[asac] Polarization paper for ALMA Science Advisory Committee

[Richard Crutcher]

POLARIZATION OBSERVATIONS WITH THE ATACAMA LARGE MILLIMETER ARRAY

Richard M. Crutcher, University of Illinois
W. J. Welch, University of California at Berkeley
Larry D'Addario, National Radio Astronomy Observatory


1. INTRODUCTION

Because of its enormous sensitivity and imaging capabilities, the ALMA
will be the premier instrument at millimeter and submillimeter
wavelengths. Polarization observations will likely be carried out far
more frequently with the ALMA than with present telescopes because the
sensitivity of the ALMA will make such observations (which always have
to deal with signals only a few percent of the total intensity) possible
for a much larger set of radio sources. However, polarization
observations place significantly more stringent requirements on
instruments than do total intensity measurements. Carefully
consideration of the instrumental requirements for successful
polarization observations should therefore be given high priority in the
design of the ALMA.

2. POLARIZATION SCIENCE

Major scientific areas that will benefit from excellent polarization
capabilities of the ALMA include the following:

Star formation. Theoretical and observational work has shown that
magnetic fields can play a significant and perhaps essential role in the
formation of interstellar clouds, in their evolution, and in the star
formation process. Needed are observations of the morphology and
strength of magnetic fields in molecular clouds. Techniques available
include: (1) measurement of linearly polarized emission from dust grains
aligned by magnetic fields; (2) measurement of linearly polarized
spectral line emission (both in thermal lines due to the
Goldreich-Kylafis effect and in maser lines such as SiO); and (3)
measurement of circularly polarized spectral-line emission produced by
the Zeeman effect. The first two techniques yield information about the
morphology of magnetic fields in the plane of the sky, while the third
gives the magnitude of the line of sight component of the field.

Supernova remnants. Synchrotron emission from SNRs is linearly
polarized, and the polarization is used to measure the direction and
estimate the strength of magnetic fields.

Normal galaxies. Synchrotron emission from the interstellar medium in
normal galaxies may be used to map magnetic fields in external galaxies
and study the morphology and estimate the strengths of extragalactic
magnetic fields. Such studies may lead to an understanding of the
amplification of magnetic fields in galactic dynamos.

Radio galaxies. Radio lobes produce polarized synchrotron emission that
may be used to map the morphology and estimate the strength of magnetic
fields.

Circular polarization observations will probably be primarily Zeeman
line work carried out for that special purpose at a small number of
frequencies. Certainly the 3-mm CN lines, and perhaps the CCS line at 33
GHz, the 1-mm CN lines, and several SO lines would be of interest. Other
lines may of course also prove to be useful as the tremendous
sensitivity of the ALMA is exploited. 
Except for the Zeeman effect, all of the above science drivers for
polarization observations with the ALMA involve linear polarization.
Requirements on the instrumental polarization are much more severe for
continuum linear polarization mapping than for Zeeman observations.
Moreover, for many if not most of the observations that will be made
with the ALMA, the polarization of thermal dust continuum or synchrotron
emission will be of scientific value EVEN WHEN THE POLARIZATION DATA ARE
NOT THE PRIMARY PURPOSE OF THE OBSERVATIONS. Thus, optimization of
instrumental characteristics of ALMA for routine linear polarization
observations would be of the greatest scientific value.

3. REQUIREMENTS

Requirements fall into three areas: (1) sensitivity - zero or minimal
loss of sensitivity when doing polarization observations; (2) Fourier
sampling - ability to obtain and include zero and short spacing
polarization data in order to carry out full synthesis mapping; and (3)
accuracy - the ability to calibrate instrumental polarization easily and
accurately (0.1% or better) over the entire primary beam. We briefly
describe these requirements in this section, and in section 4 discuss
specifics of instrument design and calibration needed to meet these
requirements.

3.1 Sensitivity

The very great effort going into giving the ALMA very high sensitivity
for mapping of total intensity also will yield high sensitivity for
polarization work so long as that sensitivity is not compromised by the
instrumental design. The fact that the ALMA will have dual receivers
with feeds sensitive to orthogonal polarizations is the first necessary
step. But if that system is to achieve its potential for polarization
work, the design must have a focus on the effect on polarization of all
aspects of the system. 

Polarization is usually less than 5%, and over large spatial areas the
percentage polarization is 1% or less. Hence, the dynamic range that can
be achieved is automatically significantly lower than for intensity
observations. In order not to further reduce sensitivity, one would like
to be able to map polarization to the limits set by thermal noise rather
than instrumental polarization.

