1. ViSP Polarimetry David Elmore HAO/NCAR Elmore@ucar.edu

2. August 11-13, 2004ViSP Polarimetry 2 Polarization Measurement The measured Stokes vector is the product of the polarimeter response matrix and telescope matrix acting upon the input Stokes vector from the Sun. To achieve the required accuracy, the uncertainty in XT  must be less than some value, but not all elements need to be less than the polarimetric accuracy requirement.

3. August 11-13, 2004ViSP Polarimetry 3 Requirement Matrix # Uncertainty in a measured normalized Stokes parameter is due uncertainty in gain, , and uncertainty in cross talk among Stokes parameters, . For the i th Stokes parameter  P i =  P i +  P j≠i. For cross talk among the polarization parameters the uncertainty in the measurement of the i th parameter due to the j th Stokes parameter,  P j≠i must be less than the polarimeteric accuracy requirement,  For cross talk into I,  P j≠1 =  P j≠1.  from Kioshi Ichimoto NAOJ

4. August 11-13, 2004ViSP Polarimetry 4 Requirement Matrix Combine the four perterbation equations into a matrix and scale the cross talk elements by typical polarization signals Where p l and p v are ‘typical’ normalized solar polarization signals, p I = 1

5. August 11-13, 2004ViSP Polarimetry 5 Requirement Matrix For ATST we have no gain requirement, but 1% is typical, therefore  = 0.01 The polarization accuracy requirement  = 5 x 10 -4 From experience with ASP, ‘typical’ values for solar polarization are, p l = p v = 0.1. Substitution into the requirement matrix gives The requirement matrix gives the accuracy to which we need to know [XT].

6. August 11-13, 2004ViSP Polarimetry 6 Measurement of XT Use calibration optics for both X & T (ASP at DST) –Calibration polarizers between polarimeter and telescope for X (In the GOS for ATST) –Calibration polarizer over the telescope for T Calibrate X, Model T –Calibration polarizers between polarimeter and telescope for X –Create a two mirror telescope model and use some external measure of unknowns in model such as of the complex refractive index of the mirror coating

7. August 11-13, 2004ViSP Polarimetry 7 Measurement of XT Calibrate X, determine T using solar spectra –Calibration polarizers between polarimeter and telescope for X –Create a model T and use solar spectra to fit the unknows factors in the model Determine X and T from solar spectra –Create a model of XT and use solar spectra to fit the unknown factors in the model Use different techniques for different [XT] matrix elements

8. August 11-13, 2004ViSP Polarimetry 8 Cross talk into Intensity Use flat field for 1,1. For remainder of first row, a simple model of XT will suffice

9. August 11-13, 2004ViSP Polarimetry 9 Cross talk from I to Q, U, and V Use solar continuum polarization (Standard operating procedure for ASP)

10. August 11-13, 2004ViSP Polarimetry 10 Scale and phase Calibration polarizers between X and T. The effect of T is small so a simple model will suffice.

11. August 11-13, 2004ViSP Polarimetry 11 Cross talk between U and V Use an accurate model of the telescope supported by external refractive index data or use solar spectra

12. August 11-13, 2004ViSP Polarimetry 12 pau