## Chapter 2POL-2 Overview

### 2.1 The instrument

The POL-2 instrument is a linear polarimetry module for the Submillimetre Common User Bolometer Array-2 (SCUBA-2), a 10,000 bolometer camera on the JCMT  . POL-2 in itself is not a detector - thus requiring SCUBA-2 and its detectors for operation. SCUBA-2 operates simultaneously at both 850 and 450 µm. The POL-2 instrument is currently commissioned at 850 µm only1.

.  Figure 2.1: POL-2 mounted on the front of SCUBA-2. The left image shows the SCUBA-2 window. The right image shows the components of POL-2 inserted in front of the SCUBA-2 window: the calibrator grid, rotating half-wave-plate (HWP) and the analyser grid. The calibrator grid is only inserted for test purposes.

#### Polarisation

In polarimetric terms light is conventionally described by the four Stokes parameters: $I$, $Q$, $U$ and $V$.

$I$ is the total intensity; $Q$ is the radiation linearly polarised in the direction parallel or perpendicular to the reference plane. $U$ is the radiation linearly polarised in the directions 45${}^{\circ }$ to the reference plane; and $V$ is the circularly polarised radiation.

POL-2 is designed to characterise linear polarisation. The $V$ parameter, consequently, is not discussed further with the focus on $I$, $Q$ and $U$.

The linear Polarised Intensity (I${}_{\text{p}}$) and polarisation angle ($\theta$) can be described as:

 ${I}_{\text{p}}=\sqrt{{Q}^{2}+{U}^{2}}$ (2.1)
 $\theta =0.5arctan\left(U/Q\right)$ (2.2)

with Q and U related to the polarisation angle and the polarised intensity by:

 $Q={I}_{\text{p}}\text{cos}\left(2\theta \right)$ (2.3)
 $U={I}_{\text{p}}\text{sin}\left(2\theta \right)$ (2.4)

where

 $Q={Q}_{\text{m}}-I.i{p}_{\text{q}}$ (2.5)
 $U={U}_{\text{m}}-I.i{p}_{\text{u}}$ (2.6)

where ${Q}_{\text{m}}$ and ${U}_{\text{m}}$ are the measured values of Q and U. I is the astronomical total intensity. IP is the instrumental polarisation. The IP affects both Q (via $i{p}_{\text{q}}$) and U (via $i{p}_{\text{u}}$).

#### How POL-2 works

POL-2 is located in front of the window to the SCUBA-2 instrument (as is seen in Figure 2.1), and covers the full field of view of SCUBA-2. The POL-2 polarimeter uses three optical components that cover the full field of SCUBA-2:

(1)
a wire-grid polariser used as a calibrator (only included in the beam for test purposes),
(2)
a Half-Wave Plate (HWP), and
(3)
a second wire-grid polariser used as an analyser.

These components can be seen in Figure 2.1. A schematic of POL-2 is given in Figure 2.2. Figure 2.2: The main optical components in a typical single-beam imaging polarimeter such as POL-2 (taken from SUN/223).

Rotating the HWP rotates any linearly polarised component of incoming radiation. The HWP rotates this incoming linear polarisation with twice the speed of the HWP angle ($\delta$) producing the effective analyser position ($\varphi$ - as defined in the POLPACK documentation), such that:

 $\varphi =2\delta$ (2.7)

The rotating linearly polarised component is transmitted or reflected by the grid, causing a modulation in the transmitted intensity. The amplitude of the polarised component transmitted by the polariser is $\sim$cos($\varphi$) while the power is $\sim$cos${}^{2}$($\varphi$). Figure 2.3: Left: If there was a single rotating analyser this would be the resulting curve of the power transmitted of the linearly polarised component. Right: With the HWP the linearly polarised component is rotated at twice the speed. It may be useful to remind the reader of the trigonometric identity:
cos${}^{2}$x = 0.5(1+cos(2x))

The radiation passing through the polarimeter is detected by SCUBA-2. The detected intensity (I${}_{\text{detected}}$) is a combination of both the unpolarised intensity (I${}_{\text{unpolarised}}$) and the linearly polarised intensity (I${}_{\text{p}}$)2. This detected intensity can be described by:

 ${I}_{\text{detected}}=\frac{{I}_{\text{unpolarised}}}{2}+{I}_{\text{p}}\cdot \left(\frac{1+cos\left(2\varphi -2\theta \right)}{2}\right)$ (2.8)

with the above equation being in terms of the effective analyser angle, $\varphi$ and the angle of the polarisation ($\theta \right)$. This can also be expressed in terms of the the HWP angle ($\delta$).

 ${I}_{\text{detected}}=\frac{{I}_{\text{unpolarised}}}{2}+{I}_{\text{p}}\cdot \left(\frac{1+cos\left(4\delta -2\theta \right)}{2}\right)$ (2.9)

#### The Half-Wave Plate

As described in the POL-2 commissioning document the HWP is constructed from five individual synthetic sapphire layers approximately 0.9 mm thick and 200 mm in diameter. The transmission properties of sapphire are generally good at the SCUBA-2 wavelengths but are dependent on the thickness and ambient temperature. The total effective transmission of the HWP integrated across the 850 and 450 µm filter bands are about 86% and 57% respectively (Savini et al. 2009 - insert full reference).

