[mmaimcal] Matching of frequency profiles for ALMA and ACA correlators

[Darrel Emerson]

Are at least some of the following true?

1. If we're prepared to give up a factor of ~2 in ACA correlator frequency
resolution, then there's no problem, because we can reweight terms
of the ACA FX correlator in order to equalize the frequency response with
the main ALMA array sinc response.  Especially true since we'll usually
want to grade responses (Hanning or whatever) to reduce frequency sidelobes.

2. Doesn't the ACA correlator support a greater number of channels
than the main ALMA array anyway (I'm not at all sure if it does or not)?
If so, then combined with (1) above that's the end of the story.

3. How often is the ultimate in ACA frequency response really going to be
needed?  Could it be that in most cases where extreme frequency resolution
and maximum number of channels are needed, the angular extent of the
source is such that the combination of ACA and main ALMA may not
be so important?  In other words, is there any tendency for spectrally
narrow emission not to be spatially very extended (the reverse of the Orion
CO spectrum.)  I don't know if this is true.

  My feeling, which may be probably completely wrong, is that it'll be
sufficiently rare that we run into a significant  imaging problem 
because of this,
since in most cases we can sacrifice FX resolution to equalize the frequency
responses, that it's not even worth the effort of making simulations to 
quantify
things further.
                        Cheers,
                                      Darrel.


Mark Holdaway wrote:

> Robert,
>
> It seems like it might be beneficial to have some imaging simulations
> of this issue.  However, given that other errors (like pointing and
> voltage pattern) are at a significantly higher level than 0.4%, it seems
> that at first glance this should be OK.   However, the effects of the
> pointing errors may be more randomized than the effect of the
> spectral sensitivity functions being systrematically different.
> It seems, if we were to simulate this, we would need to look at several
> different sorts of objects with different spectral signatures -- 
> rotating things,
> expanding things, etc.   A new dimension to the library of simulation 
> objects.
>
>    -Mark
>
> rlaing at eso.org wrote:
>
>> The purpose of this e-mail is to start a discussion on a small issue 
>> which came up during the PDR of the ACA correlator. It concerns the 
>> differences in
>> frequency profile for the 64-station (hereafter ALMA) and ACA 
>> correlators. The
>> former is an XF design, and the response for a narrow spectral line 
>> is a sinc
>> function in the frequency domain. The latter is an FX design, and the 
>> response
>> is a sinc^2 function. 
>> See
>> http://edm.alma.cl/forums/alma/dispatch.cgi/revsactive/docProfile/100643/d20050510035512/No/2005-05-09%20CORL-62.00.00.00-006-A-REP.pdf 
>>
>> (pp 45-46) and
>>
>> http://edm.alma.cl/forums/alma/dispatch.cgi/revsactive/docProfile/101003/d20050611223211/No/3-2Compatibility-freq-ch_profile.pdf 
>>
>>
>> for the material presented at the review.
>>
>> If we combine ALMA and ACA data without doing something to equalize the
>> frequency profiles, there will be imaging errors. The ACA team have 
>> looked at
>> reproducing the ALMA frequency profile from a linear combination of 
>> ACA channels
>> (second document above). This gives fairly small differences except 
>> in the case
>> of a uniform weighting function at the highest spectral resolution 
>> (see second
>> document, above).  [It is, in any case, arguably the wrong way round, 
>> as the
>> sinc^2 response of the ACA (FX) correlator has lower sidelobes.]
>>
>> In practice, it is likely that some weighting function other than 
>> uniform will
>> be used to reduce sidelobes at the cost of spectral resolution. For 
>> example: - A triangular weighting function in the time (lag) domain 
>> for the ALMA
>> correlator will produce exactly a sinc^2 response. This matches the 
>> form of the
>> ACA correlator response, but for a lower resolution. - Hanning 
>> weighting (which is actually quite close to this) will also suppress
>> the sidelobes very effectively (and the ACA correlator can reproduce 
>> this
>> profile to within 0.4% - see second document) by weighted frequency 
>> binning.
>>
>> If the ALMA correlator is used at its highest resolution with uniform 
>> weighting,
>> this approach does not work, since the ACA correlator cannot then bin 
>> over
>> narrower channels.
>>
>> The design issues are therefore as follows:
>>
>> For anything other than the maximum frequency resolution, we should 
>> use appropriate weighting functions (Hanning or triangular) to match 
>> the profiles.
>> This should probably be the default option.
>>
>> The match between the frequency responses of the two correlators at high
>> spectral resolution can be improved by increasing the length of the 
>> FFT in the
>> ACA correlator (to give narrower spectral channels) and then 
>> re-binning with
>> appropriate weights.  Is this justified by the need to match the 
>> frequency
>> profiles of the two correlators to better than the levels shown in 
>> the review
>> documentation? [There are cost and schedule implications.]
>>
>> Do we need imaging simulations in order to answer this question, or 
>> are the
>> existing calculations adequate?
>>
>> Regards
>>
>> Robert
>>
>>
>>
>>
>>
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