[alma-config] alma configuration simulations

[Mark Holdaway]

To be submitted as an ALMA Memo. 


The Importance of Including Pointing Errors in ALMA Simulations

			Mark Holdaway
			April 13 2000


Abstract:

The author believes that the simulation program being undertaken by
the ALMA Imaging and Calibration Group to choose between the Kogan and
Conway array styles is seriously flawed.  The large images proposed
for use in the simulations will either fill the primary beam or
require mosaicing for all relevant arrays, depending upon which
configuration size is being used.  In either case, pointing errors
will limit the image dynamic range to something like 1000:1.  However,
the group chose the expedient of not including any errors in the
single field simulations.  The simulated images will likely have
dynamic range of order 10,000:1 or higher.  Choosing between one
configuration style which gives 20,000:1 dynamic range images and
another which gives 10,000:1 dynamic range images is meaningless if
pointing errors will limit the dynamic range to 1000:1.  Furthermore,
the superiority of one configuration in the absence of errors is not
indicative of its superiority in the presence of pointing errors.  The
inclusion of pointing errors in AIPS++ simulation code can be
forthcoming very shortly if the ALMA Imaging and Calibration Group
commits to using AIPS++ to simulate mosaiced observations and pointing
errors.


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Currently, there are two competing sets of designs for the ALMA array
configurations: the Kogan ``donut'' configurations, and the Conway
logarithmic spiral configurations.  Both configuration sets blend into
a highly filled compact configuration on the short baseline side and a
ring-like configuration on the long baseline side.  Both configuration
designs have similar numbers of antenna moves per reconfiguration
cycle, similar total numbers of antenna pads, and similar centrally
condensed Fourier plane envelopes.

In order to distinguish between the two competing sets of
configurations, extensive simulation campaigns have been planned (ie,
see the results of the Tucson Conceptual Configuration Design Review,
or CCDR).  The simulation campaigns are aimed at testing the imaging
quality of the configurations using large (1K x 1K) images.  Something
of order five model images will be used to gauge the configuration
style's imaging characteristics.  However, the Tucson CCDR agreed that
to settle the issue of which configuration design was superior, these
simulations would be performed {\em without} any errors added to the
simulated data.

Cornwell (MMA Memo 44, 1988) predicted that pointing errors will
likely limit the dynamic range of mosaiced observations at millimeter
wavelengths, and Holdaway (MMA Memo 61, 1990) demonstrated that
pointing errors will limit the dynamic range of mosaiced millimeter
array images to something like 500-1000:1 at 230~GHz for a
$\theta_{BWHM}/32$ pointing specification.  Pointing errors will
essentially result in a parameterized direction-dependent
antenna-based gain error.  In principle, this could be solved via
pointing error self calibration and then imaging with the known
pointing errors (Holdaway, MMA Memo 95, 1993).  However, this solution
has not been at all well explored, but it will be very computationally
expensive as a DFT must be used to calculate each baseline's
model visibilities over the solution interval, rather than an FFT 
for all model visibilities in a given field.

If the 1K x 1K images have 5 pixels across the synthesized beam (as
discussed at the CCDR; the pixel size should be adjusted to match this
condition), then the size of the image will correspond to the full
width half maximum of the primary beam for an array configuration of
1.6~km; in other words, for a configuration 1.6~km or smaller, not
only will mosaicing be required to reconstruct the short spatial
frequencies, but pointing errors will also be highly important, even
for single pointing observations, as the source will fill the primary
beam.  The differences in the Kogan and Conway configuration styles
are minimal for configurations larger than 1.6~km.

Error-free imaging simulations with the trial configuration sets on
the test images are expected to produce dynamic ranges on the order of
10,000:1 or greater.  However, it will be meaningless to compare the
results of these high dynamic range simulations when an effect such as
pointing errors is expected to limit the dynamic range of beam-filling
observations to 500-1000:1.

The off-source errors of an image reconstruction when pointing errors
are present are expected to scale with the rms sidelobe level of the
point spread function (ie, Cornwell, Holdaway, and Uson, 1994).
Hence, simulations without pointing errors may indicate that one
configuration is superior; but one could imagine simulations with
pointing errors included indicating that both array configurations are
of similar quality, or that the other is superior.

In conclusion: the simulation strategy as outlined in the Tucson CCDR,
with error-free, single pointing simulated observations of large model
images, is only meaningful for the case of the most extended array
configurations (ie, 3~km or 10~km), whose structure is not in dispute
between the Kogan and Conway configuration designs.  Observations of
these large images with smaller configurations is only sensible if
mosaicing is used, and the results of the simulations are only
sensible of pointing errors are included in the simulation process.
The inclusion of pointing errors could interact with which array
configuration produces superior images.  

The inclusion of pointing errors in AIPS++ simulations can be
forthcoming shortly if the ALMA group commits to using AIPS++ for
simulating data with pointing errors and mosaiced observations.


References


Cornwell, T.J., ``The Size of the Central Element: Pointing
Considerations'', MMA Memo 44, 1988.

Cornwell, T.J., Holdaway, M.A., and Uson, J., ``Radio-interferometric
Imaging of Very Large Objects: Array Design'', A&A, 271, 693-713, 1994.

Holdaway, M.A., ``Imaging Characteristics of a Homogeneous
Millimeter Array'', MMA Memo 61, 1990.

Holdaway, M.A., ``Imaging With Known Pointing Errors'', MMA Memo 95, 1993.