TADPOL

Welcome to the collaboration wiki for TADPOL (Telescope Array Doing POLarization), one of the key projects at CARMA, the Combined Array for Research in Millimeter-wave Astronomy.

Click here for the official TADPOL website, which includes a list of collaborators and their institutions, publications, presentations, and data products.

The CARMA 1mm polarization system

Full-Stokes polarization measurements are possible in the CARMA 1mm (210-270 GHz) band. Each 10-m and 6-m telescope is equipped with two 1mm receivers, one sensitive to left circular polarization (L), the other to right circular polarization (R). The two receivers share a common feed horn; the two polarizations are separated by a waveguide orthomode transducer.

Do not confuse the FULLSTOKES and DUALPOL observing modes. DUALPOL observations offer improved SNR for spectral line observations, but measurement of all 4 Stokes parameters (I,Q,U,V) is possible only in FULLSTOKES mode.

Observing Modes

Correlator Mode	Correlations	Bands	Benefit
LL	LL	8	More tunable windows
DUALPOL	LL,RR	4	Improve SNR on spectral lines
FULLSTOKES	LL,RR,LR,RL	4	Measure Stokes I,Q,U,V

Polarization measurements require 2 extra calibrations -- XYphase and leakage -- in addition to the usual passband and gain calibrations.

XYphase (L-R phase difference)

"XYphase" (in MIRIAD lingo) is the phase difference between the L and R channels caused by delay differences in the receiver, underground fiber-optic cables, and downconverter cabling. XYphase calibration errors rotate the position angles of linear polarization vectors on the sky. For circularly polarized feeds, changing the XYphase by 180º rotates polarization vectors by 90º.

To calibrate XYphase one must observe a linearly polarized source with a known position angle. (LR and RL visibility amplitudes are zero for unpolarized sources, hence unpolarized sources provide no information about the L-R phase difference.) At cm wavelengths it's common to observe 3c286 for this purpose, but 3c286 is quite weak at 1mm.

Fortunately, at CARMA it's possible to generate a linearly polarized calibration signal by rotating wire grids into the beams of the 10-m telescopes. With the grid in place, vertically polarized radiation reaching the receiver originates from the sky, while horizontally polarized radiation originates from a room temperature load behind the grid. Since the ambient load is much hotter than the sky, the receiver sees thermal noise that is strongly horizontally polarized. The L-R phase difference can be derived, channel by channel, from LR autocorrelation spectra obtained with the grids in place. With a 10 sec integration, the signal to noise is sufficient to measure the phase difference in a 10 MHz-wide channel to an accuracy of about ± 2º. The XYphase calibration can be done while the telescopes are tracking a calibrator, a source, or blank sky -- provided the weather is good, the horizontally polarized noise power from the ambient load overwhelms any signal coming from the sky.

The XYphase corrections are derived by fitting a passband to the LR autocorrelation spectra using a new MIRIAD program XYAUTO (a hacked version of MFCAL). Rewriting the data applies the passband corrections, setting the L-R phase difference to zero for all 10-m spectra. Following this, the regular passband is fit with MFCAL, using any of the 10-m antennas as the reference antenna. Since the L-R phase difference is zero for every channel of the refant spectrum, and since the normal passband correction ensures that all LL and RR cross-correlations have zero phase with respect to the reference antenna, applying the regular passband transfers the XYphase correction to all other antennas, even those without grids.

Additional notes:

1. The master script initiates XYphase grid calibrations.
   
2. When grids are in place, CARMA data are taken with intent=P. Use select=purpose(P) during data reduction.
3. The MIRIAD header variable evector specifies the position angle of polarized radiation that gives an L-R phase difference of zero. Accordingly, the MIRIAD filler at CARMA sets evector=pi/2, corresponding to the position angle of the horizontally polarized calibration source.
   
4. A potential source of error in the autocorrelation XYphase calibration is crosstalk between the L and R receivers; these share a common LO, so they are not phase-switched relative to each other. We believe that the autocorrelation method is adequate because (1) amplitudes increase by roughly an order of magnitude when the grids are inserted, suggesting that the calibration signal is much larger than the crosstalk; and (2) LR and RL crosscorrelation phases observed on strong calibrators with the grids in place also are zeroed by the XYphase correction.

Leakage

Leakage corrections compensate for imperfections in the waveguide polarizers and orthomode transducers, which do not perfectly separate the L and R circular polarizations.

The leakage corrections are two complex numbers per antenna. Leakages can be derived from observations of a bright source (either polarized or unpolarized) that is observed over a wide range of parallactic angle, using the MIRIAD program GPCAL. The parallactic angle changes most rapidly for high declination (dec ~ 20-50º) sources near transit.

