[mmaimcal] more on polarization

[Steven T. Myers]

The latest version of the Polarization specifications is included below
as well as located at

    http://www.aoc.nrao.edu/~smyers/alma/polspecs-imcal.txt

(which will be updated as this develops further).  My first version was
closer to what I wanted, but I also added references to the Crutcher et
al. memo. 

Sorry about the flurry of emails on the list, but we do need to set down
some of these specs asap.

  -Steve

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    POLARIZATION SPECIFICATIONS AND GOALS FOR ALMA

    Version 27 March 2000

    S.T. MYERS (NRAO, Socorro)

    To get the ball rolling, here is my first go at suggested 
    polarization specs for ALMA.    

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1. Background

In his memo with suggested receiver specs 

       http://www.tuc.nrao.edu/~ldaddari/rcvrSpecs.txt

Larry writes

    Polarization: Simultaneous reception of two orthogonal
    polarizations is required, with each converted to (one or more)
    separate IF output(s).  The nominal polarization states may be
    selected separately for each band so as to minimize the receiver
    noise temperature; that is, either linear or circular is
    acceptable as the nominal polarization.  [At any frequency within
    the receiver's tuning range, the polarization states of the two
    channels should conform to:]

    [2.1 Maximum non-orthogonality              TBD, ~-25 dB]

    [2.2 Maximum polarization mismatch between any pair
        of antennas in the array                TBD, ~-20 dB]

    [Detailed specifications on polarization performance are under
    study.]

    In addition, over a limited portion of the tuning range of any
    receiver (typically 5% of center frequency), it shall be possible
    to make the nominal polarizations circular within 1.0 dB.  This
    may be accomplished by an insertable optical device, which may
    cause an increase in noise temperature not to exceed [TBD].

2. Current VLA performance

In the set of VLA/VLBA polarization calibration data that I have
been compiling the past 6 months

     http://www.aoc.nrao.edu/~smyers/calibration/

I find typical cross-polarization terms ("D-terms") of 1% at C
and X band to as much as 5% -- 6% at K and Q band.  For an
example solution, see 

     http://www.aoc.nrao.edu/~smyers/calibration/antpol.html

The effect of the off-diagonal D-terms (eg. d_RL and d_LR) on the
polarization calibration is the product of the D matrices for the
pairs of antennas.  Thus, to linear order, it is the difference (
d1_RL - d2_LR* ) between antennas 1 and 2, for example.  Also note
that technically the non-orthogonality is the same difference of the
off-diagonal terms of the same antenna.  These seem to be on the order
of the magnitude of the D-terms themselves.  The VLA D-terms on the order
of 1% - 5% seem to limit the believable fractional polarization (even
in bright sources) to around 0.5% for standard observation and
analysis schemes due to limitations in the solutions for the D-terms
using the usual software.  The VLA solutions also do not seem to be
time-stable.  I am currently looking into this problem as part of the
calibration program.

D-terms of the order of 1% imply polarization purity (which we will
take as non-orthogonality) of -20dB, while 6% corresponds to -12dB.
Note that the polarization specs (dB) are for power, not voltage,
though since the D-terms are observationally defined based on the
measured visibility amplitudes (and phases) these are correct.
[IS THIS RIGHT?]

3. However, it does seem that the polarization performance of the VLA
is acceptable to most observers and does not seem to seriously
limit the scientific applications of polarization observations.
Therefore, I would adopt Larry's specs of -25db and -20db 
respectively for allowed non-orthogonality and
mismatch as the design GOALS, and relax the specs somewhat (based on
what I interpret as the VLA performance):

    [2.1 Maximum non-orthogonality       Spec: -20dB   Goal: -25dB

    [2.2 Maximum polarization mismatch   Spec: -15dB   Goal: -20dB
         between any pair of antennas

    [2.3 Maximum deviation from stated   Spec: -12dB   Goal: -20dB
         linear or circular polarization
         (d-term amplitude)

These specs should yield polarization vector accuracies of a few
degrees which seems sufficient.  I added a third spec on the magnitude
of the cross-terms in the instrumental polarization matrix of 6% spec
and 1% goal (-12dB and -20dB respectively) as these are easier to
determine than overall non-orthogonality after passing through some
complex and undefined calibration scheme - the d-terms are small, then
their fluctuations should also be small!  
[IS THIS A USEFUL THING TO INCLUDE?]

I am worried that over-stringent polarization characteristics may
prove extremely difficult to actually acheive for ALMA, given the
experience of the VLA.  Thus I have adopted specs of only -15dB
(3%) for antenna mismatch and non-orthogonality of -20dB (1%), as well
as overall cross-terms of -12dB, and kept the previous tougher specs
as goals.  I think the 0.1% (-30dB) stated in Crutcher et al. are 
likely unattainable (see below).
[IS THIS ACCEPTABLE?]

4. With the large tuning bandwidths (as high as 30% fractional
bandwidth) it will be difficult to make OMTs, quarter-wave plates
or quasi-optical devices that will perform to the above specs over
the entire band.  For example, for a band-edge 1.15 times the band
center, a waveguide quarter-wave retarder (with a dielectric vane
for example) could have as much as a $13^\circ$ phase error at
band edge, which would roughly give a cross-polarization of 23%
(twice this for power instead of voltage)!
[DID I ESTIMATE THIS CORRECTLY?  I AM JUST TRYING TO GET ROUGH
NUMBERS HERE.]

Therefore I propose the above specs and goals to apply only to the
central 5% of bandwidth (eg. 5 GHz at 100 GHz, 32 GHz at 650
GHz), and allow the performance to deviate at band edges.

As for circular versus linear, should we specify anything beyond
these specs (eg. Larry's 1db circularity)?

>From what I hear from the engineers, getting even the VLA-level
performance will be very difficult!

5. If we want tighter specs, I think we need pretty strong scientific
drivers (such as expected fractional polarizations for dust
emission at sub-mm bands) to argue for this.  AGN polarizations
seem to be high enough (5% - 10%) that the VLA-level specs are
sufficient.  Dust polarizations of 1% should be possible to detect
and measure with (stable) d-terms of 1%.

Some science drivers are given in the memo by Crutcher, Welch and
D'Addario, who state that

    As a practical matter, the goal should be instrumental
    polarization effects of < 0.1%, after calibration.

This seems laudable, but somewhat excessive given the performance of
the VLA.  It does appear that polarizations of order 0.3%-0.5% can
be attained after calibration given the typical VLA set-up and
D-terms, so our above specs should get us reasonably close to the
desired level of accuracy.

6.  COMMENTS ANYONE?

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|:| Steven T. Myers                      |:|  Associate Scientist      |:|
|:| National Radio Astronomy Observatory |:|                           |:|
|:| P.O. Box O                           |:|  1003 Lopezville Rd.      |:|
|:| Socorro, NM 87801                    |:|  Ph:  (505) 835-7294      |:|
|:| smyers at nrao.edu                      |:|  FAX: (505) 835-7027      |:|
|:| http://www.aoc.nrao.edu/~smyers      |:|                           |:|
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