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).
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.
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.
Fig.1 A Typical Polarimetry OT Programme, with the IRPOL
iterator opened and set to 0o.
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
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
IRAF and Starlink software specific to polarimetry (TSP) are available
at the summit for reduction of your data. Alternatively, this
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,
22.5o and 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 algorithm for calculating the Stokes parameters using the Ratio
method is :
The DIFFERENCE 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).
These separations are measured from the "bottom"
beam to the "top" beam.
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
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 Ám (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
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
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 in
changes 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
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
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
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 this
postscript 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 -----
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
Back : IRPOL