[asac] [almanews] ALMA Memos 389 and 390 Released

[Stacy Oliver]

ALMA Memo #389

Radio Interferometer Array Point Spread Functions I. Theory and Statistics

David Woody
Owens Valley Radio Observatory

2001-08-31

Keywords:  radio interferometers, configurations, point spread function

	This paper relates the optical definition of the PSF to radio
interferometer arrays.  The statistical properties of the PSF including the
effect of missing UV data are derived as a function of the number of
antennas and array magnification, defined as the ratio of the primary beam
width from an individual element to the synthesized beam width.  The effect
of earth rotation synthesis on the PSF is also calculated and the merits of
various configuration strategies are discussed in terms of their PSFs.
	The concept of a pseudo-random array is introduced as an array whose
large-scale average distribution matches an idealized continuous antenna
distribution.  The small-scale difference between the actual discrete
distribution and the idealized continuous distribution produces far
sidelobes in the PSF.  It is shown that the statistical distribution of the
sidelobes, s, of pseudo-random arrays of N antennas with sparse UV coverage
is given by P(s)=N*exp(-N*s).  The average sidelobe is ~1/N and the standard
deviation is also ~1/N.  Note that the single antenna measurements are
included in the formulation of the PSF used in this work.  The expected peak
sidelobe for a pseudo-random array with a magnification mag is
smax~2*ln(mag)/N and it is predicted that optimization can reduce the peak
sidelobe to smax~2*[ln(mag)-ln(N)]/N.  Pseudo-random arrays provide a
benchmark against which proposed configurations can be compared.


View a pdf version of ALMA Memo 389.
http://www.alma.nrao.edu/memos/html-memos/alma389/memo389.pdf


____________________________________________________________________________
______________________________________________

ALMA Memo #390

Radio Interferometer Array Point Spread Functions II. Evaluation and
Optimization

David Woody
Owens Valley Radio Observatory

2001-08-31

Keywords:  radio interferometers, configurations, point spread function

	The PSF of several sample arrays, including pseudo-random and circular
arrays, are evaluated.  The distribution of sidelobes
is shown to closely follow the theoretical distribution derived in the
companion paper [1].  An optimization procedure is developed
that produces configurations with peak sidelobes close to the expected limit
given in [1] and with a smooth progression from
small peaks near the center of the PSF and the largest peaks at the edge of
the primary beam.  Plotting the peak sidelobe as a
function of the radial distance from the center of the PSF is shown to be
very useful for evaluating the PSF.  The optimized
arrays provide a benchmark against which other configurations can be
compared.

View a pdf version of ALMA Memo 390.
http://www.alma.nrao.edu/memos/html-memos/alma390/memo390.pdf

=============================================================================
ALMAnews is a broadcast service.  To unsubscribe, send an e-mail message to
majordomo at nrao.edu with "unsubscribe almanews" in the message body.