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Spectropolarimetry with UIST

This document describes the use of IRPOL2, in conjunction with the facility near-IR imager/spectrometer UIST, for spectro-polarimetry. Imaging-polarimetry is discussed on a separate page. Details of the design characteristics of the polarimetry module and its corresponding optics can be found here.

• Data Acquisition - the UKIRT-OT and OCS
• Data Reduction - the ORAC-DR
• Beam Separations
• Calculating Exposure Times
• Finding Guide Stars with IRPOL
• Instrumental Ripple, Polarisation and Efficiency

A postscript version of the old CGS4+IRPOL guide (using the old vax-based SMS system) written by Antonio Chrysostomou, can be obtained here. This contains many tips on spectropolarimetry and may be of use to IRPOL users.

The UKIRT and University of Hertfordshire would appreciate an acknowledgment in any publication which contains data obtained using IRPOL2.

Spectropolarimetry with UIST: Data Acquisition

Introduction

IRPOL2, in conjunction with UIST, comprises an external (warm) half-wave retarder (the waveplate), internal (cold) focal-plane slit-masks and an internal (cold) Wollaston prism. Two spectroscopic slit-masks are available, a 2-pixel wide mask and a 5-pixel mask. (NOTE: The 2-pixel slit should not be used with the IJ and JH grisms.) These replace the long-slits used with normal spectroscopy, allowing the user to observe extended sources. Basically, the slit-mask transmits two 20"-long (0.24" or 0.60" wide) images onto the Wollaston prism, which splits these into orthogonally-polarised e- and o-beams. These four beams are subsequently dispersed by the chosen grism to give 4 "spectra" on the array; e- and o-beam spectra of the target and e- and o-beam spectra of adjacent sky (or another region of an extended source). This is illustrated in the figure shown below.

Fig.1 A cartoon showing the divergence and projection of two slit-images onto the array. The light from the star, which is centered in the top slit, is split into e- and o-beam slit images by the wollaston prism; these two images are then dispersed orthogonally by the chosen grism to give e- and o-beam spectra on the array; the blank sky in the lower slit is likewise "split" into e- and o-beam spectra on the array.

All 1-5 micron spectro-polarimetry at UKIRT should be carried out with UIST, as described below. (In CGS4 the prism comes before the slit mask, so misalignment of the e- and o-beam images with the slit can create spurious "instrumental" polarisation.) First-time users may also wish to consult the main UIST spectroscopy web pages for details on control of UIST via the UKIRT-OT and OCS.

Controlling UIST and IRPOL with the OT and QT

The expectation is that most users will work from a "Template Sequence" in the UKIRT-OT. The "Template Library" contains a number of sequences for polarimetry. These can be copied into a new programme and modified to suit your specific needs. It is probably unwise to try and write a sequence completely from scratch.

Below we show a typical polarimetry MSB, containing three separate observations (the full blue squares); a flat and arc calibration observation, a polarised standard, and the science target (in this case BN). All observations must contain (or inherit - see below), three components - a Target component, a UIST component and a DRRecipe component, as well as "running-man" icons to move the telescope and waveplate (and to repeat sequences), and observe "eyeballs" for imaging-acquisition and to take the actual exposures.

The "Spec-Pol of BN" MSB below starts with two notes and two components (the broken blue boxes). The three observations below the second (UIST) component "inherit" the information in the target and UIST components. However, the BN observation contains a second target component which overrides the standard star coordinates. The result is that all three observations will be taken with the same UIST setup, but the flat/arc and standard observations will be taken at the position of the standard, while the BN observations will be taken at the position of BN.

• The Target Information components obviously needs to be edited; click on these to enter source coordinates AND to specify a guide star. This component may also be used to display a Digitised Sky Survey image of the target field, the slit mask, the regions blocked by the waveplate + holder, and various guide-star catalogues.
• The UIST component sets the instrument to its initial configuration; integration time, pol. slit mask, grism, etc. Make sure polarimetry is selected in this window (otherwise you may end up taking ordinary spectroscopy observations).
• Separate DRRecipe components are contained inside each observation. These should already be set correctly to the recipe specific to your chosen mode of observing, though you should check these.

Click on the radio button to the left of each observation to fold/un-fold the observations. When a line is highlighted the settings of the component will be displayed in the right half of the window. In the example below the flat/arc and standard star observations are folded up; the BN observation is open to display its contents. Look at the examples in the template library and read the notes!

