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).

Observing steps

1. Move the retarder plate into the beam: In the FAPOL window click on "Carriage is out". It will go in, initialize and tell when it is ready. You can manually select retarder positions by clicking on the menu.
   
   Note: only following angles are available on the menu: 0°, 22.5°, 45°,67.5°, 90°, 180°, 270°.
   Other angles have to be selected using the sequencer command alfoscinst.polarizer "angle".
   e.g. alfoscinst.polarizer 112.5 will move the retarder to position 112.5.
   
   
2. Imaging polarimetry:
   • Select Cal-90 (the calcite plate without a slit) in the aperture wheel.
     
     
   • Doing polarimetric imaging only, the simplest way to switch from normal imaging to polarimetric mode, which involves substantial changes of the optical path, is to add +725 units to the foc-pos (telescope focus) value for the same filter in the beam. In this way you don't need to refocus if you already had focused the telescope. Due to the substantial changes in the telescope focus, you will have to adjust the tv-focus to a value around 580. If you are starting up the night in imaging polarimetry mode, the default focus for linear imaging polarimetry is 23955 (assuming the internal focus is set to the default 1910). See also About focusing FAPOL .
     
     
   • Limit the CCD window size (e.g. by typing alfosc.polwin), and take an image to check the position of your target. You will see two images of your target, separated vertically, the ordinary component being the upper and the extraordinary one about 15" lower. In case your target overlaps with other objects in the field, change the field-rotation (tcs.field-rotation xxx).
     
     
   • Start exposing. This can be done manually or using a script.
     A standard script is available:
     alfosc.linpolexpose "number of angles" "myobject" "exposure time" "number of cycles"
     Options for number of angles are:
     4 (0°, 22.5°, 45°, and 67.5°)
     8 (0° to 157.5° in steps of 22.5°)
     16 (0° to 337.5° in steps of 22.5°)
     
3. Spectropolarimetry:
   • Now you will use both the Cal-90 plate and the Calcite plate with a polarimetry slitlet mounted above it. These are both mounted in the aperture wheel. In order to have the slitlet in focus, the internal camera focus of ALFOSC must be set to 1070 (the default internal focus value being 1910). If you restart the ALFOSC obssystem you may have to reset the internal camera focus.
     
     
   • The telescope focus offset should then be about +440 from normal ALFOSC imaging mode (without filters). NB! Important. Have the lambda/2 retarder plate in the beam when you measure the focus. Due to the substantial changes in the telescope focus, you will have to adjust the tv-focus to a value around 520. (If you are starting up the night in spectro polarimetry mode, the default focus for spectro polarimetry is 23670, assuming the internal focus is set to the default 1070).
     
     
   • If you want to observe on the parallactic angle, preset to your target using the TCS numerical key [6]. If you want to align the slit along a preferred direction (e.g. along two stars), or the default field orientation is ok, then use TCS key [4] to preset, and use slitrot afterwards to find your preferred field orientation (see below).
     
     
   • For aquisition on the slit, put in the Cal-90 plate in the aperture wheel and run alfosc.polwin to set the correct window size. Make sure you are autoguiding!
     
     If you want to align the slit along a preferred direction, then:
     • Take an image.
     • Type slitrot in the ALFOSC Sequencer window and follow the instructions. The principle is that you click on two points and get out a new value for the field rotation. This should be given into the TCS with the command: field-r xxx.
     
     When you are satisfied with the orientation, then place your target on the slit as follows:
     1. Take an acquisition image (exp t). You will see two images of your target, the ordinary component being the upper and the extraordinary one about 15" below.
     2. Type slitoff slit=xx in the sequencer window, xx being the number of your slit. Follow the instructions and put the cursor on the upper image of your target, press 'a' to determine the center, then 'q' to quit. The telescope will now move.
     
     Iterate once from step 1. Alternatively you can set the slit position yourself with slitoff xref=xxx yref=xxx.
   • Then put in the polarimetry slitlet and the grism of your choice.
     
     
   • Limit the window size (you can ask staff to write a small script that windows the readout according to your wishes). Two perpendicularly polarised spectra are produced per image. The minimum requirement is two exposures, but with 4 the difference between the transmission of the orthogonally polarized spectra is eliminated in the reductions, since the polarisation modulation of the o- and e- rays have the inverse effect in the 3rd and 4th exposure compared with the 1st and 2nd.
     
     
   • Start exposing. This can be done manually or using a script.
     A standard script is available:
     alfosc.linpolspec "number of angles" "myobject" "exposure time" "number of cycles"
     Options for number of angles are:
     4 (0°, 22.5°, 45°, and 67.5°)
     8 (0° to 157.5° in steps of 22.5°)
     16 (0° to 337.5° in steps of 22.5°)
     

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) + ZPA  


IF(PA.GT.180.)PA=PA-180.
IF(PA.LT.0.)PA=PA+180. 

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)