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

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

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

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 1074.7nm FWHM = 0.14 nm d = 0.1 nm

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

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 2 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 2 n e − n o n e For COSMO we need E∙R ≥ 1.1∙104 m2deg2

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

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

Birefringent Filter Design

Birefringent Filter Components 5 element, super-achromatic waveplate Transmission of filter is limited by polarizers - Meadowlark VL1 Predicted transmission 27% @ 1075 nm CoMP achieved 29%

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)

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

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

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

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

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)

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= − 0.50 0.50 50.0 10 −4 0.05 10 −3 0.10 10 −4 10 −3 0.05 0.10 10 −4 10 −3 10 −3 0.05

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= − 0.50 0.50 50.0 10 −3 0.05 10 −3 0.10 10 −3 10 −3 0.05 0.10 0.01 0.01 0.01 0.05

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 ,

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