Fig.2 A Typical Polarimetry OT Programme, with the IRPOL iterator opened and set to 0^o.

To understand how a typical spec-pol programme works, we focus on the opened observation of BN, above. We assume that the target and guide star coordinates have already been set-up, the UIST configuration set, and the DRRecipe has been checked in the components above the "Sequence" icon. The steps below the Sequence icon in Figure 2 define the moves on sky, the waveplate angles, and the actual exposures.

To measure the polarisation of a source, at least eight frames must be observed - an object and sky pair at each of the four waveplate angles (0, 45, 22.5 and 67.5 degrees). However, recent tests, prompted by the study of Aitken & Hough (2001) 113, 1300, indicate that sixteen exposures should be acquired - i.e. an object and sky pair at each of eight waveplate angles: 0, 45, 22.5 and 67.5 degrees, plus 90, 135, 112.5 and 157.5 degrees (see below for further details).

The waveplate is controlled using an IRPOL iterator (the "running-man" icon in Figure 2 above), which steps the waveplate to each of the angles. The IRPOL iterator highlighted is displayed in the right-half of the OT programme window, where IRPOL is set to an angle of 0 degrees. Nested below each IRPOL iterator is an Offset iterator, which slides the source up and down the slit (for the object and sky pairs). In this way, sky-subtracted spectra are obtained at each of the eight angles. (You should also find a final IRPOL iterator at the end of the sequence; this returns IRPOL to an angle of 0 degrees after the observations have been completed.) The Observe eyeballs are the actual exposures.

The two slits in the spectro-polarimetry mask are each 20" long (Fig.1). Thus, when preparing a sequence, for "sky subtraction" a point source may be offset up and down the upper slit (e.g. with +6" and -6" offsets) as is shown in the figure below. For a moderately extended source you may nod between the two slits, so that positive and negative sky-subtracted spectra are obtained in the two halves of the array. For a very extended source (which overlaps the upper and lower slits) it may be necessary to nod completely off-source (i.e. orthogonal to the slit axis), so that object spectra are followed by blank-sky spectra at each waveplate angle.

Finally, the Repeat iterator in Fig.2 could be set to greater than unity to build up signal-to-noise and therefore polarisation accuracy.

Target Acquisition

The final element in each observation is the Target acquisition eyeball. Spectro-polarimetry sources are acquired in much the same way as normal spectroscopy sources. Observers unfamiliar with this process should review the UIST Spectroscopy web pages for further details.

Spectropolarimetry with UIST: Data Reduction

Basic Reduction with TSP or POLPACK

The Starlink packages Polpack and TSP can be used to reduce spectro-polarimetry data. The following two shell scripts could, for example, be used on a sequence of eight frames (an object-sky pair at the first four waveplate angles described above):

• specpol.prg - uses Polpack
• specpol-tsp.prg - uses TSP (much simpler script)

ORAC Data Reduction for Spectropolarimetry

For spectro-polarimetry of point sources, the recipe POINT_SOURCE_POL may be used. Flats and arcs with the same instrumental setup must be observed and reduced before using this recipe on a standard star or a science target. Also, the data must be acquired in the order prescribed in the Template library, i.e. object-sky pairs observed with at least four waveplate angles. If all eight waveplate angles are used, the pipeline will give reduced output from the first four angles, then co-add the results from the second four angles to the reduced group data.

Eight or Sixteen exposures in total are required for a reducible data-set.

Briefly, the pipeline will create bad-pixel-masked, flat-fielded spectral images from each frame with the suffix _ff. An approximate wavelength calibration is assigned to each of these to give the _wce frames. Sky frames are subtracted from source frames to give the _ss spectral images. Obviously, for each block of eight frames there will be four sky-subtracted _ss frames, one for each waveplate angle.

Each sky-subtracted image will contain a positive and negative spectrum for the e-beam and a positive and negative spectrum for the o-beam (see e.g. the right-hand panel in Fig.3 above). These are optimally extracted from the spectral image and the positive and negative spectra combined. The observations at each waveplate angle therefore yield an e- and an o-beam spectrum (see e.g. Fig.4 - left panel - below); eight waveplate angles will yield sixteen spectra in total. These are stored on disk as group spectra, e.g.

 gu20040717_416_0_E,    gu20040717_416_0_0, 
 gu20040717_416_22p5_E, gu20040717_416_22p5_0,
 gu20040717_416_45_E,   gu20040717_416_45_0 ... etc.

