Spectropolarimetry with CGS4
NOTE: In almost all cases, UIST should be used for spectro-polarimetry. These pages are retained simply for reference purposes.
This document describes the use of IRPOL2, in conjunction with the facility near-IR spectrometer CGS4, for obtaining spectropolarimetric observations of point sources (e.g. stars, distant galaxies).
IRPOL2 was designed and built by the University of Hertfordshire for the UKIRT. More details of the design characteristics of the polarimetry module and its corresponding optics can be found via links from the main IRPOL2 web page. The acquisition of CGS4 spectropolarimetry data as well as their reduction are described in the following sections.
A postscript version of the old CGS4 pol guide (using the old vax-based SMS system) written by Any Chrysostomou, can be obtained here: this contains many tips on spectropolarimetry and may be of use to Pol users.
The UKIRT and University of Hertfordshire would appreciate an acknowledgement in any publication which contains data obtained using IRPOL2.
From August 2000 (semester 00B), CGS4+Pol data acquisition and reduction will be from the new ORAC system. Control of CGS4 is described in detail in the main CGS4 web pages. Below are a few additional tips.
Polarimetry with ORAC
The expectation is that most users will work from a “Template Sequence” in the OT. The “Template Library” contains a number of sequences specific to polarimetry. These can be modified to suit your specific needs. It is probably unwise to try and write a sequence completely from scratch.
The waveplate is controlled from ORAC using an IRPOL iterator (the “running-man” icon; see Figure 1 below). Thus, in addition to the “normal” offset (slide-slit) iterator, you will need a second which steps the waveplate between the four angles needed to measure the polarisation ( 0o, 45o, 22.5o and 67.5o ). In the example below object and sky observations are obtained at each waveplate angle. The IRPOL iterator highlighted is displayed in the right-half of the OT programme window; here IRPOL is set to an angle of 0o. The final IRPOL iterator at the end of the sequence likewise returns IRPOL to an angle of 0o, after the observations have been completed.
The prism inside CGS4 will of course produce orthogonal e-beam and o-beam spectra of your target. Because we cannot install a mask in front of the CGS4 entrance window, only point sources or sources less than a few arcseconds in extent may be observed with CGS4+Pol (see the CGS4 beam Separations below.) Otherwise, the e- and o-beams will overlap on the array. With this in mind, small slides along the slit should be entered into the offset iterators, so that e- and o-beam spectra do not overlap in “object” and “sky” observations. A group of eight exposures (an object-sky pair at each waveplate angle) will allow you to measure the degree of polarisation and polarisation position angle for your target. The repeat iterator in the above example could be set to greater than unity to build up signal-to-noise and therefore polarisation accuracy.
Flats and arcs should of course also be obtained in the usual way.
ORAC data reduction for Spectro-polarimetry
From August 2000 (semester 00B), CGS4+Pol data acquisition and reduction will be via the new ORAC system. Data-reduction recipes are being developed. For the time being, please use the recipe REDUCE_SINGLE_FRAMES_ONLY or QUICK_LOOK in your ORAC sequence; the latter will only display raw spectral images, and neither will put data into groups.
IRAF and Starlink software specific to polarimetry (TSP) are available at the summit for reduction of your data. Alternatively, this simple script could be used for “quick_look” polarisation measurements.
Calculating the State of Polarization
To measure the polarisation you require sky-subtracted spectra at the four waveplate angles: 0o, 45o, 22.5oand 67.5o . In principle, with a perfect Wollaston prism, you would only need two positions to calculate the polarization. However, although the Wollaston prism DOES produce orthogonally polarised beams, the attenuation of each beam differs through the prism because the optical path that each beam takes is not identical (also, the refractive index for the two orthogonal states is different). By measuring the other waveplate positions, it is possible to cancel these differences out. N.B : This should not be considered as an overhead as the same signal is being measured at each waveplate position.
There are a number of methods employed for calculating the Stokes parameters (I, Q, U) from the data. Two are outlined below.
The RATIO method
The algorithm for calculating the Stokes parameters using the Ratio method is:
The DIFFRENCE method
The algorithm for calculating the Stokes parameters using the Difference method is:
The e and o in these equations refer to the intensities of the e- and o-beams at the relevant waveplate positions, given by the suffixes. The same calculation gives the U Stokes parameter by substitution of the 22.5o and 67.5o positions for the 0o and 45o, respectively.
Both methods efficiently correct for transmission changes between individual observations (in other words, pol observations are possible in non-photometric, or “cirrusey”, conditions, although the pol angle measurement will be less accurate). The RATIO method works well for bright objects but can fail for faint or noisy sources (and 100% polarized calibration sources) when the algorithm attempts to take the square root of a negative number. The DIFFERENCE method should be used in these instances.
Once the q and u Stokes vectors are obtained, the state of polarization (i.e. degree of polarization and position angle) can be calculated according to the equations :
To correct for the position angle calibration, a rotation of +7o should be applied to the polarization vectors.
