From: Bill Cotton
Subject: Re: SKA Simulation Working Group - Aims and Strategies
Date: Tue, 15 Apr 2003 15:26:39 -0400 (EDT)

Steven,

   I gather that one of the initial roles this working group would
fill is adding some technical input to the ultimate choice for the
design of SKA.  This is clearly a good thing to do, but I think we need
to take a step back and look at the bigger picture before getting
bogged down in simulations.

   The imaging properties of SKA are very important but I will argue
that we don't really know how to do even the most basic imaging
operations.  Until we understand this problem better, doing
simulations to compare the properties of the different designs will
generate much more heat than light.

   The vast majority of aperture synthesis work done to date has been
either with transit instruments or arrays of steerable elements whose
power patterns can be considered constant during a given observation.
The constant beam pattern assumption isn't quite correct, but with the
further assumption that everything of interest is in the well behaved
parts near the center, we have been able to get away with this
assumption. 

   Thus, the "standard" derivation of radio aperture synthesis has a
built-in assumption that what is being imaged is constant, the sky
multiplied by the antenna power pattern.  This is not the general case
and most (all?) of the potential LOFAR designs grossly violate this 
assumption.  Most (all?) include major elements fixed to the ground
with a resultant beamshape that depends on the zenith angle.  The
sensitivity of SKA should be such that imaging the full field of view
will be necessary much of the time.  This further aggravates the
problem as the power pattern far from the pointing center is more
variable.  An "image" derived in the usual "grid and FFT" technique is
not the convolution of the sky with any single function.  Somehow,
knowledge of the variable beam shape must be folded into the image
formation process and cannot simply be added as a minor correction at
the end. 

   This problem is not intractable, but the optimum solution may well
be different for the different designs and I'm not aware of any
working software that currently does this.  This problem makes 
simulated data from the different designs even more difficult to
compare unless we are prepared to put in the design and development
work for each of the proposed designs.  Neither the time nor the
resources necessary to do this seem to be available.  When a design is
chosen, solutions to the data processing problems must be found and at
that point simulations become very useful.

   For the purpose of comparing array designs, I would suggest that we
look for better defined (at least more obtainable) criteria such as: 

1) What are the major foreseeable problems for image formation, beam
formation and other major operational modes?  Software costs will be a
major issue so the complexity of the computing problem to be solved is
a significant issue.

2) Image quality in terms of sidelobe levels is largely a matter of uv
coverage; designs with larger numbers of elements will in general do
better.  Statistics of sidelobe levels inferred from u-v plots are
about as useful as simulated images and far easier to produce.
RMS and peak sidelobe levels at a variety of declinations would be a
fairly objective measure of potential image quality.

3) Surface brightness arguments go the other way.  Designs with larger
if fewer elements have better surface brightness sensitivity.  We need
some way of quantifying this and it's impact on the science targets.

4) Polarization performance is harder to get a handle on but is a
major issue.

-Bill