Finally, these data are processed by Polpack to produce the following:

 Intensity spectrum        - gu20040717_416_sp-I
 Q stokes-parameters       - gu20040717_416_sp-Q
 U stokes-parameters       - gu20040717_416_sp-U
 Polarisation percentage   - gu20040717_416_sp-P 
 Position Angle            - gu20040717_416_sp-TH
 Polarised intensity       - gu20040717_416_sp-PI

   > figaro
   > xtplane cube=gu20040717_416_sp-P ystart=0.5 yend=0.5 image=temp
      Warning: The data in the reference IMAGE have been re-shaped but the variance
      array was never updated. It will now be deleted.
   > ystract image=temp xstart=0.5 xend=0.5 spectrum=IJ-pol-spectrum
   > splot spectrum=IJ-pol-spectrum

   > kappa
   > ndfcopy gu20040717_416_sp-P IJ-pol-spectrum trim

A FITS binary table is also produced by the pipeline; gu20040717_416_pol.FIT, together with binned and thresholded versions (gu20040717_416_bin.FIT and gu20040717_416_pth.FIT) using the selection criteria: polarisation between 0 and 50%, S/N greater than 3, standard deviation less than 5% and intensity greater than 0.

Example e- and o-beam spectra from data taken at one of the eight waveplate angles are shown below (left). The spectra below-right show the final, reduced data: percentage polarisation and position angle plots (the gu20040717_416_sp-P and gu20040717_416_sp-TH files) derived from e- and o-beam spectra obtained at all eight waveplate angles.

Extracted e- and o- beam spectra	Percentage polarisation and Position Angle

There is at present no DR for Spec-polarimetry of extended sources. Frames may be partially reduced with REDUCE_SINGLE_FRAME or REDUCE_SINGLE_FRAME_NOFLAT. e- and o-beam spectra may then be extracted from the individual flat-fielded bad-pixel-masked frames and the ratioing done off-line with TSP or PolPack. Here is a simple script that could be used for this.

Additional Background Info - Calculating the State of Polarization

To measure the polarisation you require sky-subtracted spectra at at least the four waveplate angles: 0^o, 45^o, 22.5^o and 67.5^o (preferably also at 90^o, 135^o, 112.5^o and 157.5^o). 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 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 if data for the 0^o and 45^o WP positions are replaced in the above equations by data from the 22.5^o and 67.5^o positions, etc.

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 :

Beam Separations

The Wollaston prism in UIST acts as the polarimetric analyser, splitting the incoming radiation into the orthogonally polarised e- and o-beams, as described above. 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 (the UIST spec-pol pixel scale is 0.12 arcsec).

These separations are measured from the "bottom" beam to the "top" beam.

The wavelength dependence of the beam divergence is not very steep, though there may be a small amount of curvature of the spectrum along the dispersion direction, particularly when using the lower resolution grisms.

Calculating Exposure Times

To calculate the integration time needed for polarimetric observations with UIST you should apply the following equation to the sensitivity tables provided for spectroscopy (see main spectroscopy pages). Usually in polarimetry, a certain polarisation accuracy is needed to have any confidence in the result. For instance, if a source is 1% polarised an accuracy of at least ~0.3% would be necessary. This polarisation accuracy is converted into a required signal-to-noise on the flux (i.e. not per waveplate position) using this simple equation :

For example, to obtain a polarisation accuracy of 0.5% a S/N ~ 283 in the total, on-source integration time (not including overheads associated with telescope and waveplate moves) is needed. Note, however, the potential limitations on maximum signal-to-noise achievable with each instrument; discussed below.

In the thermal the above calculation is skewed slightly by the extra background that is introduced by the waveplate (which is, of course, in the incident beam). This will reduce the sensitivity slightly. Observers should account for this by reducing the sensitivity by ~0.5 mag with the L and M-band grisms.

EFFICIENCY: When writing telescope proposals, please remember that polarimetry observing involves telescope nods, reading out the array, AND waveplate moves. These factors all conspire to make observing less efficient. In your proposal you should therefore DOUBLE your observing time request to cover these overheads (i.e. assume 50% efficiency).

Signal-to-Noise Limitations

There is a limit to the signal-to-noise (S/N) that is possible with each of our instruments, because of inherent uncertainties in flat-fielding, variable sky levels and (for bright targets and therefore short exposure times) read-noise. Although tests have not been carried out with UIST, with UFTI measurements towards a 9th magnitude standard star (without IRPOL in place) suggest that a S/N per pixel of 2000 can be reached in the expected integration time. The fact that such high values of S/N can be reached is a reflection of the very "flat" UFTI array and the negligible read noise.