The HWP rotates the incoming linear polarisation with twice the speed of the wave plate angle. The HWP is typically rotated at 2 Hz, providing a fast modulation of any linear polarisation by 8 Hz (see Equation 2.9). The data acquisition rate is $\sim$175 Hz, yielding 20 samples per cycle. The atmosphere is stable on the order of 2 Hz and can be removed. Figure 2.4: The incoming polarised radiation (with a polarised angle, $\theta$, of zero) is attenuated by the HWP. The HWP rotates at 2Hz (through $2\pi$) so we see the signal is modulated at 8Hz as the instrument scans at 8′′/s. Figure 2.5: The three blades that combine to form POL-2 are partially extended showing the two wire grids and the achromatic HWP. The two wire grids are the calibrator grid and the analyser grid. The rotating HWP is located between these two fixed grids. The calibrator grid is only inserted for test purposes. Stiffeners can be seen on all three blades. The one for the HWP is particularly thick. Their purpose is to reduce vibrations while the HWP spins.

### 2.2 Instrumental Polarisation

At the angular resolution of JCMT, planets such as Uranus should appear as unpolarised point sources. In practice, however, POL-2 observations of such sources exhibit a measurable level of polarisation – albeit typically less than 1.5% at 850 $\mu$m. This is evidence that some part of the incoming astronomical radiation is being partially polarised by one or more of the components of the telescope/POL-2/SCUBA-2 that are in the light path. This polarisation is referred to as "Instrumental Polarisation" (IP).

In order to establish the true Q and U from an astronomical source, it is necessary to correct for this effect. For the case of a low degree of polarisation in the incoming radiation and a low degree of IP, the following is a good approximation for correcting the measurement for the effects of the IP:

 $Q={Q}_{\text{m}}-I.i{p}_{\text{q}}$ (2.10)
 $U={U}_{\text{m}}-I.i{p}_{\text{u}}$ (2.11)

where ${Q}_{\text{m}}$ and ${U}_{\text{m}}$ are the measured values for a single bolometer sample at some point on the sky. $Q$ and $U$ are the true (corrected) values, $I$ is the astronomical total intensity at the same point on the sky (i.e. the total intensity after removal of the sky and electronic backgrounds) and $i{p}_{\text{q}}$ and $i{p}_{\text{u}}$ are factors that may vary slowly with focal plane position and/or azimuth and elevation.

IP correction of a POL-2 map therefore requires a total intensity map of the same area of the sky to be available. This total intensity map is referred to as the IP reference map.

Whilst flat mirrors or surfaces will produce a small, constant polarisation across the beam, curved mirrors and other structures (for example the secondary mirror supports) will produce more complex polarisation effects, and these may distort the beam shape. Side-lobes can often show up with strong (typically 10-20%) polarisation but these effects are usually far from the main-beam. Calculations of typical antenna patterns for symmetrical Cassegrain antennas have not predicted strong polarisation in the main beam.

The JCMT IP footprint is stronger than might be expected from the above considerations above (though typically less than 1.5% of the total intensity), and has the following distinctive features:

(1)
the polarisation intensity is elevation dependent,
(2)
there is ellipticity of the beam and it is elevation dependent, and
(3)
the beam is elongated in the horizontal direction.

The dominant source of IP at the JCMT is the woven Goretex membrane, used as a wind blind. This membrane introduces both losses and polarisation. This effect is elevation dependent.

### 2.3 Observing mode

The standard POL-2 observing mode, POLCV_DAISY, is a “scan and spin” mode, in which the telescope is moving continuously in a Daisy-type pattern while the HWP spins.

The POLCV_DAISY scan mode is similar to the established Daisy scan mode routinely used for non-polarimetric SCUBA-2 observations of point-like or compact sources. However, it is slightly altered to allow for a slower telescope scanning speed. Figure 2.6: Left: Scan pattern from a typical SCUBA-2 CV_Daisy observation. Right: Scan pattern from a POL-2 Daisy. The standard POLCV_DAISY scan parameters are given in Table 2.1

The telescope must scan slowly enough to obtain sufficient data at each point on the sky to allow good $Q$ and $U$ values to be determined. The current commissioned scan pattern has a size of 200′′ and a scan speed of 8′′/s. The data reduction splits the data stream into short segments and determines a pair of $Q$ and $U$ values from each segment.

The length of each such data segment is the time it takes the telescope to traverse a pixel in the generated map. With the current scanning parameters this is 0.5 and 0.25 seconds for 850 and 450 µm, respectively. The modulation generated by any polarisation is 8 Hz at the current HWP rotation speed (2 Hz).

The standard POLCV_DAISY scan parameters are given in Table 2.1 and shown in Figure 2.7.

