Re: Astrometry errors

[Andrew Bennett <andrew.bennett@ns.sympatico.ca>]

On Sat, 04 Nov 2000 15:38:24 +0100, Jure Skvarc 
<jure.skvarc@ijs.si> wrote:

>Andrew reported that he gets 0.1" probable error (? is this average error or
>median?) in RA and DEC with TYCHO 2 catalog and recent Mark IV images.  This is
>almost too good.
Surprised me too, after the struggle to get down to 1 arcsec!

>  It would be nice to know more details, such as the maximum
>magnitude of the stars taken in the comparison and what is their signal, number
>of stars used for fit etc...

The data source is CD15 (short and long exposures).

I match Tycho2 stars not flagged as having other stars close
by or other pathology.

The PSF is estimated by fitting 30 coefficients to the 
30 brightest (but clearly not saturated) matched Tycho2 sources.
All stars are refitted using the final PSF; this is an optimum 
least squares fit to X1, X2 and A. As previously reported ad
nauseam, the optimum least squares fit is better than aperture
methods, especially for weak sources against a high sky
background. People with nice dark skies may disregard this comment.

For the longer exposures, almost all the Tycho2 sources are matched;
300 or so per image going to beyond M=12. My analysis of the shorter 
exposures does not go as deep so there are fewer matches.

The figure I quoted is the probable error or semi-interquartile range.
There are lots of outliers (mostly the result of other close sources,
I think) so the standard deviations are much worse. The worst
outliers are pruned as part of the astrometric fit: since this fit
is least-squares, this pruning is essential. The results are thus
a little bit optimistic.

Some typical results
H3R1659.830 (short V-band exposure) 246 matched sources
p.e. RA 0.204 Dec 0.205 arcsec; Mag 0.0688
H3R1659.832 (long V-band exposure) 344 matched sources
p.e. RA 0.138 Dec 0.169 arcsec; Mag 0.1126
H4R1659.830 (short I-band exposure) 185 matched sources
p.e. RA 0.283 Dec 0.225 arcsec; Mag 0.1453

And the last two I measured before my previous post:
H4R1659.832 (long I-band exposure) 272 matched sources
p.e. RA 0.098 Dec 0.098 arcsec; Mag 0.2377
H4R1659.836 (long I-band exposure) 367 matched sources
p.e. RA 0.104 Dec 0.106 arcsec; Mag 0.2009

Why the long exposure I-band images are consistently
better than the V-band when the PSF is clearly fuzzier
for the I-band, I do not know
The larger magnitude errors for the long exposures is
simply the result of going deeper in magnitude.
The larger magnitude errors for the I-band compared
to V-band arises mostly from converting the B and V
catalog magnitudes.
> 
>					Jure Skvarc

>
>Stupendous Man wrote:
>> 
>>   Now, on the other hand, if you are talking about the Mark IV images --
>> which are stare-mode frames, not scans -- then the main source of
>> astrometry errors is distortion in the PSF and in plate scale
>> near the corners of the chip.  I'm not sure which is more important;
>> perhaps Andrew Bennett or Jure Skvarc could give us an informed opinion.
>> 
>>                                               Michael Richmond
I, at least, have no idea! All the errors disappear into
the cubic fit ... the last time I tried higher order, there
was a hint of 5th order in there too. The PSF variation is
certainly highly significant. If forced to pronounce on it, I
would say it was the dominant error. With brute force fitting
to good catalog positions, the distinction doesn't matter.

Andrew Bennett, Avondale Vineyard, Nova Scotia, Canada.