Eduardo,

> By eye I can see that an isophote far from the center actually gives 
> you a very good estimate of the actual center of the PSF. However, I 
> find no way to recover these coordinates by using ELLPRO.

First a caveat: ESP has not been supported for a good many years.
Even then there were known issues, some of which I touch upon below.

In the GAIA ESP interface there is a Results tab that gives X, Y,
semimajor axis, flux, PA, ellipticity, as well as a small plot of the 
profile.

Also there is an output catalogue (specified by OUTCAT) which gives the 
above to greater precision and more statistics for each elliptical 
isophote.  The ellipse centre co-ordinates are in Columns 3 and 4.  The 
default in Gaia is make a GaiaEspCat.txt.  This is a text file with a 
schema at its head. Sadly, although this was a standard Starlink format 
I've been unable to persuade Mark Taylor to add it to the STIL interface 
so could be read directly by TOPCAT.  Run from the command line ELLPRO 
can create a FITS table if you supply the file extension .fits for 
Parameter OUTCAT table.

> In the attached figure the problem is perhaps more clearly explained. 
> The white points are produced by the Contouring tool in GAIA.

My personal experience with ESP's profiling has not been good. At faint 
isophote levels it becomes unstable and indeed can move inward instead 
of outward progression to lower surface brightness in broad annuli often 
leading to isophotes crossing.  It was supposed to at least follow the 
Jedrzejewski method.  Alas my last-century requests to the Image 
Processing Software Strategy Group failed to divert effort to correct 
the blatant problems, so I went elsewhere for a bright-galaxy 
surface-photometry tool.  It is something I've long wanted to rectify, 
also to permit constraints like fixed ellipticity as in BEAMFIT, and use 
world co-ordinates not just pixels.

> The green circle is my estimate of the best fit to those points. However, 
> at this radius of isophote ELLPRO reports a fit like the white circle, 
> which is clearly off the centre of the set of points.

As to why ELLPRO seems to be off centre there may be clues from the 
various Fourier moments listed in the catalogue.

It's bizarre behaviour like this that had me not trusting the profiling 
at faint levels.  I'm not convinced that the minimisation to the best 
ellipse is working correctly.

One other thought, what's the origin and current WCS of your image?

> My only explanation for this is that ELLPRO must somehow be using a 
> different set of points, so the problem may be the way the contour 
> points are extracted from the image before fitting. However, I have no 
> way to check this because ELLPRO doesn't dump the points it uses for 
> fitting.

The documentation says the modelling is tuned. "It has been created as a 
robust application which attempts to generate ellipse profiles by 
placing a trial ellipse profile on a galaxy and then adjusting the 
ellipse characteristics to ensure the minimum possible variation in 
intensity around the ellipse. To do this it employs minimisation 
routines that are tuned for normal galaxies." Your image of the 
secondary and spider does not look like a normal galaxy, well at least 
for non-cosmological redshifts.  Still it's your contour is almost 
circular ELLPRO ought to be able to cope.  What happens if you 
adaptively smooth the lower levels?  Does the displacement of the centre 
persist?

> Is there any way to get these points to test this idea?

I don't know of one, apart from hacking the code to dump these data.

> Also, is there any way to force some parameters of the fitting process 
> to remain fixed? I'd like to force the eccentricity to be 0.

Only the centre I think.

Malcolm
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