5.3 Polarimetry

5.3.1 Absolute Calibration

ACS contains a set of six filters that are sensitive to linear polarization; there are three visible polarizer filters with their polarization directions set at nominal 60° angles to each other, and three UV polarizer filters arranged in a similar manner. These filters are typically used in combination with a spectral filter which largely defines the spectral bandpass. In most cases observers will obtain images of the target in each of the three filters. The initial calibration steps for polarization data are identical to that for data taken in any other filter—the data are bias-corrected, dark-subtracted, and flat-fielded in the normal manner. The polarization calibration itself is accomplished by combining the set of images (or the resulting counts measured on the images) in the three filter rotations to produce a set of I, Q, and U images, or equivalently, a set of images giving the total intensity, fractional polarization, and polarization position angle.

ACS/WFC polarization data are taken with a 2048 x 2048 subarray. Post-SM4 WFC subarray observations are not de-striped by default, and thus are also not corrected for CTE loss by the data pipeline for storage in MAST. Users wishing to work on de-striped, CTE-corrected data will need to set the PCTECORR flag to "PERFORM" in the primary header, update the PCTETAB keyword to the correct reference file, and run acs_destripe_plus from the acstools Python package. See the subarray data processing example notebook for assistance.

5.3.2 Instrumental Issues

The design of ACS is far from ideal for polarimetry. Both the HRC and WFC optical chains contain three tilted mirrors and utilize tilted CCD detectors. These tilted components will produce significant polarization effects within the instrument that must be calibrated out for accurate results. There are two primary effects in the tilted components—diattenuation and phase retardance. Diattenuation refers to the fact that a tilted component will likely have different reflectivities (or transmissions) for light which is polarized parallel and perpendicular to the plane of the tilt. This can be an important source of instrumental polarization, and can also alter the position angle of the polarization E-vector. The second effect, phase retardance, will tend to convert incident linear polarized light into elliptically polarized light. These effects will have complex dependencies on position angle of the polarization E-vector, and hence will be difficult to fully calibrate. Additional discussion of these effects can be found in WFPC2 ISR 1997-11, ACS ISR 2004-10, and ACS ISR 2007-10.

The instrumental polarization, defined as the instrument's response to an unpolarized target, provides a simple measure of some of these effects. Figure 5.5 shows the instrumental polarization derived for the HRC through on-orbit observations of unpolarized stars (HST programs 9586 and 9661). The instrumental polarization is approximately 5% at the red end of the spectrum, but rises in the UV to about 14% at the shortest wavelengths. Also shown is a rough model for the effects of the M3 mirror together with a very crude model of the CCD. The mirror is aluminum with a 606 Å thick overcoat of Magnesium Fluoride and has an incidence angle of 47°. Since details of the CCD are proprietary, it has been simply modeled as Silicon at an incidence angle of 31°; no doubt this is a serious over-simplification. Figure 5.6 shows the same plot for the WFC, which has an instrumental polarization around 2%. Here the IM3 mirror is a proprietary Denton enhanced Silver Coating with an incidence angle of 49°, and the CCD has an incidence angle of 20°. While the lower instrumental polarization of the WFC seems attractive, users are cautioned that the phase retardance effects are not known for the Denton coating, and have some potential to cause serious problems—if sufficiently large, the retardance could produce a large component of elliptical polarization which will be difficult to analyze with the linear polarizers downstream.

Figure 5.5:Instrumental Polarization for the HRC




Figure 5.6: Instrumental Polarization for the WFC


The ACS polarizer filters were characterized prior to installation in ACS by Leviton and the results as summarized in Figure 6.1 of the ACS Instrument Handbook. The cross-polarized transmissions are essentially zero for the POLV set, but are significant in the UV (5% to 10%) and far-red (20%) for the POLUV set.

One further issue for polarizer data is added geometric distortion. The polarizers contain a weak lens which corrects the optical focus for the presence of two filters in the light path. The lens causes a large scale distortion which appears to be well-corrected by the drizzle software. There is also, however, a weak (±0.3 pixel) small scale distortion in the images caused by slight ripples in the polarizing material. There is presently no correction available for this. There is also the possibility of polarimetric field dependences; while there has been study of intensity flats for the polarizers, the polarization field dependencies are not known.

5.3.3 Flats

Flat fields for the ACS polarizers were obtained in the laboratory and corrected for low frequency variations using the in-flight L-flat corrections which were derived for the standard (non-polarizer) filters. The pivot wavelength of the combined optical components is typically within 1% when the standard filters are used in combination with the polarizers instead of with the clear filters. To assess the accuracy of this approximation, in-flight observations of the bright Earth using the F435W+POLUV filters were compared with the F475W+POLV filters with the corrected laboratory flats. The HRC Earth flats agreed with the corrected lab flats to better than 1%, where the largest deviations occurred near the edges of the detector.

5.3.4 Polarization Calibration

An extensive series of on-orbit polarization calibration observations were carried out in Cycles 11 and 12 (programs 9586, 9661, and 10055). These included observations of unpolarized and polarized standard stars, the star cluster 47 Tuc, and an extended reflection nebula. Additional observations of polarized standards were taken over a wide and well-sampled range of HST roll angles to help quantify the angular dependences which are expected as the wavefront interacts with the diattenuation and phase retardation in the mirrors and CCD.

Preliminary calibrations, based largely on data in programs 9586 and 9661, are available for use by polarization observers. The number of polarimetric observations obtained with ACS is very small compared to other modes. As a result of this, the polarimetric mode has not been calibrated as precisely as other modes because of limited resources. For details, please see Cracraft & Sparks 2007 (ACS ISR 2007-10).

