Subject: Astrometric Accuracy as a function of Separation
From: Dave Monet
Submitted: Sat, 08 Mar 2003 11:29:07 -0700
Message number: 91
(previous: 90,
next: 92
up: Index)
This is a multi-part message in MIME format.
--------------040204010508090709040701
Content-Type: text/plain; charset=us-ascii; format=flowed
Content-Transfer-Encoding: 7bit
Given the deafening silence on lsst-general, I thought that I would
spam folks with a couple of notes about the growth of astrometric
error as a function of the separation that I prepared for the Pan-STARRS
folks using CFHT Megacam data. YAMS (yet another Monet snoozer).
-Dave
--------------040204010508090709040701
Content-Type: text/plain;
name="megacam.2"
Content-Transfer-Encoding: 7bit
Content-Disposition: inline;
filename="megacam.2"
Thanks to Gene for clarifications, and my apologies to the CFHT system for
mis-crediting only the IfA.
I think that I have found marginal evidence for the size scale of the
turbulence on the short exposure images (3 by 1-second) discussed in the
previous note. Since I don't really understand seeing, please feel free
to educate me if the following doesn't make sense.
Using the subset of brighter stars (i.e., the hope is that the astrometry
is not dominated by photon statistics), I identified all N*(N-1)/2 unique
pairs. For each pair, I computed the mean separation and its standard
deviation from the 3 three exposures. (Yes, this is small number
statistics, but 1-second Megacam exposures are far from optimal.)
I then merged the lists from all CCDs (2880 unique pairs), and sorted on
separation. You do not get a uniform cloud of points if you then plot
sigma_separation as a function of separation. To clarify the result,
I split the list into bins of 30.0 arcsec (about 162 pixels) and
extracted the 25, 50 (==median), and 75 percentile values for
sigma_separation. This statistical summary is as follows.
Middle of N 25% 50% 75%
bin (arcsec) <--------- mas ------->
-------------------------------------------------
15.00 32 12.6 22.4 35.3
45.00 60 16.3 27.5 39.9
75.00 90 26.2 38.6 50.0
105.00 129 19.7 35.5 56.6
135.00 181 28.0 42.8 62.3
165.00 175 26.9 41.3 57.9
195.00 174 26.5 40.8 57.8
225.00 206 29.2 42.6 62.6
255.00 185 30.8 49.5 71.5
285.00 153 32.0 46.6 66.2
315.00 161 30.7 48.0 71.0
345.00 155 29.4 44.9 70.3
375.00 155 37.0 46.7 61.0
405.00 145 33.1 51.7 65.9
435.00 139 32.3 47.4 63.4
465.00 118 36.3 49.4 66.4
495.00 98 33.5 49.5 68.1
525.00 91 32.7 52.0 67.4
555.00 85 34.3 52.3 66.1
585.00 69 35.8 54.5 80.4
Perhaps it is only my aforementioned rose colored glasses, but I think that
there is evidence that smaller separations are measured with better accuracy,
and that the asymptotic limit is reached at about 3 arcmin. Sure this
is small number statistics and there aren't a lot of photons, but the
curve of sigma_separation seems pretty well behaved, or at least compared
to other such curves that I have seen. I think that the data reduction is
simplified because 3 arcmin is only 1000 pixels. I didn't need to
solve the problem of tying all CCDs to a common coordinate system.
I will attack the 60-second exposures next, but this may take more work
because the prediction is that the patch will be larger than one CCD.
Fire away. My Nomex suit has a few more holes in it after yesterday's
on-site visit by John Wick, but it still covers most of the critical bits.
-Dave
--------------040204010508090709040701
Content-Type: text/plain;
name="megacam.5"
Content-Transfer-Encoding: 7bit
Content-Disposition: inline;
filename="megacam.5"
I have run enough of the 60 second frames Megacam frames through my
processing loop to get to the seeing results that are similar to those
presented in a previous note. CFHT + 60 seconds is no longer in the
realm of low photon count and small number statistics, so I have a bit
more confidence in these results.
The first difference is that the 60-sec frames were dithered by about
an arcmin from each other. Hence, it is mandatory to a transformation
between the dithered exposures. In the X (==along row) direction, a linear
transformation is needed to reduce the RMS error from about 30mas to
about 5mas. In the Y (==along column) direction, a linear transformation
reduces the RMS error from about 60 mas to about 8 mas, and adding
quadratic terms further reduces this to about 6 mas. Therefore, I used
the linear transformation in X and the quadratic transformation in Y
for the rest of the analysis.
(For those who are not familiar with Megacam, there are 9 CCDs per row
and 4 rows. Each CCD has 2 amplifiers, and the data that I was given
were formatted in the 2 possible ways. For the 1-sec exposures, I was
given 36 images each 2K by 4.5K that come from a per-CCD readout
scheme. For the 60-sec exposures, I was given 72 images each 1K by 4.5K
that come from a per-amplifier scheme. Hence, it is quite reasonable that
the mapping is Y needs more terms that the mapping in X because the CCD
is 2.25 times longer in Y.)