For spectro-polarimetry the S/N is limited by the multitude of variable atmospheric absorption features in the near-IR, as well as possible flat-field variations. On the same 9th magnitude source as discussed above, a maximum S/N of 200-300 was measured on sky-subtracted/flat-fielded spectra (a 60 second flat-field was used) with CGS4; this limit was reached after only 2 minutes of integration time. Of course, dividing by a standard helps considerably, by removing most of the atmospheric absorption lines and leaving only the "true" per-pixel statistical noise. Clearly, a good standard (with appropriate airmass/spectral type) must be observed if high S/N is needed with ordinary spectroscopy. Fortunately, with IRPOL's dual-beam capabilities, both e- and o-beams are observed simultaneously (and of course at exactly the same airmass). Hence, when ratioing these spectra to measure the polarisation you also compensate for atmospheric "noise" and so can expect to attain a much higher S/N.

Guide Stars for IRPOL

The IRPOL waveplate is positioned in the beam within ISU2; the plate is held in an opaque circular holder which is lowered into the beam by the Telescope System Specialist. Consequently, the waveplate holder obscures some of the field that may be used to find guide stars (should your target be too faint for the fast guider) - this Bird's Eye View of IRPOL through the hole in the primary illustrates this nicely.

The field-of-view accessible for guide stars with IRPOL is illustrated in the figure below; your target (central coordinates) are assumed to be located at the position of the cross. The waveplate holder is shaded grey and blue in the figure. Ideally, guide stars should be found within the inner white circle..

A guide star may be used outside the waveplate holder (outside the blue box, though inside the yellow circle, in the above diagram). Space is limited here and in some places blocked by the drive belts and arms of the holder (see the Birds-eye view). Because of the way IRPOL is mounted above the tertiary, these guide stars should be to the north-east or south-west of the target, and offset by 150"-250", depending on their exact location (250" is the radius of the full field for the guider). Of course care should be taken with guide stars near the edges of the waveplate holder when slides are used in your observing sequence.

A postscript version of the above figure is available here for printing.

Instrumental Ripple, Polarisation and Polarisation Efficiency

It has been found that spectro-polarimetry data often suffer from modulation or "ripple" in polarization and position angle. This artifact is probably due to multiple reflections between parallel surfaces within the waveplate, which then acts like a Fabry-Perot interferometer. A summary is given in the UKIRT Newsletter; more complete details and analysis are presented by Aitken & Hough (2001) 113, 1300.

To correct for this effect, we recommend that spec-pol users observe at eight waveplate angles. The additional angles, the nominal four incremented by π/2, are available in the OT, and supported by the DR pipeline. In this case and object-sky pair would be observed at 0, 45, 22.5 and 67.5 degrees, plus 90, 135, 112.5 and 157.5 degrees.

Instrumental Polarisation

The instrumental polarisation is expected to be low, certainly much less than 1%. We encourage all users to observe an unpolarised standard (and to communicate their results with JAC staff!). Some results are given here.

Polarisation Efficiency

Measurements of the polarisation efficiency at I, J, H and K have been secured with CGS4 (May 1999); we expect little change in these values with UIST, which uses the same prism material. The results obtained with the 40 l/mm grating in CGS4 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 in CGS4 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 with CGS4 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: P(%) = -398.1 + 272.6(wavelength) - 37.5(wavelength)²
M band: P(%) = -1014.1 + 463.1(wavelength) - 48.4(wavelength)²

Position Angle Calibration

To calibrate measurements of polarisation position angle with UIST + IRPOL, observers should also make their own deep observations of at least one polarised standard. Some targets have been observed by staff and visiting observers. Their results are tabulated here. At present, it is thought that a correction of about -20 degs is needed in the H and K bands with UIST spectro-polarimetry observations. UIST imaging-polarimetry observations indicate a similarly large correction.

The above p.a. correction is considerably larger than that derived for UFTI and IRCAM3, where a correction of -6 degrees has been measured. This is somewhat surprising, since the waveplate is above the tertiary mirror, so the orientation of the polarisation angle should be similar for all instruments. The difference may be due to the fact that the dispersion of the e- and o-beams, and so the axis of the prism, is not perfectly aligned with the columns of the arrays in any of the instruments.

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