The Magnesium Fluoride (MgF2) prism within CGS4 acts as the polarimetric analyser, splitting the incoming radiation into the orthogonally polarised e- and o-beams. This divergence is dependent on the refractive index of the material and is wavelength dependent.
The beam separations given here are in units of pixels and are measured for the long focal length camera (0.61 arcsec per pixel).
It should be noted that the wavelength dependence of the beam divergence is not very steep. This means that there will be a small amount of curvature of the spectrum along the dispersive direction when using the low resolution gratings.
Spectropolarimetry and the Echelle
After some initial testing with CGS4, the echelle and the Wollaston prism it has been decided that it is not possible to use this observing mode. The root of the problem lies with the fact that (for historical reasons) the Wollaston prism is situated ahead of the slit wheel. Because of this the slits need to be aligned with the e– and o-beams from the prism (which results in tilted spectra for CGS4 spectropolarimetry with the low resolution gratings). It is impossible to align the echelle slits with these beams due to the angle that the echelle slits are mounted in the slit wheel.
We have investigated whether the normal low resolution slits could be used. Unfortunately, with this configuration the slits cannot be aligned along the radial axis of the CVF the result of which is that the e– and o-beams sample disparate parts of the spectrum. The typical wavelength difference between the 2 spectra is 0.15 – 0.3 �m (dependent on wavelength), well beyond the wavelength coverage of the echelle. Additionally, it is not clear that the two spectra would originate from the same order.
The only viable option for performing echelle spectropolarimetry, is to use the old CGS4 wire-grid as an analyser rather than the Wollaston prism. The price to pay for this will be that the polarisation accuracy is probably limited to ~ 1%, and that the data would then be extremely susceptible to varying atmospheric conditions. Photometric conditions would be needed.
Instrumental Polarisation and Polarisation Efficiency
The instrumental polarisation at J,H and K is believed to be low, typically well below 0.5%. However, observers should note that the precision of polarisation measurements may be limited by the accuracy with which the prism can be aligned with the slit, combined with the accuracy of the “slide slide” manoeuver. With the narrower slits, polarisation measurements may also be subject to changes in the seeing.
The Wollaston prism in CGS4 is situated before the wheel that contains the slits; consequently, incoming radiation encounters the prism before it passes through the slit. This means that the ordinary and extra-ordinary (o- and e-) beams produced by the prism must both pass precisely through the slit if accurate measurements of (sub-1%) polarisation are to be made. Any slight miss-alignment of the slit with respect to the prism will result in an apparently high instrumental polarisation. Indeed, seeing variations will result inchanges in the e/o ratio over time and therefore the apparent polarisation of any source that is observed repeatedly.
During engineering time in May 1999, observations of the same unpolarised standard were repeated nine or ten times (with the same instrumental set-up). Although the mean polarisation was of the order of 0.5%, the individual measurements varied quite considerably. The standard deviation to the mean polarisation measured was 0.4-0.5% for the 1-pixel slit, and 0.7% for the two pixel slit. Statistical errors on the position angle were of the order of 30-40 degrees.
Difficulties in reaching a very high signal-to-noise ratio (approaching 1000), due to flat-fielding errors and noise associated with variable sky levels and (with bright sources) significant read-noise, may also have contributed to the uncertainties described above.
Although the CGS4 slits will be carefully aligned with the prism before any spectro-polarimetry run, users should be aware that a more precise measurement of polarisation (with overall errors of the order of 0.3% – 0.5%) is more likely with the wider slits. It is also important that observers set aside some time (1-2 hours) at the beginning of their run for repeated observations of an unpolarised standard with the chosen instrument set-up (wavelength, grating, etc.).
Further observations of unpolarised standards are planned for the near future.
Measurements of the polarisation efficiency at I,J,H and K were secured on 29 May 1999. The results obtained with the 40 l/mm grating indicate an efficiency exceeding 99% at all four wavebands (see thispostscript plot of the complete data set: note that the stokes I plot reflects the fact that 3 different sources, BS4358, BS4929 and BS5553, were observed; hence the difference in the absolute flux measurements.) Observations with the 150 l/mm grating yield a polarisation efficiency of 100.2% (+/- 0.03%) at K (2.08 microns). Overall, these results are in good agreement with earlier studies.
L’ and M-band measurements were obtained in August 1999 with the 40 l/mm grating. The L and M-band waveplates are zero-order plates (the waveplate for IJHK observations is an achromat). Consequently, the efficiency will be non-linear across these wavelengths. At L’ the efficiency peaks at 97% at around 3.65 microns and drops off, approaching 86% at longer wavelengths. At M the efficiency peaks at 94% at 4.8 microns and decreases to less than 90% towards the edges of the window. Plots of the L’ and M-band measurements, together with 2nd order polynomial fits, are available here:
L-band efficiency —– M-band efficiency
The fits used are:
L’band: P(%) = -398.1 + 272.6(wavelength) – 37.5(wavelength)^2
M band: P(%) = -1014.1 + 463.1(wavelength) – 48.4(wavelength)^2