Even after including the higher order terms in the fit, it is still
the case that the Y solution is typically 30% to 50% worse than the
X solution. As I have noted in a few previous notes, this behavior
persists in essentially all astrometric solutions, and I have no
obvious explanation for it.
In exactly the say way of finding all unique pairs on a CCD and
doing statistics on their separations (after transforming to the
common coordinate system for all exposures), here are the binned
results for 3 exposures (680453o, 680455o, 680457o) each of duration
60 seconds for amplifiers 00 - 17 (the top row of Megacam).
Middle of N 25% 50% 75%
bin (arcsec) <--------- mas ------->
-------------------------------------------------
15.00 11473 2.2 3.6 5.6
45.00 29647 2.9 4.7 7.1
75.00 40999 3.5 5.6 8.4
105.00 45780 4.0 6.4 9.5
135.00 44558 4.4 7.1 10.3
165.00 39748 4.9 7.7 11.0
195.00 34975 5.1 7.9 11.2
225.00 32212 5.1 7.9 11.2
255.00 30010 4.9 7.7 10.8
285.00 27711 4.7 7.3 10.3
315.00 25513 4.5 6.9 9.9
345.00 24035 4.3 6.8 9.7
375.00 21930 4.3 6.6 9.3
405.00 20585 4.1 6.5 9.1
435.00 18254 4.1 6.4 9.1
465.00 16800 4.1 6.4 9.1
495.00 14706 4.1 6.5 9.2
525.00 13144 4.1 6.4 9.0
555.00 11260 4.1 6.3 8.9
585.00 9513 4.0 6.2 8.9
For those with short memories and/or are e-mail challenged, here is the
table from my previous note for the 1-second exposures.
Middle of N 25% 50% 75%
bin (arcsec) <--------- mas ------->
-------------------------------------------------
15.00 32 12.6 22.4 35.3
45.00 60 16.3 27.5 39.9
75.00 90 26.2 38.6 50.0
105.00 129 19.7 35.5 56.6
135.00 181 28.0 42.8 62.3
165.00 175 26.9 41.3 57.9
195.00 174 26.5 40.8 57.8
225.00 206 29.2 42.6 62.6
255.00 185 30.8 49.5 71.5
285.00 153 32.0 46.6 66.2
315.00 161 30.7 48.0 71.0
345.00 155 29.4 44.9 70.3
375.00 155 37.0 46.7 61.0
405.00 145 33.1 51.7 65.9
435.00 139 32.3 47.4 63.4
465.00 118 36.3 49.4 66.4
495.00 98 33.5 49.5 68.1
525.00 91 32.7 52.0 67.4
555.00 85 34.3 52.3 66.1
585.00 69 35.8 54.5 80.4
I don't think that the turn-over beyond about 250 arcsec is real. Since
the 60-sec exposures were dithered, the longer distances measured on a
single CCD are confined to a smaller area of the CCD. I think
that the important part is the growth of error between 0 and 200 arcsec.
My "chi-by-eye" sees a factor of about 6 whereas SQRT(60/1) would predict
a factor of about 7.8. I think that there are a couple of competing
effects, but I am not sure which (if either) enters. For the short exposures,
we really are photon starved, so there might be a degradation of the
astrometric error due to a component of centroiding error. I was able
to use much brighter stars in the 60-second exposures so centroiding
error is not an issue. However, we might be running up against the
limitations of my centroiding algorithm, the metric performance of the
CCD, or other effects that place limits on the ultimate astrometric
accuracy. I need to think about these issues.
So Nick will claim that Kolmogorov rules and SQRT(Texpose) is all we have
to worry about, and I will claim that this seems to be mostly true
except when we run into the hard stops of the real world.
-Dave
PS
To avoid confusion, let me state that when I compute a linear transformation,
between coordinate systems, I mean I use least squares to determine the
coefficients (a,b,c,A,B,C) in
X = a + bx + cy
Y = A + Bx + CY
By a quadratic fit, I mean I find (a,b,c,d,e,f,A,B,C,D,E,F) in
X = a + bx + cy + dx**2 + exy + fy**2
Y = A + Bx + Cy + Dx**2 + Exy + Fy**2
I have found that others use the same terms for different transformations.
--------------040204010508090709040701--
LSST LSST LSST LSST LSST Mailing List Server LSST LSST LSST LSST LSST LSST
LSST
LSST This is message 91 in the lsst-general archive, URL
LSST http://www.astro.princeton.edu/~dss/LSST/lsst-general/msg.91.html
LSST http://www.astro.princeton.edu/cgi-bin/LSSTmailinglists.pl/show_subscription?list=lsst-general
LSST The index is at http://www.astro.princeton.edu/~dss/LSST/lsst-general/INDEX.html
LSST To join/leave the list, send mail to lsst-request@astro.princeton.edu
LSST To post a message, mail it to lsst-general@astro.princeton.edu
LSST
LSST LSST LSST LSST LSST LSST LSST LSST LSST LSST LSST LSST LSST LSST LSST LSST