Subject: Quick results from astrometric experiments

From: Dave Monet

Submitted: Wed, 23 Feb 2005 06:33:42 -0700

Message number: 297 (previous: 296, next: 298 up: Index)

In support of the ramp-up to the SRD, I wanted to pass along a few thoughts
that have arisen from the astrometric analysis of some short-exposure data
taken with Subaru and at CTIO.  I prepared a longer version that I sent to
some folks, but to avoid spamming the masses I did not include it in this
note.  If you want to see data, plots, and words, just let me know.

My major worry about systems with large A*Omega is how well they can do
astrometry.  Indeed, my goal during the pre-survey phase is to understand
enough of the issues so that I can estimate the accuracy.  This enables the
justification of various science cases, and is input for engineering trades.
On the basis of two very nice sets of short exposures, one from the Subaru
public archive and one taken by Chris Smith at CTIO last month,  I think that
I can spot a trend.  (See? I can do real astronomy, too!)  At least for
the case of differential astrometry (i.e., the ability to measure changes
in position) these data sets agree that the seeing places the limit on
astrometric accuracy.  If you have plenty of photons, a simple summary is

   10-sec exposure in 1-arcsec seeing gives about 7-milliarcsec accuracy

So far, this appears to be independent of the telescope aperture, and this
accuracy is measured from a single solution over the area of a 2Kx4K CCD
with 0.2-0.3 arcsec/pixel scale (800-1000 arcsec).  This number appears
to scale as

   astrometric error scales as   Seeing_FWHM/SQRT(N_exposure*T_Exposure)

more or less as I expected.  (Please!  Seeing pundits should make comments
and suggest what I have missed or other experiments to do.)  If this is
really what is going on, then the astrometric figure of merit (again, for
the large aperture, short exposure, good site limit) is simply

   astrometric FoM = N_exposure*T_exposure = Total_Time_On_Target

So far as I have been able to test, it doesn't make too much difference
if this is one really long exposure or a lot of very short exposures.
Sure, the depth of each image is a function of telescope area, QE, noise,
etc., but the astrometric accuracy seems to be limited by how long we
average the damage done by the atmosphere.

This is really a bummer because it brings the cadence and schedule into
the figure of merit, and as we know these are not simple issues.  However,
it seems that a first step in including astrometry into an overall system
metric would be to define a simple measure of the efficiency as

    E_schedule = T_expose/T_cycle

which is a measure of the fraction of the time that the shutter is open
during the nominal observing cadence, and then include this as

    effective etendue scales as A*Omega*E_schedule

The LSST design has already worried these issues.  I am pretty far out of
the loop, but I think that the numbers are T_expose = 10sec and that
T_cycle = 15 sec for an E_schedule = 0.67.  I think (but please correct
me) that Pan-STARRS is similarly high (T_expose = 30sec and T_cycle = 40sec
for an E_schedule = 0.75).  Other systems that I have examined do not have
such high efficiencies, particularly those with very short exposure times.

So in summary, it seems that astrometry doesn't really care whether you
take a few long exposures or many short exposures so long as the system is
optimized to keep the shutter open.

Many thanks to Chris and the SMOKA archive.
-Dave

PS
Sorry if I confuse the issues, but the results of the Subaru and CTIO
data analysis are pretty convincing.  More such data would be nice,
and data sets from a smaller aperture in a good site with a big
camera would be interesting.  If the 7-milliarcsec figure holds, then
all sorts of neat astrometric projects can be done by LSST, Pan-STARRS, etc.

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