1. COSMO Large Coronagraph Preliminary Design Review
Birefringent Filter Design and Polarimetry Steven Tomczyk
National Center for Atmospheric Research
Boulder, Colorado – Nov 16, 2015

2. Birefringent Filter Design
Relevant documents:
COSMOLC-DE-7001 (Tunable Filter Design and Development)
COSMO TN 22 Birefringent Filter Crystal Requirements

3. Birefringent Filter Requirements
COSMO LC 1 degree FOV, 1.5m aperture
Sets system étendue at 1.39 m2 deg2
Conservation of étendue - 100mm filter needs 15° full FOV
Fabry-Perot won’t work over such steep angles
Spectrograph requires too many slit positions
Birefringent filter selected
Spectral resolution set by need to resolve Stokes V signature

4. Optimal Tunable Filter
Following Babcock (1953), S/N in magnetic measurement
S N ∝ λ V λ,w F λ,Δλ,d dλ λ I λ,w +B F λ,Δλ,d dλ 1/2
w = line width
Δλ = filter width
d = displacement
B = background
Optimal Filter
FeXIII nm
FWHM = 0.14 nm
d = 0.1 nm

5. Filter Resolution Requirement
Required resolution (dots) is about 8000 over the COSMO Filtergraph wavelength range

6. Wide-field Birefringent Filter
For a wide-field birefringent filter, the wavelength shift is given by (Title and Rosenberg, 1979):
Δλ λ =− 1 4 n o n e − n o n e sin 2 θ= 1 𝑅 ,
Ω=4π sin 2 θ 2 sr ,
E=A Ω,
E∙R= πA F , where F= 1 4 n o n e − n o n e
For COSMO we need E∙R ≥ 1.1∙104 m2deg2

7. Crystal Selection E∙R= πA F ≥ 1.1∙ 10 4 m 2 deg 2 Crystal no ne ne-no
Diameter (mm)
πA/F
Length (mm)
(m2deg2)
MgF2
1.384
1.396
0.012
1.12E-03
120
1.04E+05
605
LiNbO3
2.286
2.203
-0.086
1.80E-03
100
4.49E+04 84
SiO2 (quartz)
1.543
1.552
0.009
6.09E-04 50
3.33E+04
807
KDP
1.494
1.46
-0.034
2.61E-03 99
3.04E+04
214
TeO2
2.26
2.142
-0.118
2.70E-03
7.51E+03 62
BaB2O4
1.658
1.584
-0.073
4.25E-03
4.77E+03
YVO4
1.993
2.215
0.222
6.31E-03 38
1.85E+03 33
CaCO3 (calcite)
1.656
1.485
-0.171
1.05E-02 40
1.23E+03 42
TiO2 (rutile)
2.583
2.865
0.282
3.69E-03 25
1.37E+03 26

8. Birefringent Filter Design
Lithium Niobate (LN)
Thickest elements 22 mm
Super-achromatic waveplates (5 plastic elements)
Tilted wire grid polarizers
Electro-optically tuned

9. Birefringent Filter Design

10. Birefringent Filter Components
5 element, super-achromatic waveplate
Transmission of filter is limited by
polarizers - Meadowlark VL1
Predicted transmission nm
CoMP achieved 29%

11. Birefringent Filter Components
Need crystals with uniformity of birefringence
44 crystals tested, 0.5 to 25 mm thick, 75 – 100 mm diameter
Commercially available crystals are uniform enough (just)

12. Electro-optical Tuning
Work led by Shibu K. Mathew (USO)

13. Electro-optical Tuning
Single crystal shift, x2 for split element
Need +/- 9kV at 1074nm, +/- 3kV at 530nm

14. Electro-optical Tuning Speed
Tests limited by response of power supply
Potential for very fast tuning

15. Polarimetry
Noise scales inversely with polarimeter modulation efficiency (see del Toro Iniesta and Collados, 2000)
Will use efficient 2-element polymer polychromatic modulator
𝜎 𝐼,𝑄,𝑈,𝑉 = 𝜎 𝜀 𝐼,𝑄,𝑈,𝑉
𝜎= 𝑁

16. Polarimetry
Requirement: 1 G magnetic field in 900 s using FeXIII 1074 nm
In weak field limit
𝑉=−𝑘 𝐵 𝐿𝑂𝑆 𝜕𝐼 𝜕𝜆
𝑉 𝐼 0 𝑎𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒 =1.3⋅ 10 −4 𝐵 𝐿𝑂𝑆 (G)

17. Response matrix relates observed and actual Stokes vector
Polarimetry
Response matrix relates observed and actual Stokes vector
𝑋= 𝐼>𝐼 𝑄>𝐼 𝑈>𝐼 𝑉>𝐼 𝐼>𝑄 𝑄>𝑄 𝑈>𝑄 𝑉>𝑄 𝐼>𝑈 𝑄>𝑈 𝑈>𝑈 𝑉>𝑈 𝐼>𝑉 𝑄>𝑉 𝑈>𝑉 𝑉>𝑉
𝑆 𝑜𝑏𝑠 =𝑋 𝑆 𝑖𝑛 ,
∆𝑋= − 𝑎/ 𝑝 𝐿 𝑎/ 𝑝 𝐿 𝑎/ 𝑝 𝐶 𝜀 𝑎 𝜀/ 𝑝 𝐿 𝜀/ 𝑝 𝐶 𝜀 𝜀/ 𝑝 𝐿 𝑎 𝜀/ 𝑝 𝐶 𝜀 𝜀/ 𝑝 𝐿 𝜀/ 𝑝 𝐿 𝑎
Following Ichimoto et al., 2008, we need to calibrate the response matrix elements to an accuracy of
ε = 10-4 (to meet 1 G magnetic field error),
a = 0.05 (following Ichimoto et al.),
PL = maximum linear polarization = 0.1,
PC = maximum circular polarization = 10-3 (corresponding to 10 G).
∆𝑋= − − − − − − − −

18. Polarimetry COSMO LC needs 10-4 precision in V/I, not accuracy
V is anti-symmetric wrt line center, need amplitude to determine magnetic field (Lin, Kuhn, Coulter, 2004)
Can calibrate I > Q,U,V using data itself, look in continuum where polarization is absent (e.g. Lites and Ichimoto, 2013)
Adopted ∆𝑋= − − − − −

19. Calibration Insert calibration optics with known Mueller matrix
References:
Elmore, D.F., “A polarization calibration technique for the advanced stokes polarimeter”, 1990, NCAR Technical Note NCAR/TN-355+STR, NCAR, Boulder, Colorado.
Ichimoto, et al., “Polarization Calibration of the Solar Optical Telescope onboard Hinode”, 2008, Solar Phys. 249, 233.
Insert calibration optics with known Mueller matrix
Polarizer
Retarder
Polarizer + Retarder
Rotate them
𝑆 𝑜𝑏𝑠 =𝑋 𝑀 𝑐𝑎𝑙 𝑆 𝑖𝑛 ,

20. Calibration For COSMO LC, calibration optics cannot calibrate O1
But studies show O1 polarization should be very small
This will be verified