3.2 Fourier sampling

A large fraction of polarization mapping with the ALMA will be of
extended objects. Hence, procedures for obtaining short and zero spacing
polarization data that will not degrade the quality of the
interferometric data are essential. Single-dish polarization
observations have traditionally been done by rotating a polarizer and
detecting the total intensity of the time-modulated signal. Because this
involves subtracting two big numbers (intensities in two different
polarization states) to determine a small number (a Stokes Q, U, or V),
it is very difficult to achieve calibrated instrumental sensitivities of
0.1%. New methods of single-dish polarization mapping must be developed
for the ALMA.

3.3 Accuracy

The goal should be to map Stokes V, Q, and U limited by thermal noise
and not by instrumental effects. As a practical matter, the goal should
be instrumental polarization effects of < 0.1%, after calibration.
Moreover, this spec must be met over the entire primary beams of the
telescopes in order to map over the single primary beam and to mosaic
map.

A significant difference between standard intensity (Stokes I) mapping
and polarization mapping is instrumental polarization. For intensity
mapping, the primary beam is a relatively simple and stable function, so
the instrumental response (dirty beam) can be predicted from the UV
coverage. Knowledge of that instrumental response can therefore be used
to deconvolve it out of the final maps. The instrumental response in
Stokes parameters Q, U, and V depends in addition to the UV coverage on
the polarized instrumental response over the primary beams of the
various antennas, and in general this may vary strongly and in a
complicated manner with position in the primary beam, time, pointing
position, etc. In order to deconvolve the polarized dirty beams out of
the final polarization maps, the polarized dirty beams must be known at
the noise level of the maps. If the instrumental polarization due to the
antennas is stable in time, one can measure it once and take it out.
Time variable instrumental polarization (due to elevation effects for
example) requires great loss of sensitivity due to time spent on
calibration and/or limitations on polarization fidelity. Failure to know
the polarized response of the instrument over position and time is the
major limitation on the accuracy of polarization mapping.

4. MEETING THE SCIENCE REQUIREMENTS

4.1 Instrumental polarization issues

As noted above, science drivers imply that most polarization work will
be in linear polarization. The main science driver for circular
polarization work is Zeeman work, for which the requirements are less
severe (see below). Thus, if it is necessary to optimize the ALMA for
observations of linear or circular polarization, the science implies
optimization for linear polarization observations. If this is not
possible for all bands, consideration should be given to optimization
for linear polarization observations at a prime polarization band;
perhaps the 345 GHz band is best.

The science goal is that the total instrumental polarization be less
than 0.1% without major loss of observing time for calibration. This
tolerance cannot be met without calibration, but achieving the closest
possible approach to zero instrumental polarization must be a design
criterion in order to meet the science goal. Meeting this goal requires
consideration of the following areas:

- Absolute polarization of each of two (nominally orthogonal
polarization) ports.

- Orthogonality of the polarizations of the two ports of one
antenna.

- Uniformity of polarization among antennas of the array.

- Orthogonality of opposite ports between antenna pairs of the array.

- Variation of each of the above with direction of arrival over the main
beam.

- Temporal stability of each of the above, short- and long-term.

- Effects of elevation dependence; designs that call for the antennas to
be stiff or that allow them to sag with refocusing both require
attention to the polarization effects.

Although one often speaks of linearly or circularly polarized feeds, it
should be noted that "feeds" are never purely linearly nor purely
circularly polarized, though they are often a close approximation to one
of these. The mathematics makes it clear that so long as the telescopes
have orthogonal polarization receivers, one can derive the full
polarization information (i.e., all four Stokes parameters). One can
choose any pair of orthogonal polarization states as "basis" states, so
that any arbitrary state is describable as a linear combination of them.
To be accurate, it is the polarization state of the whole antenna that
matters. For most radio telescopes, this includes the main reflector;
subreflector; other mirrors (flat or curved); other optical elements
(including wire grids and lenses); and finally something to convert the
free-space, multi-mode beam into a guided, single-mode wave.  The last
element is often a polarization-insensitive horn followed by a
"polarizer" with two single-mode ports, each coupling to a different
polarization of a plane wave incident on the whole antenna.  Each of
these cascaded elements affects these final two polarizations.  Those
elements that have sufficient symmetry can be treated as
polarization-insensitive. In the simplest case only the polarizer is
significant, but in practice the situation is often more complicated.

