[alma-config] History

[John Conway]

Hi,

 I get the feeling that the discussion about uniform/complete 
uv coverage is trailling of a bit as we pause for needed
thought and simulation.  However as I have said in earlier emails 
its worth getting to the  bottom of this one since its 
so fundamental  to our problem of choosing a uv coverage for 
ALMA. Given this  I'll with trepidation make a few 
more comments - this time of an historical nature 

(I appoloize in advance if any of what I say is inaccurate, it has 
been reconstructed  by me from secondary sources, those who are older 
and around at the time  might have corrections. I also note 3 people on the 
mailing list who have been through Cambridge, England or are still
there and my Jodrell Bank based origin might bias me(!), still I say
mainly nice things.).


Taking an historical view be useful in understanding the 
uv coverage debate. In an earlier email Bryan noted:  

> my feeling is that we would need a better imaging formulation to handle 
> the case of nearly complete u-v coverage, which followed more 
> traditional signal processing techniques.  one of our current problems 
> is that we are tainted (in some sense) by the past.  radio 
> interferometry has always been about sparse sampling of the u-v plane, 
> and in that case it turns out that non-linear deconvolutions work very 
> well.  maybe it is time to try to get entirely beyond that stage with 
> ALMA?


However if one goes back to the very  beginning of aperture synthesis  
one sees that the development originally was from arrays with
'complete out to uvmax uv coverage' to somewhat sparser arrays,
it is interesting to consider why this happened.


RYLES APERTURE SYNTHESIS
---------------------------

Pioneering interfermetric imaging was conducted in the 50's by 
groups in Australia and Jodrell Bank, however it was in the 60's
that the full flower of aperture synthesis came about at Cambridge
under Martin Ryle. In his 'supersynthesis' technique, using an E-W baseline,
Earth rotation and moving the antennas it was possible to measure
all uv spacings out to uvmax with intervals of a dish diameter 
or less, so that the ringlobes were effectively beyond the edge 
of the antenna primary beam. This was a very beautiful creation 
(and the  main reason Ryle later got the Nobel prize). Taking the direct
FT transform gave the dirty map, however these had quite severe 
lambda sidelobes due to the sharp edge of the uv coverage at umax. 
These however could be very effectively removed
by 'apodising', by applying a gaussian taper to the data. The 
resulting image had a well defined resolution and was a 
unique inversion of the data, one could be absolutely certain of 
that the source really looked like this at the defined resolution
(again very beautiful). The only downside of this was 
that for general imaging applications the taper caused you to lose about 
a factor of two in both sensitivity and resolution (for simple model
fitting one could utilize the longer baselines more, but this
is not a case of general imaging but of applying 'a priori' information 
that the source has  a simple form).


CLEAN
-----

In these days of innocence in the 1960s I guess nobody had even thought of 
those  diabolical  tools  CLEAN and MEM (or maybe they did but computers
were in their infancy), therefore  apodisation to remove sidelobes and 
its side effects were I guess thought  of as the price of doing business 
(if there had been a simple perfectly unique method of removing the 
sidelobes on a perfectly regular E-W array  without losing sensitivity 
Ryle - being a very clever chap 
would have invented it). Then I guess, some damm foriegners starting
building interferometers, and these people did not have the 
purity of vision of Ryle. In particular  at WSRT people started with 
applying an iterative technique to remove sidelobes called CLEAN 
(Hogbom 1974, since Hogbom was I think Swedish I guess we can claim 
this as a Swedish  invention). Astronomers started using this technique 
and it proved  a great success. Here was an alternative to appodisation in 
which you could apparently keep all your sensitivity and resolution,
- you could 'have your cake and eat it'. 


However as I understand it Ryle never ever accepted the use of CLEAN 
(..nor I think self-cal but thats another story..). He saw more 
clearly than anyone else perhaps what CLEAN was really doing, CLEAN 
did not give a unique image reconstruction, it was choosing one
of an infinity of possible solutions which fitted the data (and 
cheekily not even telling us the criteria on which it was making its 
choice!). Put in exactly equivalent terms CLEAN was estimating what the FT of
the true image was at uv spacings that had not been measured. in this
sense it was guessing new extraploted-interpolated data to add to the 
actual data that had been collected. Ryle I think must have
considered it preferable 
to effectively delete a significant fraction of the real data collected
via appodisation rather than add this  estimated/invented data 
to the measured data to make a nice synthesised beam shape. 
You could certainly see Ryles point, he had invented a unique method 
of imaging sources without any  guesswork, and this silly algorithm was 
making muddy the beautiful  invention of aperture synthesis. Meanwhile
astronomers at WSRT, Australia and in VLBI were using CLEAN quite 
effectively to make astrophysically useful maps without apodisation.

