# Circular Polarimetry with UFTI and UIST

**Introduction**

Circular polarimetry is similar to linear polarimetry in the sense that incoming radiation passes through a waveplate and a wollaston prism. However, instead of a halfwave plate one uses a quarterwave plate, to convert the circularly polarized light of the incoming beam into linearly polarized light, so that it may be analysed in the usual way. The position angle of the linear polarized vector is defined by the position angle of the quarterwave plate and by the sense of rotation (left or right) of the incoming circularly polarized beam.

*The quarter waveplate available at UKIRT is on loan from the University of Hertfordshire in the U.K.. It is therefore available to all UKIRT users, in collaboration with the Univ. of Herts. Please contact Chris Davis at JAC (c.davis at jach.hawaii.edu) if you are interested in using the quarterwave plate.*

The quarterwave plate is mounted in the normal IRPOL2 holder inside ISU2 (below the UKIRT mirror cell; above the UKIRT tertiary/dichroic mirror). Note that the available field of view for guide stars – through the waveplate – is smaller than the field available for linear polarimetry through the larger halfwave plate. The quarterwave plate also vignettes some of the UFTI and UIST field of view (see below).

Because the quarterwave plate is not exactly quarterwave for all wavelengths, the circular polarimeter is partly sensitive to linear polarisation, which for many astronomical sources considerably exceeds the circular polarisation component. Therefore, one may depolarise the linear component by mounting a *halfwave* plate ahead of the quarterwave plate and setting it into continuous rotation. The best cancellation occurs when the exposure time used with UFTI or UIST is *(1) an integer multiple of the rotation period of the halfwave plate *and *(2) much larger than the rotation period*. This should eliminate systematic errors due to linear polarisation, and invert but leave otherwise intact, the true circular polarization. The rotating halfwave plate is controlled by a separate electronics box which is not normally mounted on the telescope (*Note to SS: the day crew must be asked to mount this on ISU2 – and dig out the two cables – well before the run*).

**Circular Polarimetry with UIST and UFTI**

If you are unfamiliar with polarimetry at UKIRT, it is extremely important that you read the main UFTI, UIST Imaging or UIST Spectroscopy web pages on polarimetry. Below we give only additional information specific to circular polarimetry.

Because IRPOL2 is mounted above the UKIRT tertiary, polarimetry is potentially possible will all instruments at UKIRT. However, as noted above, the field-of-view of the circular wave plate is limited. For imaging circular polarimetry, UIST and UFTI essentially see the same field on the sky; thus, the vignetting is similar with both cameras. The figure below shows the situation with UIST. The vignetting does not affect circular spectro-polarimetry.

*Raw Circular Polarimetry Images with UIST*

Both UIST and UFTI use a focal-plane mask, comprising two 20″-wide horizontal apertures; two 20″-long slits are used for spectro-polarimetry. The wollaston prism, downstream of the masks in each instrument, will then project e- and o-beam images (or spectra) of the two apertures onto the array (see above). Usually the DR uses the lower e- and o-beam images for a sky measurement. In imaging sources can be jittered left-right to account for bad pixels, etc. (left-right is east-west with UFTI, but north-south with UIST!); with spectro-polarimetry the target can be nodded up and down the slit in the usual way.

**Data Acquisition and Reduction**

The “safest” observing mode is to obtain data with the quarterwave plate at four angles; 0, 90, 45 and 135 degrees (i.e. angles twice as large as those used for linear polarimetry). However, *if the fast axis of the quaterwave plate is known, data at only two angles are required* (see below). At each wave plate angle, the source should be jittered within the available field-of-view, as per linear polarimetry. In imaging mode, jitters should be limited to less than 20″ left-right. The “normal” imaging polarimetry recipes, POL_JITTER and POL_ANGLE_JITTER, have been adapted so that they will also reduce circular polarimetry data (thanks to Malcolm Currie for his work on this).

Darks, flats+arcs and/or sky flats should be obtained in the usual way. With the quarterwave and halfwave plates installed, in imaging mode the sky background through the broadband H and K filters in UIST is about 10 counts per second, so 60 second exposures at jittered positions on the sky and at each waveplate angle should be ok. Longer exposures will be needed at J; the sky background will be about 2 counts per second. Dome flats may be preferable at shorter wavelengths. The DR recipes SKY_FLAT_POL and SKY_FLAT_POL_ANGLE may be used to reduce the sky flat observations..

Circular spectro-polarimetry is possible with UIST. Again, data should be obtained as per standard spectro-polarimetry; UIST imaging acquisition should be used to put the source on the slit, and an object/sky pair observed at each of the quaterwave plate angles.

