Re: Undersampling

[Tom Droege <droege@wwa.com>]

I read the referenced technical discussion on Andrew's web page with
interest.  (Well, some of it made my eyelids droop.) In the discussion
Andrew has some worries about astrometry.  

I think we should not be very concerned about astrometry.  I think our
primary astrometry concern is how well we can separate stars that are
close.  We do not really care where they are.  But we do care if we have
one star or two close stars.  Of course we care to a few arc seconds so we
get the identification right.  

I argue that the analysis should be biased to separate close stars as
opposed to finding the accurate location of stars.  Without any analysis my
gut feeling tells me that a narrow PSF helps to separate stars at the
expense of accurate location.  Experts please comment?

Why should we not care about astrometry?

Well the USNO is busy making an all sky catalog that will cover our
magnitude range and which will be far more accurate.  I recently received a
CD ROM from Dr. Norbert Zacharias which contains the first part of their
all sky survey.  It is good to 20 mas from R=9 to 14.5, and to 70 mas for R
= 16.  This, I believe, is much better than we can hope to do.  

Not that we should not try.  They are presently doing the south, and it
looks like a few years until they get to the North (comment Arne?).  But
their apparatus is designed for accurate astrometry.  We are designed for
photometry.  We complement each other. 

I think we should concentrate on photometry as a function of time.  So the
analysis should be biased to produce the best possible photometry, which
includes assigning the photons to the right star.  

Tom Droege 

At 01:01 AM 5/21/00 +0100, you wrote:
>I have been looking at this since David McClain brought
>the subject up at the beginning of last month. My full
>cogitations can be found at
>http://www3.ns.sympatico.ca/andrew.bennett/tass/sample.html
>
>I conclude that the undersampling resulting from an FWHM as low
>as 1.0 pixels does not present any problem provided that we use properly
>chosen algorithms for data reduction. The Aperture Sum estimate of
>amplitude is essentially unaffected, provided the CCD pixels occupy
>a substantial fraction of the CCD area, which we believe they do. 
>Least Squares estimation remains accurate provided one has a good
>estimate of the PSF. The Median method of position estimation is 
>badly affected by undersampling (as is already well known) and should 
>not be used with such a small FWHM. Other methods of position
>estimation are available which are adequate to our needs; Least
>Squares estimation (using a good PSF estimate) works well.
>
>Andrew Bennett, Avondale Vineyard, Nova Scotia, Canada.
>
>