# 6.1 Polarimetry

HRC has been unavailable since January 2007. Information about the HRC is provided for archival purposes.

## 6.1.1 Introduction

ACS offers two sets of polarizers, one optimized for near-UV/blue wavelengths (POLUV) and one optimized for visible/red wavelengths (POLV). Table 6.1 lists the filters that can be paired with the polarizers, as well as their availability (SUPPORTED, AVAILABLE but unsupported, or UNAVAILABLE). Note that the following filters are not able to be used with the polarizers: F850LP, F892N, and all of the Linear Ramp Filters. Rudimentary spectropolarimetry is possible by using the polarizers in conjunction with the dispersing elements. The large number of possible spectropolarimetric modes prevents automatic calibration of these modes by STScI, so observers must request additional orbits for their own spectropolarimetric calibrations. For normal polarimetric imaging, the location of the target remains fixed on the detector as successive images are obtained using a suitable filter and each of the constituent polarizers of the desired set. The varying intensities of the source in the successive images provide the basic polarimetric data for the source.

Table 6.1: Filters that can be used in conjunction with the ACS polarizers.

Polarizer set

Filters

Availability

POL0UV
POL60UV
POL120UV

F220W
F250W
F330W
F435W [a]
F660N [a]
F814W

unavailable
unavailable
unavailable
available
available
available

HRC NUV short
HRC NUV long
HRC U
Johnson B

POL0V
POL60V
POL120V

F475W [a]
F502N
F550M
F555W
F606W [a]
F625W
F658N [a]
F775W [a]
G800L

supported
available
available
available
supported
available
available
supported
available

SDSS g

Johnson V
SDSS r

SDSS i

a These filters are part of ACS calibration programs 13964 and 14407 to calibrate the polarizer/filter combination to 1% or better

## 6.1.2 Performance of ACS Polarizers

At least three polarized images are required to determine the degree and position angle of polarization as well as the total intensity of the source. Each set of ACS polarizers comprise three polarizing filters with relative position angles 0°, 60°, and 120°. The polarizers are aplanatic optical elements coated with Polacoat 105UV (POLUV set) and HN32 polaroid (POLV set). The POLUV set is effective throughout the visible region; its useful range is approximately 2000 Å to 8500 Å. The POLV set is optimized for the visible region of the spectrum and is fully effective from 4500 Å to about 7500 Å.

The relative performance of the POLUV and POLV polarizers are shown in Figure 6.1. The POLV set provides superior perpendicular rejection in the 4500 Å to 7500 Å bandpass, while the POLUV set delivers lower overall rejection across a wider range from 2000 Å to 7500 Å. Performance degrades at wavelengths longer than about 7500 Å, but useful observations may still be obtained up to approximately 8500 Å. In such cases, imperfect rejection of orthogonally polarized light must be considered during data analysis.

The ACS polarizers are effectively perfect. Consequently, the Stokes parameters (I, Q, U) can be computed using simple arithmetic. Using im1, im2, and im3 to represent the images taken through the polarizers POL0, POL60, and POL120 respectively, the Stokes parameters are:

 (1)
 (2)
 (3)

These parameters can be converted to the degree of polarization (P) and the polarization angle (θ) measured counterclockwise from the axis as follows:

 (4)
 (5)

A more detailed analysis, including allowances for imperfections in the polarizers, is given by Sparks & Axon 1999, PASP, 111, 1298, who found that the important parameter in experiment design is the product of expected degree of polarization and signal-to-noise. For three perfect polarizers oriented at 60° relative position angles (as in ACS), the uncertainty in the degree of polarization P (which ranges from 0 for unpolarized light to 1 for fully polarized light) is approximately the inverse of the signal-to-noise per image. Specifically, Sparks & Axon found:

 (6)

where σP is the uncertainty in the degree of polarization, and <S/N>i is the signal-to-noise of the ith image. The uncertainty in the polarization angle, σθ, is given by:

 (7)

This analysis pertains to ideal polarizers with no instrumental polarization. However, the ACS polarizers (especially the POLUV polarizers) allow significant leakage of cross-polarized light and the instrumental polarization of the WFC is ~2% (see ACS ISR 2004-09). The instrumental polarization of the HRC ranged from a minimum of 4% in the red to 14% in the far-UV. Other effects, such as phase retardance in the mirrors, may be significant as well. Please consult the STScI webpages for more detailed information, especially the ACS Data Handbook and ACS ISRs.

## 6.1.3 Implementation of ACS Polarizers

The ACS polarizers are easy to use. The observer selects a spectral element (filter or grism) and then takes successive images with the three polarizers of the VIS set (POL0V, POL60V, POL120V) or the UV set (POL0UV, POL60UV, POL120UV). Once the spectral element and polarizer set are specified, the scheduling system automatically generates the slews that place the target in the optimal region of the field of view.

Because the POLUV and POLV sets are housed on separate filter wheels, the number of spectral elements available to each set is restricted. The available elements are determined by the relative performance of the polarizers and the near-UV limitations of the WFC caused by its silver mirror coatings. The POLUV set is mounted on Filter Wheel 1 and may be crossed with any filter mounted on Filter Wheel 2. The POLV set is mounted on Filter Wheel 2 and may be crossed with the G800L grism or any of the other associated filters in Table 6.1. GOs must plan their own calibration observations for those filters listed as AVAILABLE in the table.

