Polarization Calibration of the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO)

J. Schou 0 1 2 3 J.M. Borrero 0 1 2 3 A.A. Norton 0 1 2 3 S. Tomczyk 0 1 2 3 D. Elmore 0 1 2 3 G.L. Card 0 1 2 3 G.L. Card e-mail: 0 1 2 3 0 Present address: J.M. Borrero Kiepenheuer-Institut fr Sonnenphysik , Schneckstr. 6, 79104 Freiburg, Germany 1 J. Schou ( ) W.W. Hansen Experimental Physics Laboratory, Stanford University , Stanford, CA 94305-4085, USA 2 D. Elmore National Solar Observatory/Sacramento Peak , 3010 Coronal Loop, Sunspot, NM 88349, USA 3 A.A. Norton James Cook University, School of Engineering & Physical Sciences , Townsville, QLD 4810, Australia As part of the overall ground-based calibration of the Helioseismic and Magnetic Imager (HMI) instrument an extensive set of polarimetric calibrations were performed. This paper describes the polarimetric design of the instrument, the test setup, the polarimetric model, the tests performed, and some results. It is demonstrated that HMI achieves an accuracy of 1% or better on the crosstalks between Q, U , and V and that our model can reproduce the intensities in our calibration sequences to about 0.4%. The amount of depolarization is negligible when the instrument is operated as intended which, combined with the flexibility of the polarimeter design, means that the polarimetric efficiency is excellent. 1. Introduction Precise polarimetry requires the calibration of the polarimeter and associated telescope. Polarimeter calibration is typically performed by measuring the response of the polarimeter to known polarization states created by calibration optics placed at the output of the telescope (Skumanich et al., 1997; Beck et al., 2005). Telescope polarization is measured by placing polarizers over the entrance aperture of the telescope (Beck et al., 2005; Selbing, 2005) or by using the symmetry and anti-symmetry expected, or more precisely, not expected, in spectral Stokes profiles in Zeeman-sensitive lines (Collados, 2003; Kuhn et al., 1994). In-flight calibration optics were avoided on the Helioseismic and Magnetic Imager (HMI) instrument, as they were on Hinode, due to the risk of a mechanical failure leaving a calibration optic in the beam and also for complexity, mass, and power considerations. Absence of calibration optics limits the types of calibrations that can be performed after the instrument has been placed into operation and places particular importance on ensuring that groundbased calibrations are comprehensive and consider the range of possible environmental and instrumental drifts. As with the Hinode ground-based calibration (Ichimoto et al., 2008), the HMI polarimeter and telescope are calibrated together by placing calibration optics in front of the telescope and treating the entire optical path as the polarimeter. The HMI instrument differs from most other instruments by having redundant polarization selectors (see Section 2.3). This was done to improve the reliability but has the consequence that it is necessary to derive a calibration valid for all settings of the polarization selectors rather than only for the expected combinations. The design of observing sequences is discussed by Borrero et al. (2007). As a matter of convention, the angles in the system are measured counterclockwise from horizontal as viewed from behind the instrument toward the Sun, with horizontal being the plane in which the light travels from the window through the filter system, i.e. the plane at which the cut in Figure 1 is made (see Sections 2 and 5.1.1). Horizontal polarization is I + Q, while I + U corresponds to polarization at a 45 degree counterclockwise angle from horizontal, again as seen from the instrument. The remainder of this section contains a brief description of the requirements of the instrument. Sections 2 and 3 contain descriptions of the instrument with an emphasis on the polarimetric aspects and the test setup, respectively. Section 4 contains a description of the polarimetric model used to describe the instrument and test equipment. Section 5 contains descriptions of the various tests and the analysis, while Section 6 describes the main results obtained. Section 7 describes how the results obtained will be used to calibrate the instrument, the accuracy achieved, and the plans for on-orbit calibrations. Section 8 presents the conclusion. In the appendices, details of the polarimetric models of different types of optical elements are given and the sequences run are described. 1.1. Requirements HMI measures a linear combination LHMI of the solar Stokes vector: LHMI = OISun, where O is the modulation matrix. In order to demodulate and obtain the Stokes vector, the demodulation matrix [D] must be known and applied: IHMI = DLHMI = DOISun. In reality there are systematic errors and the error matrix E = DOtrue I, where Otrue is the actual modulation matrix and I the identity matrix, will not be identically zero. To derive a requirement for maximum allowable elements in E , it may be noted that the requirement on the noise in Q, U , and V is 0.3% of I in ten minutes and that systematic errors of less than 0.1% of I on Q, U , and V will thus only result in a marginal increase in the overall error. With typical values of Q/I , U/I , and V /I of around 0.1, it thus follows that the cross terms between Q, U , and V of less than 0.01 are desirable. From I to Q, U , and V values less than 0.001 are needed. The terms into I are less critical as they more or less correspond to a flat-field error and a total contribution of 0.01 should be adequate. This results in a requirement that the absolute values of E should be less than 0.01 Emax = 00..000011 To be able to construct left- and right-circular polarization [LCP and RCP] from a single camera and to keep a 50-second or better overall cadence for the Doppler and Line-of-Sight (LOS) field, a requirement was imposed to be able to derive V with less than 5% leakage from each of Q and U, across the field of view using only the motor positions available (see Sections 2.3 and 7.2.4). Some of the measurements required to finally verify some of these requirements are deferred to on-orbit operations. This is discussed in Section 7.3.1. How errors relate to magnetic-field properties is discussed by Norton et al. (2006). 2. Instrument Description The overall layout of the instrument is described by Schou et al. (2010). The parts of the instrument relevant to the polarimetry are shown in Figure 1. In order, the light passes through a front window, the primary lens, the secondary lens, a focus block (or calibration lens), three polarization-selector waveplates (PS1, PS2, and PS3), an Image Stabilization System [ISS] fold mirror, another focus block (or calibration lens), and a polarizing beamsplitter, all of which are described below. Following these elements are a Lyot filter, two Michelson interferometers, and a beamsplitter dividing the light to a pair of shutters and cameras (front and side) for higher cadence and redundancy. It may be (...truncated)