Polarization Observations with FORS

FORS2 can measure linear polarization and circular polarization in imaging and spectroscopic modes. It is possible to determine position angle and degree of the linear polarization or the circular polarization of an object by using a remotely controlled rotatable lambda/2- or lambda/4-plate in front of the Wollaston prism.

Description of the FORS Polarization Modes

The retarderplates are of the ``superachromatic'' type (after Serkowski). It proved impossible to procure waveplates of sufficient size; therefore mosaics of 3*3 plates of 45.5*45.5mm each are used (inter-plate gap 3mm) with a resulting free mosaic diameter of 138mm. The position angles can beset with an accuracy of 0.1 degree.

It will be however required to correct for chromatic zero angles in caseof linear polarimetry. This is explained in the user manual in more detail. The figure below will show the amount of chromatism of the wave plate.With a mouse click on the image you will receive the fits table with the tabulated values measured with a Glan Thomsen Prism (which was mountedat the M2 spider and aligned in a never ending tricky procedure):

Optical Components

Wollaston Prism Ratarder Plate Mosaic
Wollaston Prism Retarder Plate

Polarimetric Standard Stars

The following list of polarimetric standard stars has been provided by the FORS consortium based on Commissioning data taken with FORS1. Thereare prepared OBs available on Paranal as well as selected unpolarized targets. Please note that there are additional errors not included in the error budget: With broad band filters the zero angles of the retarder plates will depend slightly on the colour of the target,... This is the most likely reason why Vela1 95 has these odd values for the polarization position angle in U and B. The targets are selected from Whittet et al. or from the catalog of Mathewson and Ford. NGC 2024 NIR1 was suggested by I. Appenzeller.

 

star filter mag. p in % PA in degree
NGC 2024 NIR1 B 13.75 8.27 +- 0.03 137.6 +- 0.1
  V 12.10    
M78 HD 38563A B   3.42 +- 0.04  96.1 +- 0.4
  V 10.42    
Vela1 95 U   6.59 +- 0.15 169.8 +- 0.7
  B   7.55 +- 0.05 173.8 +- 0.2
  V 12.1 8.24 +- 0.03 172.1 +- 0.1
  R   7.89 +- 0.04 172.1 +- 0.2
  I   7.17 +- 0.04 172.2 +- 0.2
Hiltner 652 U   5.03 +- 0.04 179.7 +- 0.2
  B   5.72 +- 0.02 179.8 +- 0.1
  g   6.18 +- 0.04 179.6 +- 0.2
HDE 316232 B 10.97 4.57 +- 0.02   4.3 +- 0.2
  V 10.29    
BD -14 4922 B 10.58 5.62 +- 0.04  50.5 +- 0.1
  V 9.73    
BD -12 5133 B 11.5 4.32 +- 0.05 148.4 +- 0.3
  V 10.8    

 

A real example for a standard star measurement - calibration plan datataken 2002-04-04

Unpolarized nearby star WD1620-391 - R_BESS

angle f_o f_e
0 28229 28454
22.5 28282 28403
45 28396 28519
67.5 28290 28522
                 f_o - f_e                    f_o - f_e 
Q/I = 0.5 * --------- ( 0.0 deg) - 0.5 * --------- (45.0 deg) = -0.001
f_o + f_e f_o + f_e

f_o - f_e f_o - f_e
U/I = 0.5 * --------- (22.5 deg) - 0.5 * --------- (67.5 deg) = 0.001
f_o + f_e f_o + f_e

The flux integrated in a wide aperture is given in adu (with 1.46e-/adusince I have normalized the flats in the lower left quadrant - 4-port mode). f_o and f_e are the flux in the ordinary (top) and extraordinary (bottom) beam of the Wollaston. The result is pretty consistent with readout noise of about delta Q / Q = 0.5 / sqrt(28400 * 2 * 1.46).

Polarized highly reddened star Vela1 95 - R_BESS

angle f_o f_e
0 29324 25387
22.5 26313 28002
45 25139 29794
67.5 28056 26630
                 f_o - f_e                    f_o - f_e 
Q/I = 0.5 * --------- ( 0.0 deg) - 0.5 * --------- (45.0 deg) = 0.078
f_o + f_e f_o + f_e

f_o - f_e f_o - f_e
U/I = 0.5 * --------- (22.5 deg) - 0.5 * --------- (67.5 deg) = -0.029
f_o + f_e f_o + f_e

p = sqrt(Q**2 + U**2) = 0.083

theta = 0.5 * atan(U/Q) = 169.8

theta_0 = theta + 1.2 = 171.0 (see FORS user manual chapter 4)

According to the FORS user manual the retarder plate zero angle -1.2 degreehas to be subtracted for the measurement with the R_BESS filter and the final result would be 171.0 degree accordingly. Please note that only generic bias frames and generic imaging twilight flats (no Wollaston, no half wave plate) were used for the data reduction. Flatfielding with flats taken seperately at 0,22.5,... degree retarder plate angle will reduce the instrument performance dramatically, since the flat field structuresare not anymore nulled (1st order approx.) in the equations for Q and U.

Important update on the instrumental polarization:

We have found strong linear instrumental polarization in the corners of the field of view. This spurious polarization field shows a high degree of axial symmetry and smoothly increases from less than 3x10^{-4} on the optical axis to 7x10{-3} at a distance of 3 arcmin from it (V band).

Spurious polarization in an empty field and 47Tuc
radial dependance

In case of the V band the spurious polarization can be modeled witha radial function:

p(r) = 0.057 r² in [%]

PA(x,y) = arctan( (y-yc) / (x-xc))

depending on the radial distance from the center of the field of view (xc,yc)and the position angle PA(x,y).

In case of the other filters and spectro-polarimetric measurement there is no data available yet. The corrective functions can be estimated with an observation of a globular cluster (like 47 Tuc) with the respective filters. Please contact us (<usd-help@eso.org>) in cases in which the correction of the spurious polarization is critical for your science.

Please note that there should be no problem for spectro-polarimetric observation of single targets in the center of the field of view orsingle targets in imaging polarimetry in the center of the field ofview. In case of the circular polarization the spurious polarization was found one order of magnitude smaller (see Bagnulo et al. 2002).

Further information regarding the calibration of FORS polarimetry data can be found in our list of technical papers.