The polarizer sets were designed primarily for use with the HRC, where they offered a full unvignetted field of view (29 × 26 arcsec2) with any allowed imaging, spectroscopic, and coronagraphic combinations. When used with the WFC, the polarizers provide a vignetted, rectangular field of view that fits inside the WFC1B-2K sub-array. Although this field of view is significantly smaller than the normal WFC field of view, it is approximately five times larger than that obtained with the HRC. To avoid the gap between the WFC CCDs and to optimize readout noise and CTE effects, the scheduling system will automatically slew the target to pixel (3096, 1024) on the WFC1 CCD whenever the WFC aperture and polarizer sets are selected. To reduce camera overhead times, a 2048 × 2048 subarray image centered on the target will be readout from WFC1 (Table 6.2).

Occasionally observers desire non-polarized images of targets at the same location on the detector as their polarized images. Doing so was straightforward with the HRC; one merely had to take an exposure without the polarizer in place. However, WFC polarimetry automatically invokes a large slew from the non-polarimetric imaging position. To obtain a non-polarized image at the same physical detector location as the polarized images, one must specify the WFC1B-2K aperture instead of the WFC aperture (Table 6.2).

Table 6.2: Examples of polarizer and non-polarizer exposures in a Phase II proposal. HRC apertures are no longer available but are shown for archival purposes.

Aperture

Filters

Comment

HRC

F606W, POL0V

1024 × 1024 image centered at usual HRC aperture.

HRC

F606W, POL60V

Same but with POL60V.

HRC

F606W, POL120V

Same but with POL120V.

HRC

F606W

Non-polarizer image centered at same detector location as polarizer exposure.

WFC

F606W, POL0V

Target automatically placed at WFC1 pixel (3096, 1024); 2048 × 2048 image.

WFC

F606W, POL60V

Same but with POL60V.

WFC

F606W, POL120V

Same but with POL120V.

WFC1B-2K

F606W

Non-polarizer image at same detector location. Target at WFC1 pixel (3096, 1024); 2048 × 2048 image.

## 6.1.4 Challenges and Limitations of ACS Polarimetry

The most accurate ACS polarimetry was obtained in the visible bands (i.e., F606W) with the HRC and POLV polarizers. This mode had the advantage of very high rejection of perpendicular polarization and known mirror coatings with readily modeled properties. Because the WFC mirror coatings are proprietary, models of their polarization properties (e.g., the phase retardance of the IM3 mirror) are unavailable. Consequently, calibrating WFC polarized images is much more difficult than calibrating the HRC images. The ACS Team has an ongoing campaign to photometrically calibrate WFC polarimetry with both sets of polarizers. Data has been obtained which should provide improved calibration for the following filters, in combination with the appropriate set of polarizers: F435W, F475W, F606W, and F775W. We encourage users to periodically check the ACS webpage and published ISRs for any updates.

UV polarimetry with ACS is challenging because the POLUV polarizers have relatively poor orthogonal rejection. In addition, while the instrumental polarization of the HRC was 4% to 7% in the visible, it rose to 8% to 9% in the UV and reached 14% at 2200 Å (see ACS ISR 2004-09). Far-UV polarimetry is especially challenging because the POLUV properties are not well-characterized shortwards of 2800 Å, and they appear to change rapidly with wavelength. Moreover, the low UV transmission of the POLUV polarizers and the poor rejection in the far-red exacerbate the red leaks seen in the far-UV spectral filters.

The ACS team recently examined the impact of the pixel-based CTE correction algorithm on the ability to accurately measure polarization in ACS observations (ACS ISR in prep.). The study used simulated observations of point sources with different fractional polarizations, source brightnesses, and background levels. The study found that the pixel-based CTE corrected images induced ~0.1% additional polarization signal for 100% polarized sources farthest from the serial register, and that the induced signal decreases with decreasing polarization. Overall, this induced polarization effect is negligible compared to other sources of polarization uncertainty, therefore the net effect of CTE loss on ACS polarimetry is minimal.

The polarizers contribute a weak geometric distortion that rises to about 0.3 pixels near the edges of the HRC field of view. This distortion is caused by a weak positive lens in the polarizers that is needed to maintain proper focus when multiple filters are in the beam. The POLV polarizers also have a weak ripple structure intrinsic to their polaroid coatings. These ripples contribute an additional ±0.3 pixel distortion with a very complex structure (see ACS ISR 2004-10 and ACS ISR 2004-11). All these geometric effects are correctable with the AstroDrizzle software. However, astrometry will be less accurate with the polarizers because of residual errors and imperfect corrections.

Finally, the POL0V and POL60V filters contain bubbles which impact the PSF and flat fields. These bubbles are far out of focus and appear as large concentric bright and dark rings (400 pixels diameter in WFC, 370 pixels in HRC) and streaks in the flat fields. The worst case appeared in HRC POL60V images, where the amplitude of the artifacts reaches ±4% in the flats and the affected region was roughly centered at pixel (x, y) = (835, 430). Polarimetric combinations involving POL0V or the WFC are relatively minor, with typical amplitudes of ±1%. Observers requiring precision polarimetry should avoid these regions of the field of view. Although the polarizer flats attempt to correct these features (see ACS ISR 2005-10), the corrections are imperfect and dependent on the brightness and angular size of the target. The locations of these features and their effects can be discerned more accurately by examining the P-flats for the respective spectral filter crossed with the visual polarizers.