The sensitivity can be reduced if the polarizer introduces noise, or if
a significant fraction of the observing time must be devoted to
calibrating the instrumental polarization in order to achieve the
required sensitivity. The BIMA system, which has only a single receiver
per telescope, employs a transmission polarizer consisting of a grooved
dielectric plate in front of the receiver to select the desired
polarization basis state; this plate adds significantly to the noise of
the system. Second, if the polarization state of each antenna is
complicated (for example, if it differs significantly from the desired
basis state or varies both in time or over the field of view), a large
fraction of the observing time must be spent in calibration, which will
significantly reduce the sensitivity. Hence, a design that has the
lowest instrumental polarization and the lowest possible, most time
stable instrumental polarization will maximize sensitivity.

The optical design is crucial for polarization mapping over extended
areas. The best optical system is a "straight through" design, with no
off-axis elements or oblique reflections. Both will produce instrumental
polarization that varies over the primary beam of the telescopes. If an
off-axis system is necessary, careful calibration of its instrumental
polarization effects will be necessary. Since this will be time
consuming, it will be important that the optical system be kept
invariant so that a calibration may be used over a long period of time.
It would make sense to choose a primary band for linear polarization
work (probably 345 GHz would be best) and optimize the optics of that
band for polarization. Again, ideally, this would be on axis. If that is
impossible, at least a dual-mirror system should be chosen with
reflections designed for the polarization basis state of each channel.
Having reflections as close as possible to normal (to the mirror) for
the primary polarization band should be a design consideration.

Another issue is whether there is a significant advantage to a choice as
close as possible to a linear or a circular basis state, and second,
what deviation from a particular basis state may be tolerated without
making the calibration less accurate and/or more difficult and time
consuming. Although in principle even large instrumental polarization
effects may be calibrated, in practice the best approach is to have the
polarization state of each antenna to be intrinsically as close as
possible to the desired ideal state. In practice, accurate polarimetry
must account for the actual polarization state of the antenna;
extraordinary efforts to produce a basis state that approaches circular
or linear to high accuracy is not important.

Cotton (1998; MMA Memo 208) discussed calibration of interferometer
polarization data and the merits of linear or circularly polarized
feeds. There are a number of strong disadvantages of linear feeds,
including especially the facts that p-q (orthogonal polarizations) phase
fluctuations can significantly increase the noise in linearly polarized
data, that no polarization "snapshots" are possible since extended
observations are required to measure calibrator Q and U, and that any
p-q phase difference corrupts polarization data. Circularly polarized
feeds overcome these disadvantages for polarization work, and have the
additional advantages that calibrator polarization only weakly affects
gain calibration, that there is good separation of source and
instrumental polarization with parallactic angle, and that instrumental
polarization can be determined from a calibrator of unknown
polarization. 
If, as argued above, linear polarization science observations will be
the most important, having the polarization basis states as close as
possible to circular would be best. 

Since Zeeman observations are spectral-line observations, the observed
polarization is a relative measurement. That is, the circular
polarization as a function of frequency must be measured. The most
important instrumental polarization effect is beam squint - the pointing
of the two circularly polarized beams in slightly different directions.
More generally, beam squint may be considered to be the total (including
sidelobes) difference in instrumental positional response between the
two senses of circular polarization. In the presence of velocity
gradients in molecular clouds, beam squint will produce false Zeeman
signatures. However, so long as the primary beam squint is not too bad,
and especially if it is known and stable, its effects can be calibrated
and corrected. Small (< 5%) impurity in instrumental circular
polarization and difference in gain between the two polarization
channels can be calibrated out using standard Zeeman analysis
techniques. Moreover, simultaneous observations of thermal continuum
and/or of non-Zeeman spectral lines within the observation window may be
used to calibrate the instrumental circular polarization. 

4.2 Calibration issues

Since the instrumental polarization tolerances will not be zero, what is
the best overall strategy for calibration to determine the actual
polarization of each antenna? Moreover, besides knowing polarizations of
the antennas, it is also necessary to know the complex gains of the
receivers.  To a large extent, this is the same as is required for
observations of sources that are assumed unpolarized or where only total
intensity is to be measured.  An exception is that polarimetry requires
knowledge of the ratio of the complex gains of the two channels, whereas
total intensity measurement does not.  Conventional astronomical
calibration determines the amplitudes of these gains separately (and
hence their ratio) provided that the calibrator's polarization is known
(preferably unpolarized); it can determine the phase difference only if
the calibrator is appropriately polarized (preferable strongly so). 
What, then, is the best overall strategy for receiver gain calibration?