Despite this success through the 1970s CLEAN (or any other 
deconvolution method, until later in the 
80s after the Ryle exra when Steve Gull promoted MEM as at least a 
well-defined deconvolution process) was I think not really accepted 
at Cambridge.  Even  in the early 1980s when I was a PhD student at 
Jodrell Bank, apodisation was still known as 'Cambridge Clean'.
The rest of the world however accepted in effect a 'Faustian
Bargain' in return for using deconvolution instead of apodisation
one got all the resolution and sensitivity of the array 
but at the expense of adding some uncertainty to the reconstruction.
This is the bargain most of us have lived with since, sometimes
we push it to far, as in the case of sparse VLBI arrays in 
the 70s and 80s, in which the uncertainty generated by applying 
deconvolution to sparse arrays reaches levels which effect the 
astrophysics. Howvever despite the above cases I think the Faustian 
bargain has  usually been worth it.



THE VLA
--------

The next generation of interferomter 
after  those of the 60's and 70's (some T's and rings as well as E-W)
was the VLA, and this certainly departed significanly from Ryles 
complete uv coverage supersynthesis array
concept. I'm afraid that I really am not sure of all the arguments 
that caused it to be designed as it was. It certainly does 
not have complete uv  coverage out to umax, but is heavily 
tapered. I think  the main arguments were  just based on 
synthesied beam shapes (from what Ron Ekers said in Toronto)
and people expected to do long tracks and 'dirty imaging'. 
However at least  in the later stages of its design  the 
designers must thave been concious of developments with CLEAN etc. 
In any  case in  terms of how it has actually been -used-  from 1980 
onwards the VLA has employed deconvolution algorithms for reducing 
virtually all observations. The VLA is therefore the premiar
example of the 'Faustian Bargain' between having a sparse
incomplete tapered uv coverage and then using deconvolution 
to estimate which of the many possible image which fit the
data is the best estimate. It has now been running for nearly 
20 years and I would submit that it has been 
very successful - I don't think there are many astrophysical
questions which have been effected by the uncertainties 
introduced by deconvolution. 



APPLICATION TO ALMA
--------------------

Of course in contrast to the VLA one can argue that 
ALMA images will be more complex, then again ALMA 
has 6 times as many baselines; I think therefore 
its worth taking the VLA practical experience as a guide in 
designing ALMA. But also as Dave and Bryan have suggested it is 
also worth taking stock and wondering whether going back to arrays 
with more  complete  uv coverage and (after appodization) uniqueness 
(i.e. going back to a 'Ryle-ist' philisophy) are worth it. 
My feeling is that except in cases  of high SNR and when one 
is only interested in the smoothest structures (D-array) 
the increases in reliability are
not worth the costs in sensitivity/resolution which come from 
apodisation. If one of course tries to use such uniform 
arrays without appodisation  and wants to remove the 15% 
sidelobes that exist one must then apply 
an  algorithm which estimates the image FT beyond the uv edge - and 
hence the main argument of uniquness for having 'complete uv coverage' 
(really 'complete uv coverage out to umax'), is then subverted.


All the above history/philosphy is worth thinking about to put the 
uv coverage question into perspective, however  
as I noted in previous emails, maybe its all somewhat 
second order in practice. For  ALMA whatever the 
design geeometry the arrays equivelent in size to 'NRAO baseline D' 
will inevitably have complete uv coverage  even in just a snapshot,
because the antennas are so densely packed. The ALMA array 
of size C, whatever the design, will have almost complete coverage
after a full track (with a factor of 1.5 variation in uv cell occupancy
depending on whether a uniform array of one with 1/3 of the uv points 
are placed outliers for a tapered array).  For high SNR observations in these  
two arrays one can, as an option, apply apodisation and get unique image 
reconstruction, a la Ryle. As one goes to larger  arrays sensitivty 
becomes more of  a critical issue arguing against apodisation. In addition
a compelete filling of all  uv spacings with cell
size equal to the antenna diameter becomes impossible anyway, hence 
these arrays should ideally have a heavy taper. The loss in resolution 
for an array of given maximum baseline is irrelevant if there exists
a bigger array. The exception as  Mark has noted,- if there is limited 
real estate-  is the very largest array in which we choose a ring/loop 
because it gives the highest resolution from a limited area 
(not really because of its magic uniformity propeties).
  

 John.