FORS1 Polarization - A Test

F. Patat - M. Romaniello

The field reported below was retrieved from the archive. It was observed using 4 HWP angles, taking 5 exposures per HWP position, 15 minutes each, so that the equivalent exposure time on the Ordinary and Extraordinary beams is 75 minutes per HWP angle. Observations were carried out in dark time. The data were processed using bias and sky flats (no HWP, no Wollaston) taken within one day from the science observations. Sky flats were used directly on the observed frames, therefore leading to a non perfect correction (pixel to pixel variation are removed, but large scale gradients are not exactly taken into account). The redundancy achieved using N=4 HWP positions (instead of the minimum N=2) should however remove this effect, at least with some approximation.

Go with the mouse on the picture to see an example of reduced intensity image (f_o+f_e) for one of the HWP angles.

The sky background level achieved in each image (ord or ext) is around 3100 ADU (~5000 e-) and the SNR (per pixel) reached in the combined intensity (f_o + f_e) image is around 225. The purpose of this test is to measure the background polarization, whatever background means (sky, light concentration, ?). Before we proceed we like to show two effects. The first is the clear presence of light concentration, as shown in the following picture:

The light concentration is of the order of 3% (peak-to-peak), as one can easily see in a diagonal cross-cut:

The second is the presence of at least one reflection

which looks like carrying the imprints of the HWP mosaic. This is probably caused be the saturated star in the right upper corner of the image. The fact that it is not split in two parts (as the sky image is), suggests that the reflection takes place after the Wollaston Prism. A close inspection to the images taken at different angles shows that the reflex does rotate but it does not move significantly (see also the last figure in this page).

The polarization map one obtains if she does not subtract the sky background is reported in the following picture, which was obtained binning U and Q images with 30x30 boxes. The corresponding signal to noise in the single ordinary and extraordinary images becomes about 6750 per resolution element at the sky level. This implies a polarization signal-to-noise ratio (SNR) of about 68 for a 1% polarization. This SNR is sufficient to make negligible any polarization bias effect, and the errors on polarization degree and polarization angle become very low. For this reason, one is confident that all features seen in the following picture are real.

It is clear that there is a spatially dependent pattern with some symmetry. Maximum polarizations are of the order of 2.5% and tend to take place at the lower right and upper left corners. Whatever the reason for such pattern is, the effect is that if one does not subtract its contribution (before computing the normalized Stokes parameters), this is going to affect the final result, especially in the regions where an hypothetic target becomes fainter (e.g. a galaxy or an extended nebula).
It must be noticed that when one is studying a point-like object, this background effect is removed, since the background is computed locally in each ordinary and extraordinary image. This is unfortunately not the case when the target covers a fair fraction of the field and no local background subtraction is possible.

Most of the observed polarization is certainly due to real sky polarization (see for instance Wolstencroft & Bandermann, 1973, MNRAS 163, 229), but the pattern is must unlikely to be totally determined by the sky itself.

To show that the effect is real and not due to reduction artifacts, in the following picture we present the observed images (bias and flat-field corrected with sky flats) for 0 (upper left), 22.5 (upper right), 45 (lower left) and 67.5 (lower right). All images are displayed with the same intensity cuts and were divided by the same sky flat.

As one can see, there are clear polarization patterns. See, for example, the gradients in the upper slitlets of right images (22.5 and 67.5). Background polarization is clearly visible in the 67.5 image, where the difference between ordinary and extraordinary beam is indeed apparent.

As a further test, we have reduced the data obtained on 2003-12-05, when the [unpolarized] standard star EG21 was observed using 4 HWP angles. The star was placed in the lower right corner of the image, in order to detect any spurious polarization in this region of the field of view. The data were bias and flat field corrected (using sky flats) with calibrations taken within one day. A full reduction has given the following results for the polarization degree and polarization angle:

where the numbers quoted in parentheses are the estimated RMS errors.

Given the fact that the observed star is supposed to be unpolarized, this result suggests the presence of an instrumental polarization which points (at least in this position) towards the field center.

We note that this is not in contraddiction with the results we got on the sky background. In fact, if such instrumental pattern really exists and it has a radial structure, it certainly interacts with the input polarization field and it tends to produce a null net polarization where the two fields are perpendicular and with comparable intensity. This would explain the low polarization regions observed in the lower left and upper right corners of the empty field.