These points must be considered in the contexts of both interferometer
mode observations and single-dish mode observations.  The single-dish
mode is the more difficult. 

For the ALMA, it may be that the engineering reality is that all
receivers will be connected to antenna ports that are approximately
linearly polarized, and thus a poor approximation to being circularly
polarized.  MMA#208 states that the principal reason for this is that it
allows larger bandwidth; this is roughly true at centimeter wavelengths,
but it is not correct for the ALMA.  At the shorter wavelengths, various
antenna elements besides the polarizer are either impossible to
construct or are excessively lossy if they operate on waves that are
nearly circularly polarized.  An element that selects a single linear
polarization with very low loss and very large bandwidth is easily built
(a wire grid), whereas nothing similar exists for circular
polarization.  It is possible to insert a "quarter wave plate" to
convert circular to linear polarization with good accuracy over a narrow
band, but with some noise penalty due to ohmic losses. Thus, engineering
reality may preclude the possibility of having the ALMA optimized for
linear polarization by having near-circular polarization feeds, except
as a potential add-on, with limitations. It should be clear that this is
an engineering limitation and not a decision that optimizes for
polarization science.

Many of the difficulties cited by Cotton in MMA#208 would be overcome by
having a calibration source of known polarization with a very strong
linearly-polarized component (assuming that we are more interested in
mapping the linear polarization component than the circular one of
unknown sources).  Although such things do not exist in the natural sky,
it should be straightforward to have one built into each ALMA antenna.
One attractive possibility for the calibration of the dual polarization
receivers is to provide an intense millimeter wavelength CW signal that
can be coupled into the receivers at their inputs.  Such a signal could
be coupled into the receivers through a small aperture in the middle of
the secondary mirror. It could be highly linearly polarized but at a
position angle of 45 degrees, so that it couples equally and coherently
to both the horizontal and vertical polarization receivers.  In this
way, it could provide a very accurate relative calibration of the two
receivers. A total power spectral correlation measurement would provide
both amplitude and phase calibration between the two receivers. 
Presumably this CW millimeter wavelength signal could be tuned to
different frequencies as needed. 

A further possibility would be that the same coherent millimeter CW
signal could be injected into every front end. For example, the signal
might be provided as the beat note between two optical laser signals. 
In this case, the coherence of the signals would allow the phase (and
amplitude) relative calibration of all the receivers, including their
two polarizations.

This internal polarization calibration source would of course calibrate
the system from the feeds on; instrumental polarization of the primary
and secondary reflecting surfaces would have to be calibrated
astronomically. In order not to spent excess time on such calibrations,
the design should focus strongly on making the instrumental polarization
that must be calibrated astronomically as stable in time, elevation
angle, and position over the beam as possible.

Obtaining single antenna and short spacing polarization data will be a
challenge for the ALMA. A plan to obtain such intensity data by
"on-the-fly" mapping with the ALMA antennas should work for polarization
also so long as full polarization information is obtained and the system
is sufficiently stable. A stability of at least 1 part in 10,000 seems
to be necessary, sufficient, and achievable, but this spec needs to be
investigated specifically for polarization calibration. A system to
cross-correlate the signals from the orthogonally polarized receivers on
each antenna in order to produce single-dish polarization data while
"on-the-fly" mapping is being carried out should work, but needs to be
investigated. A system which requires physical rotation of polarizers
should be avoided; it would be difficult to achieve the required
accuracy and would be time consuming.

5. RECOMMENDATIONS

The sections above describe the science drivers and the required
polarization performance of the ALMA. Specific recommendations have been
discussed in section 4. However, millimeter-wave polarimetry is not yet
a mature field. We therefore strongly recommend that the systems for
polarization observations with the ALMA be implemented and tested at the
earliest possible time. Use of existing millimeter-wave interferometers
is likely to be useful, but implementation of polarization capabilities
from the beginning on the first ALMA test interferometer is essential if
the ALMA is to fulfill its promise for polarization.

-- 
Richard M. Crutcher
Chair, Department of Astronomy
University of Illinois
1002 W. Green St.
Urbana, IL  61801
Voice: 217/333-9581
Fax: 217/244-7638