ACS contains a set of six filters which 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 arrayed 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.
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 an 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
) and (ACS ISR 2004-10
The instrumental polarization, defined as the instrument’s response to an
unpolarized target, provides a simple measure of some of these effects. Figure 5.9
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°
. The details of the CCD are proprietary so we have simply modeled it as Silicon at an incidence angle of 31°
; no doubt this is a serious over-simplification. Figure 5.10
shows the same plot for the WFC, which has an instrumental polarization around 2%. Here the IM3 mirror is a proprietary Denton enhance 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, we caution 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.
The ACS polarizer filters were characterized prior to installation in ACS by
Leviton and the results as summarized in Figure 5.1 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 polametric field dependences; while there has been study of intensity flats for the polarizers, the polarization field dependencies are not known.
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, we compared in-flight observations of the bright earth using the F435W+POLUV filters and 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.
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.
We present a preliminary calibration for use by polarization observers which is
based largely on data in programs 9586 and 9661. 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.
The strategy here was to create a calibration based upon the small amount of data
which have been analyzed. This calibration can be applied to either aperture photometry results, or to the images themselves (i.e., for an extended target). We began by calibrating the polarization “zeropoint” using corrections which were derived from observations of unpolarized standard stars. Corrections C(CCD, POLnXX, 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 5.8
, and have been scaled such that Stokes I will approximate the count rate seen with no polarizing filter.
Next we compute the fractional polarization of the target. We include a factor
which corrects for cross-polarization leakage in the polarizing filters. This correction is useful for the POLUV filters, and values of Tpar
can be found in Figure 5.4 of the ACS Instrument Handbook
Finally we compute the position angle on the sky of the polarization E-vector. The
parameter PAV3 is the roll angle of the HST spacecraft, and is called PA_V3
in the data headers. The parameter
contains information about the camera geometry which is derived from the design specifications; for HRC we have
, and for the WFC we have
. Note that the arc tangent function must be properly defined; here we use a definition where the result is positive in quadrants I and II, and negative in III and IV.
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°
We have modeled the full instrumental effects and the above calibration together in
an effort to determine the impacts of the remaining uncalibrated systematic errors. We believe 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.) We have checked this calibration 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. We have not given a calibration for F220W, F250W, or F814W, as we believe these are 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, we have seen one incidence of a 5°
PA error for F775W, suggesting this waveband is not calibrated as well as the others.