Linear polarimetry with FAPOL
Linear polarimetry is made using a 1/2 wave plate in the FAPOL unit
and a calcite plate mounted in the aperture wheel. The calcite plate
provides the simultaneous measurement of the ordinary and the
extraordinary components of two orthogonally polarized beams. The 1/2
wave plate can be rotated in steps of 22.5° from 0° to 337.5°.
As a standard, 4 angles are used (0°, 22.5°, 45°, and 67.5°),
other possible exposure sequences are 8 angles (0° to 157.5° in
steps of 22.5°)
or 16 angles (0° to 337.5° in steps of 22.5°).
Each image will contain two images of the
same object separated by about 15", and is therefore suitable
for point-like targets. In this way for the standard observing mode using
4 positions of the 1/2 wave
plate plus the beamsplitting of the calcite into the orthogonal o-
and e- rays, gives a total of 8 images, with which the ratio of the
transmission coefficients of the two o- and e- beams can be eliminated
in the reductions. The first position gives the 0° and 90°
position angles, the next the 45° and 135°, then 90° and
180°, and at last 135° and 225°.
The calcite plates produce a vignetted field of about 140" in diameter.
Verify with staff that 1/2 wave plate is installed in FAPOL (this is
the default setup). The 1/2 wave plate is a retarder which is used to rotate the plane of linearly polarised light. The ordinary and extraordinary components of a ray are shifted in phase by half a wavelength, i.e. the phase delay is 180°. By integrating at 4 different angles of the 1/2 wave plate: 0.0°, 22.5°, 45° and 67.5°, one obtains flux measurements of both the o- and e- components at 0°, 45°, 90° and 135°.
Let O(i) and E(i) be the intensities of the ordinary and extraordinary
images obtained through the calcite plate for each of the i=1,2,3,4 angles
of the 1/2 wave plate. The percentage of linear polarisation (P) and its
orientation on the plane of the sky, the equatorial position angle (PA),
are found as follows: Q(i) = E(i)/O(i) QM = Q(1) + Q(2) + Q(3) + Q(4) PX = (Q(1)-Q(3))/QM PY = (Q(2)-Q(4))/QM P = SQRT((PX)2+(PY)2)*100 PA = 28.7*ATAN2(PY,PX) + ZPAwhere ZPA is the zero-point corection of position angle. High polarisation standards are always needed to calibrate the equatorial position angle. Observe two standards which have sufficiently separated angles. The 1/2 wave plate is usually put in at the same orientation each time, so with time we will provide a rough zero-point correction of the angle. Intrinsic polarization across the field of the calcites is currently under investigation. At the moment we recommend observing your target at the same spot where you observe a Zero polarisation standard star. When calculating average linear polarization, the Stokes parameters PX and PY should be averaged (not P and PA). The standard error of the mean P comes as quadratic mean of the errors for PX and PY: ep=SQRT(((epx)2+(epy)2)/2.) and epa=28.7*ATAN2(ep,P) Observing stepsFollow observing instructions in the ALFOSC Cookbook. |
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