**Focus**

Note that with the extra waveplate the UIST+Pol fine-focus at the telescope *may* need checking. (In Oct ’06 circular spectro-polarimetry data were ascquired with no additional focus offset.)

**Finding Guide Stars with Circ-Pol**

The quarterwave plate used for circular polarimetry is smaller than the linear halfwave plates. This can make finding guide stars even more challenging! The field-of-view through the quarterwave plate is ~35 arcsec in radius. However, the aperture in the UIST (and UFTI) polarimetry mask is offset from the centre of the plate (see below). Consequently, WITH UIST, guide stars may be up to 15 arcsec EAST of your target, or 55 arcsec WEST of the target. See the diagramme below for an estimate of the accessible field of view. A similar situation exists with UFTI, though the GS should be within 15 arcsec North or 55 arcsec South of the target.

**Installing the waveplates and cabling up the electronics **

The *quarterwave plate* is installed in the normal IRPOL2 arm in ISU2. However, the quarterwave plate is smaller than the usual halfwave plates, so an additional circular holder is needed. Once installed, the IRPOL2 arm should be lowered into the beam.

The *halfwave plate* is mounted into a separate platform which includes a motor for rotation of the plate. The platform + motor are then mounted on top of the quarterwave plate inside ISU2; tighten the four screws to lock the mount in place on top of the IRPOL2 arm.

**The two wave plates in their mounts**

*Two cables*, a coax and a BNC cable, connect the motor on the platform to an electronics box that is usually installed inside one of the blue cabinets on the telescope. Both cables are connected to the back of the electronics box. The box is probably powered on at the power strip in the same rack.

**The electronics box used to rotate the halfwave plate**

With both wave plates installed and the motor cabled up, switch on the electronics box; the halfwave plate should immediately start to rotate (on the electronics box only the green power and system lights should be on). The speed of rotation can be adjusted from the front of the box (silver dial). With the blue “overflow” knob set to OSC. FREQ., the red “gate time” knob set to 1s, and the speed on the LED display set to .98, the rotation rate should be about 1 revolution every 2 seconds. *A rate of 1Hz was used in 2006.* The halfwave plate should be left in continuous rotation for the duration of the observations.

The quarterwave plate is of course controlled either from the IRPOL Epics window or from an IRPOL iterator in the OT and OCS (see the UIST Imaging or Spectro-polarimetry web pages for full details).

*(Thanks to Tim Gledhill for taking the photos…)*

**Circular Polarimetry – Some Background Information**

Light is a transverse electromagnetic wave with perpendicular E and B vectors. We consider the E-vector only, since this is what we observe, and define the orientation of E in terms of E(x) and E(y) (two orthogonal waves with the same frequency). If one adds E(x) and E(y) in quadrature then, *depending on the ratio of the two amplitudes and the value of the phase difference*, linear, circular or in general elliptically polarised light can be produced.

Linear and circular are special cases where E(x) and E(y) are in-phase and 1/4 of a wave (45 degrees) out of phase, respectively. The quaterwave plate works by *retarding* one of the two E vectors (E(x) say) by 1/4 of a wave, bringing the two vectors into phase and thus converting circular polarised light in to linear polarised light. This light can then be analysed as linearly polarised radiation.

Light is usually made up of unpolarised (natural) and polarised light. By measuring the intensity through a polariser (a wave plate) at different orientations, the intensity varies from I(max) to I(min) such that the light is *linearly* polarised by an amount [I(max)-I(min)]/[I(max)+I(min)]. The total intensity is simply I(max)+I(min). The orientation of the polariser corresponding to I(max) is the position angle of the electric vector of the polarised light.

Four parameters are necessary for measuring the state of polarisation; the * Stokes Parameters*. Q and U describe linear polarisation, while V describes circular polarisation. The total intensity, I, includes both natural and polarised intensities.

The incoming radiation is split into orthogonally-polarised e- and o- beams by a * Wollaston prism*. The intensity of a target is derived from the sum of these intensities, averaged over the different waveplate angles. The ratio of the e- and o- beams gives the polarisation.

**Waveplate angles**

Above we note that observing at four angles, 0, 45, 90 and 135 degrees, will give a circular polarisation measurement. These angles are effectively points on a sine wave, in which the maximum e-beam/o-beam ratio is the amplitude. The peaks of the sine wave correspond with the fast axis of the quaterwave plate (the fast axis is not necessarily at one of the four waveplate angles).

If the orientation of the fast axis is known, then the stokes V parameter can be derived from observations at just two angles, the angle of the fast axis and at this angle plus 90 degrees. i.e.

