (example)

Rectangular shows the SOT field of view.Interval of contours indicates the tolerance of each Mueller matrix element.

31

Hysteresis of (3,4) element (=linear retardation) of the CLU Mueller matrix against temperature

after vibration after 2nd /3rd cold cycle after 1st cold cycle initial

after 4th cold cycle

torelance

32

- 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.

Can CLU polarization be

regarded as … T [C] 14 16 18 20 22 24 26 28 30 32 34 36 38 40

negligible? No Mar

uniform in SOT FOV? No Yes

constant with T? No Mar Yes

single value function of T? No Yes

stable against T-cycle?

10C<T<40C Yes

-15C<T No Mar Yes

stable against vibration? No Mar Yes

answers

Summary of the CLU polarization-thermal properties :

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Summary- Polarimeter response matrices (X) were obtained experimentally using entir

e 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.

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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

IDL procedure to obtain NFI X

If ‘delay’ and ‘Tmat’ are not specified, experimental data are used, thusX is the most probable X(t1) for use of real sun data.