Leakages are a function of frequency, and thus it is best to apply the leakage corrections separately for data in the LSB (windows 1,3,5,7) and USB (windows 9,11,13,15). Since the CARMA receivers have no moving parts, the leakages are extremely stable with time. We have found that it is best to solve for leakage terms using the calibrator in each track, rather than applying the grand-average leakage solutions computed using multiple tracks.

Ripples in leakage corrections

An instrumental problem that remains unsolved is small scale structure (i.e. ripples) in the polarization leakage corrections. The ripples have not been a big problem for TADPOL because (1) for wideband observations the ripples tend to average out, and (2) over the course of a 4- or 5-hour observing track, as the parallactic angle of the source changes, the remaining errors tend to wash out. The ripples are, however, a big concern for projects that want to measure polarization in narrow frequency channels (e.g. searches for the Goldreich-Kylafis effect in molecular lines), or for short time intervals (e.g. SgrA* polarization monitoring).

The ripples signify that there are two or more paths by which signals with one polarization leak into the opposite polarization. These paths have different delays, so the leakage signals beat with one another. One path surely is imperfections in the waveguide circular polarizers, which are expected to generate leakages at the ∼5% level. The other may be signals that reflect off one SIS mixer and couple into the opposite mixer, or crosstalk between the RCP and LCP IFs in the receiver cabin or the correlator room. We are investigating these problems; unfortunately, measurements of the leakages in narrow bandwidths require long observations of strong calibrators.

Setting up the observing script

Here is the typical frequency and correlator setup that we use for TADPOL observations. We measure dust continuum in bands 1,3,5 and ¹²CO/SiO in band 7. Note that only 2BIT mode is allowed for the 500 MHz bandwidths in FULLSTOKES mode.

tuning = {
  'restfreq' : 223.821,  # [GHz] LO1 freq
  'sideband' : USB,    # Sideband for first LO (LSB or USB)
  'IFfreq'   :   0.0,   # [GHz] IF frequency
}

def setCorrelator(tuning):
  clearastroband(0)
  configastroband(1, "FULLSTOKES", BW500, tuning['restfreq'] + 6.0,   AUTO, 'none', 'none', bits=CORR_2BIT)   
  configastroband(3, "FULLSTOKES", BW500, tuning['restfreq'] + 7.5,   AUTO, 'none', 'none', bits=CORR_2BIT)
  configastroband(5, "FULLSTOKES", BW500, tuning['restfreq'] + 8.0,   AUTO, 'none', 'none', bits=CORR_2BIT)
  configastroband(7, "FULLSTOKES", BW31,  tuning['restfreq'] + 6.717, AUTO, 'none', 'none', bits=CORR_2BIT)  # CO in USB, SiO in LSB

Two new keywords in the sources dictionary -- "intervalPol" and "tintpol" -- set up the XYphase calibrations on the 10-m telescopes. These calibrations are performed just after the gain calibrator is observed, roughly once per calibration cycle.

sources = {
  'target'       :    'L1157',
  'mosaicTarget' :      False,
  'tintTarget'   :         15,  # [minutes] time per cycle *** per pointing ***
  'phaseCal'     : '1927+739',
  'tintPhaseCal' :          3,  # [minutes]
  'callist'      :       None,
  'intervalPol'  :       0.66,  # [hours] interval for XYphase grid measurements
  'tintPol'      :        0.5,  # [minutes] integration time with grids in
}

Data reduction

Key data-reduction steps for polarization data:

1. Derive XYphase corrections with XYAUTO, rewrite data with UVCAT to apply.
2. Derive normal passband with MFCAL, rewrite with UVCAT to apply. At this point all passband and XYphase corrections have been applied.
3. Fit gains vs time with MFCAL; either fit leakages with GPCAL or copy pre-fitted leakages into data with GPCOPY. Data are fully calibrated.
4. Map all 4 Stokes parameters: invert vis=$vis.pb map=$MAP.I.mp,$MAP.Q.mp,$MAP.U.mp,$MAP.V.mp stokes=I,Q,U,V ...

Here are 2 sample scripts: pol_basic.csh is a bare-bones polarization reduction script, with minimal data inspection. It expects that all correlator windows have been set up in wideband mode. reduce.csh is a fancier script that is customized for TADPOL observations. It expects that correlator windows 1,3,5,9,11,13 are BW500 for continuum polarization measurements, while window 7 is centered on the 5-4 SiO line and window 15 is centered on the 2-1 12CO line. The narrow windows are used to map outflows.

Techical publications

• CARMA Memo 54: detailed description of the waveguide circular polarizer.

Contact Info

Chat Hull
chat@astro.berkeley.edu

Dick Plambeck
plambeck@astro.berkeley.edu