 Parameter Value Half-wave plate rotation frequency 2 Hz Antenna scanning speed 8′′/s R${}_{0}$ (map pattern radius)† 133′′ R${}_{t}$ (turn radius) 99′′ R${}_{a}$ (nominal avoidance radius) 77′′

Table 2.1: The scan parameters used in the POLCV_DAISY mode. †This radius is not the size of the resulting map. Figure 2.7: Detail of POLCV_DAISY. ${R}_{0}$ is the map pattern radius, ${R}_{\text{t}}$ the turn radius, and ${R}_{\text{a}}$ is the nominal avoidance radius. For more details see Table 2.1.

### 2.4 The raw data

SCUBA-2 is the detector for POL-2, and as such, the raw data format of POL-2 data is the same as a typical SCUBA-2 observation. The sequence for both observations is:

(1)
dark noise,
(2)
flat-field,
(3)
science scans, and
(4)
flat-field.

The SEQ$\text{_}$TYPE keyword in the FITS header may be used to identify the nature of each scan. When you access raw data from the CADC archive http://www3.cadc-ccda.hia-iha.nrc-cnrc.gc.ca/jcmt/you will get all of the files listed above.

Critically the INBEAM keyword in the FITS header may be used to identify if POL-2 is in the beam, and hence differentiate between SCUBA-2 and POL-2 observations.

Tip:
Use the Kappa command fitslist to see all FITS headers in a particular NDF. To obtain a specific header simply use the command fitsval :
% fitsval s8a20160112_00056_0001.sdf INBEAM
pol

The FITS header information may also be viewed via the Gaia View / FITS header drop-down menu option.

Shown below is an incomplete list of the raw files for a single sub-array (in this case s8a) for a short POL-2 observation. The first and last scans are the flat-field observations, which occur after the shutter opens to the sky at the start of the observation and closes at the end (note the identical file size); all of the scans in between are science scans.

% ls -lh /jcmtdata/raw/scuba2/s8a/20160112/00056
-rw-r--r-- 1 jcmtarch jcmt 5.6M Jan 12  2016 s8a20160112_00056_0001.sdf
-rw-r--r-- 1 jcmtarch jcmt 7.9M Jan 12  2016 s8a20160112_00056_0002.sdf
-rw-r--r-- 1 jcmtarch jcmt  25M Jan 12  2016 s8a20160112_00056_0003.sdf
-rw-r--r-- 1 jcmtarch jcmt  25M Jan 12  2016 s8a20160112_00056_0004.sdf
-rw-r--r-- 1 jcmtarch jcmt  25M Jan 12  2016 s8a20160112_00056_0005.sdf
...
-rw-r--r-- 1 jcmtarch jcmt  25M Jan 12  2016 s8a20160112_00056_0025.sdf
-rw-r--r-- 1 jcmtarch jcmt  25M Jan 12  2016 s8a20160112_00056_0026.sdf
-rw-r--r-- 1 jcmtarch jcmt  25M Jan 12  2016 s8a20160112_00056_0027.sdf
-rw-r--r-- 1 jcmtarch jcmt  22M Jan 12  2016 s8a20160112_00056_0028.sdf
-rw-r--r-- 1 jcmtarch jcmt 7.9M Jan 12  2016 s8a20160112_00056_0029.sdf

The SCUBA-2 data acquisition (DA) system writes out a data file every 30 seconds; each of which contains 22 MB of data. The only exception is the final science scan which will usually be smaller (7.9 MB in the example above), typically requiring less than 30 seconds of data to complete the observation.

Note: All of these files are written out eight times, once for each of the eight sub-arrays. It should also be noted that the POL-2 instrument has not yet been fully released from commissioning at 450 $\mu$m (a “shared risk” approach is currently in use).

The main data array in each NDF is a cube, with the first two dimensions corresponding to bolometer columns and rows within a sub-array, and the third dimension corresponding to time slice index (sampled at roughly 200 Hz).

A standardised file naming scheme is used in which each file name starts with the sub-array name, followed by the UT date of the observation in the format yyyymmdd, followed by a five-digit observation number, followed by the sub-scan number. The name ends with the standard suffix .sdf used by all Starlink NDF data files. For instance, the files listed above hold data from the s8a sub-array for Observation 34 taken on 12th January 2016.

##### Units/Calibration

Raw POL-2 data come in uncalibrated units. The first calibration step is to scale the raw data to units of pico Watts (pW) by applying the flat-field solution. This step is performed internally by the Smurf command calcqu – used to calculate I, Q and U time-streams from the raw data – but can be done manually when examining the raw data.

If the purpose of a given POL-2 observation is to determine the percentage polarisations or vector angles within a source/region of interest then the data may remain in pW. On the other hand, if the purpose is to establish the absolute polarised intensities then a value for the Flux Conversion Factor (FCF) is required.

The resulting map may have the FCF applied to convert it into units of janskys. As is recommended with SCUBA-2 observing, it is advisable to check that the FCF value applied to the data is sensible (and must be done manually). For more details see Chapter 4.5.

1450 µm data can in fact be processed using the same commands as 850 µm data, but the noise levels and other possible artefacts have not yet been fully characterised. Note, the default pixel size at 450 is 4 arc-seconds

2The total intensity of the source, $I$, is ${I}_{\text{unpolarised}}+{I}_{\text{p}}$.