ATST Calibration

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ATST Calibration

• Paul Seagraves
• HAO/NCAR
• paul_at_ucar.edu

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THEORETICAL MODEL calculated inverse
vectors to trace inverse a b c d
e f 1 1 0 0 .5 (XT) 1 1 1 1 1 1
1 1 0 0 .5 g h i j k l 1 -1 0 0
1 -1 0 0 0 0 1 -1 0 0 m n
o p q r 0 0 1 0 0 0 1 -1 0
0 0 0 1 0 s t u v w x 0 0 -1 0
0 0 0 0 1 -1 0 0 -1 0
0 0 0 1
0 0 0 1 0 0 0 -1
0 0 0 -1
X Polarimeter theoretical modulation model gt
4x4 matrix.T Telescope theoretical model gt 4x4
matrix.(XT) Parenthesis indicates it is not
clear X T are separate.
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THEORETICAL MODELFor ATST, the author has done
a matrix trace model to obtain T. T
iscalculated as the average Mueller matrix over
the traces. Non normalincidence of matrix
traces on X have been ignored. X and 'vectors
to trace has not been used. Present
calculation of T indicates vector tracing through
(XT) would add little info.'vectors to trace'
are known ideal polarization pure
states(Q,-Q,U,-U,V,-V). So long as there is
no zero row, two pure statesmay be omitted
'vectors to trace' matrix would still have an
inverse.Unpolarized light, column vector
(1,0,0,0), can be substituted for onepure
state.For use as a calibration the theoretical
model depends on knowing or measuring all the
optical and geometry parameters.
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CALIBRATION OPTICS observed vectors
calibration optics vectors 1 1 1 1 1 1 ...
N (XT) Q Q U U V V ... G H I J
K L ... Q -Q 0 0 0 0 ...
M N O P Q R ... 0 0 U -U 0 0
... S T U V W X ... 0 0 0
0 V -V ...
delta,
(XT)(1,1) 1 mount angleFor ATST,
ILLUSTRATIVE PURPOSES ONLY, it is assumed
calibration opticscan be placed in front of the
telescope.(XT) Least squares fit for the 4x4
instrument matrix.N() Normalization operator,
divides to get 1's in the first row of the
observed vectors.
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CALIBRATION OPTICSNormalization N() is needed
to remove overall gain factors becausetransmitted
energy may vary with optics setting and through
observing period. Fixing the (1,1) element of
(XT) is required for normalization.Linear light
pure states (Q,-Q,U,-U) are produced by a
linear polarizer. Circular states V,-V are
produced by a waveplate after the linear
polarizer. V,-V actually are not pure states but
will depend on phase change 'delta of the
waveplate and thus depend on wavelength.
Rotation of 'mount angle error also varies
V,-V.Due to normalization N() there are 18
independent measurements in'observed vectors'.
17 parameters will fit by least squares15 in
(XT), delta, mount error. There is not enough
information if apure state is dropped.The
calibration depends on 'known' light sources
which has representationfor stokes states
(Q,-Q,U,-U,V,-V).
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SPECTRA CALIBRATION observed profiles
calculated profiles ...
(XT)A ...
... ...
... ...
... ...
(XT)A Least squares fit for 4x4 calibration
matrix. ((XT)A)(1,1) 1 for normalization.A Po
larization effects between known 'calculated
profiles' of well behaved solar features and the
instrument matrix (XT). A single column of
represents a 4xn matrix, 4 stokes components over
n points in wavelength.
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SPECTRA CALIBRATIONThis calibration depends on
having spectra where partial polarization states
Q,-Q,U,-U,V,-V are well represented that agree
well with spectra function over wavelength.
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Center single ray mueller matrixdirection
cosines 0.0000000 0.0000000
-1.0000000oxides nm 10.00
10.00reflectance 0.8162549 1.0000000
-0.0054650 0.0000000 0.0000000 -0.0054650
1.0000000 0.0000000 0.0000000 0.0000000
0.0000000 0.9990041 -0.0442824 0.0000000
0.0000000 0.0442824 0.9990041direction
cosines 0.0000000 0.0000000
-1.0000000oxides nm 10.00
10.00reflectance 0.8162502 1.0000000
-0.0053790 0.0000000 0.0000000 -0.0053830
0.9997643 -0.0000000 0.0000000 -0.0000000
0.0000000 0.9988257 -0.0436334 0.0000000
-0.0000000 0.0436008 0.9985923
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direction cosines 0.0000000 0.0000000
-1.0000000oxides nm 10.00
10.00reflectance 0.8162502 1.0000000
-0.0053790 0.0000000 0.0000000 -0.0053830
0.9997643 -0.0000000 0.0000000 -0.0000000
0.0000000 0.9988257 -0.0436334 0.0000000
-0.0000000 0.0436008 0.9985923direction
cosines 0.0000000 0.0007272
-0.9999997oxides nm 10.00
10.00reflectance 0.8162502 1.0000000
-0.0053786 -0.0000379 0.0000022 -0.0053828
0.9997600 0.0028321 0.0001705 -0.0000211
-0.0028218 0.9988216 -0.0436312 0.0000022
-0.0003071 0.0435979 0.9985924
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traces with y gt 1500mm blockeddirection
cosines 0.0000000 0.0000000
-1.0000000oxides nm 10.00
10.00reflectance 0.8162496 1.0000000
-0.0054397 0.0003396 0.0000000 -0.0054431
0.9997986 -0.0002473 -0.0027453 0.0003387
0.0001396 0.9987956 -0.0441206 0.0000000
0.0027528 0.0440927 0.9985962traces with y
oxide gradiant 10 to 20 nm.direction cosines
0.0000000 0.0000000 -1.0000000reflectance
0.8095532 1.0000000 -0.0054379 -0.0000015
-0.0000000 -0.0054420 0.9996864 0.0000696
0.0014783 -0.0000015 0.0000831 0.9984420
-0.0502565 -0.0000000 -0.0014828 0.0502190
0.9981308