*V = (R _{v} – 1) / (R_{v} + 1) *

where

*R _{v} = SQRT( [I_{e}/I_{o}]_{a} / [I_{e}/I_{o}]_{a+90} ) *

*a* being the angle of the fast axis.

If, however, *a* is not known, then data acquired at the four nominal angles, 0, 90, 45 and 135 degrees, will give the V Stokes parameter. This is determined by adding in quadrature the result from the above equations for observations at 0 and 90 degrees with the result for 45 and 135 degrees.

The angle of the fast axis can be established by observing a source of circularly polarised light (BN is a good target) through the quarterwave plate. a is the angle at which the difference in e- and o- intensities is at a maximum. (At a+90 degrees e/o will be flipped.) At angles shifted by 45 degrees from the fast axis – i.e. where our sine wave is at zero – e- and o-beams are equal, as in the example below.

*Circular spectro-polarimetry of BN*

Current orac-DR recipes assume that data will be taken at four angles, 0, 45, 90 and 135 degrees. The recipes simply assume that these four angles correspond to 0, 22.5, 45 and 67.5 degrees in linear polarisation, and thus produce images or spectra * labelled* I, Q, U, P and theta (remember we are not measuring linear polarisation, so these labels are not necessarily meaningful). Because the fast axis of the quaterwave plate at UKIRT is thought to be close to 45 degrees, then U/I (from the ratio of e and o at 22.5 and 67.5 degrees; equivalent to 45 and 90 degrees in the circular case) gives a polarisation value, while Q/I gives no polarisation. The recipes add these two polarisation measurements in quadrature, though effectively the second measurement is adding only noise.

**Displaying Circular Polarisation**

The percentage circular polarisation, V/I, can be displayed as a grey-scale image, with e.g. black showing positive and white showing negative polarisation, or as vectors with vertical vectors showing positive and horizontal vectors showing negative polarisation. The length of the vector then illustrates the percentage polarisation. (As viewed by the observer, right-circularly polarised light rotates clockwise and is positive; left-circularly polarised light rotates anti-clockwise and is negative.)

A good test object for circular polarisation is the BN object in Orion (5h 35m 14.12s, 5� 22′ 22.9″, J2000), where circular polarization to the east and west of the source IRc2, approaching +17% in the K band, has been measured by Chrysostomou et al. (2000).

**PATT proposals and exposure times**

As noted earlier, users need to collaborate with the University of Hertfordshire. Please contact Chris Davis for details (c.davis at jach . hawaii . edu).

When writing your proposal, assume similar overheads as for linear polarimetry, plus one hour at the start of the run to set up and test the additional equipment. When calculating exposure times use the same equation to estimate the S/N needed to attain the polarisation accuracy, dP, of your observations. The integration time required to reach this S/N can be calculated from the UIST and UFTI sensitivity web pages.

S/N = sqrt(2)/dP

However, be aware that the second waveplate will probably introduce additional background at longer wavelengths.

Time should also be dedicated to observing standard stars.

**Circular Polarimetry with UIST**

Circular Polarimetry with UIST was “commissioned” in Spring 2004. The image below shows results from an early version of the DR pipeline. At the time the angle of the fast axis of the quarterwave plate was not known. BN was therefore observed at 0, 45, 90 and 135 degrees. These four datasets were reduced using a *linear polarimetry* DR recipe. The recipe thus produced “Q” and “U” images which the DR displayed as if linear polarisation were being measured. In this case, however, the length of the vectors (Q^2 + U^2) actually represents V/I, the degree, or percentage, of circular polarisation. The angles of the vectors should all be the same, reflecting the orientation of the quarterwave plate fast axis with respect to the dispersion axis of the prism, except when the circular polarisation changes sign, in which case the vectors flip by 90 degrees. In UIST the prism disperses exactly E-W (the grism wheel stepper motor is set so that the prism disperses along columns).

*Circular polarisation from 4 WP angles*

The above observations indicate that the fast axis of the quarterwave plate, with respect to the wollaston in UIST, is between 30 and 45 degrees. This result was confirmed in October 2006, when circular spectro-polarimetry, again at four quaterwave plate angles, was acquired on BN itself (see spectra above). Although the fast axis still needs accurate measurement, future observations at just two quarterwave plate angles should be sufficient to measure the circular polarisation of any given target.

**References & further info.**

Bastien P., 1991, in “The physics of star formation and early stellar evolution”, Lada & Lada eds, (Kluwer), p.709.

Chrysostomou A.C., Gledhill T.M., Menard F., Hough J.H., Tamura M., Bailey J., 2000, MNRAS, 312, 103