The ACS Team is currently working to improve the calibration of the polarizers using data from two programs (13964 and 14407). These proposals follow up earlier polarimetry calibration programs. Observations will be taken of the polarized star,Vela1-81 (GSC 08169-01120), and the unpolarized source G191B2B (EGGR-247). The stars will be observed through the F435W, F475W, F606W, F658N, F660N, and F775W filters with their respective polarizers. Each of the filter/polarizer combinations will be used at three different roll angles, in order to better quantify the instrumental linear polarization (such as from mirrors in the camera), and errors in the polarization angles of the filters. The F606W observations were done at a single roll angle as a sanity check of earlier observations. Updates will be posted on the ACS website.

The strategy was to create calibrations based upon the small amount of data that have been analyzed. This calibration can be applied to either aperture photometry results, or to the images themselves (i.e., for an extended target). The calibration process began with the polarization "zeropoint" using corrections which were derived from observations of unpolarized standard stars.

An update to the acstools Python package in December 2020 adds the polarization_tools module that provides conveniences for the following equations and calibration coefficients. Astropy table versions of the efficiency corrections (Table 5.6) and cross-polarization leak terms (Table 5.7) are included are included for convenience. An example notebook demonstrating the basic functionality of the polarization_tools module is available.


Efficiency corrections C(\mathrm{CCD}, \mathrm{POLnXX}, \mathrm{spectral\ filter}, n) were applied to the observed count rate robs in each of the three polarizers (POLnUV or POLnV, where n = 0, 60, 120). These corrections are tabulated in Table 5.6, and have been scaled such that Stokes I will approximate the count rate seen with no polarizing filter.

r_n = C(\mathrm{CCD}, \mathrm{POLnXX}, \mathrm{spectral\ filter}, n) r_{\mathrm{obs}, n}


Next, an "instrumental" Stokes vector is computed for the target.

I = \dfrac{2}{3}\left(r_0 + r_{60} + r_{120}\right)\\ Q = \dfrac{2}{3}\left(2r_0 - r_{60} - r_{120}\right)\\ U = \dfrac{2}{\sqrt{3}}\left(r_{60} - r_{120}\right)


Next, the fractional polarization of the target is computed. Also included is a factor which corrects for cross-polarization leakage in the polarizing filters (see Table 5.7 for the average correction factor per filter for a spectrum flat in wavelength).

P = \dfrac{\sqrt{Q^2 + U2}}{I} \times \left[\dfrac{T_{\mathrm{par}} + T_{\mathrm{perp}}}{T_{\mathrm{par}} - T_{\mathrm{perp}}}\right]

 
Finally, the position angle on the sky of the polarization E-vector is computed. The parameter PAV3 is the roll angle of the HST spacecraft, and is called PA_V3 in the data headers. The parameter \chi contains information about the camera geometry which is derived from the design specifications; for HRC, \chi = –69.4°, and for the WFC, \chi  = –38.2°. Note that the arc tangent function must be properly defined; here, the result is defined as positive in quadrants I and II, and negative in III and IV.

\theta = \dfrac{1}{2}\tan^{-1}\left(\dfrac{U}{Q}\right)+\mathrm{PAV3} + \chi

 
For example, a target that gives 65192, 71686, and 66296 counts per second in the HRC with F606W and POL0V, POL60V, and POL120V, respectively, is found to be 5.9% polarized at PA = 96.9°.

The full instrumental effects and the above calibration have been modeled together in an effort to determine the impacts of the remaining uncalibrated systematic errors. These will cause the fractional polarizations to be uncertain at the one-part-in-ten level (e.g., a 20% polarization has an uncertainty of 2%) for highly polarized sources; and at about the 1% level for weakly polarized targets. The position angles will have an uncertainty of about 3°. (This is in addition to uncertainties which arise from photon statistics in the observer's data.) This calibration has been checked against polarized standard stars (~5% polarized) and found it to be reliable within the stated errors. Better accuracy will require improved models for the mirror and detector properties as well as additional on-orbit data. No calibration has been provided for F220W, F250W, or F814W, as they are believed to be too unreliable at this time. There is also some evidence of a polarization pathology in the F625W filter, and observers should be cautious of it until the situation is better understood. In addition, one incidence of a 5° PA error for F775W has been observed, suggesting this waveband is not calibrated as well as the others.

Table 5.6: Efficiency Correction Factors C(CCD, POLnXX, specfilt, n) for Polarization Zeropoint

CCD

POL Filter

Spectral Filter

n = 0

n = 60

n = 120

HRC

POLUV

F330W

1.7302

1.5302

1.6451


 
POLV

F435W

1.6378

1.4113

1.4762


 

POLV

F475W

1.5651

1.4326

1.3943


 
POLV
 

F606W

1.4324

1.3067

1.2902


 
POLV
 

F625W1

1.0443

0.9788

0.9797


 
POLV
 

F658N1

1.0614

0.9708

0.9730


 
POLV
 

F775W

1.0867

1.0106

1.0442

WFC

POLV

F475W

1.4303

1.4717

1.4269


 
POLV
 

F606W

1.3314

1.3607

1.3094


 
POLV
 

F775W

0.9965

1.0255

1.0071

1 Not scaled for Stokes I


Table 5.7: Flat-Spectrum (with Wavelength) Average Cross-Polarization Leak Correction Factors

CCDPOL FilterSpectral FilterTparallelTperpendicularLeak Correction
HRCPOLUVF330W0.48100.04701.2167

POLUVF435W0.52470.04161.1724

POLVF606W0.51585.591 x 10-51.0002

POLVF625W0.51472.874 x 10-51.0001

POLVF658N0.51742.355 x 10-51.0001

POLVF775W0.60430.07321.2758
WFCPOLVF475W0.42391.524 x 10-41.0001

POLVF606W0.51575.591 x 10-51.0002

POLVF775W0.60410.07371.2778