Re: [APML] OT: M16 Collaboration

[Ray Butler <ray.butler@nuigalway.ie>]

Not particularly addressed to Robert; rather for anyone who's interested 
in deconvolution:

>Hi Wei-Hao,
>The h-alpha was taken in very good seeing. I would think the
>FWHM was probably sub 2" and then with deconvolution 
>possibly bringing it close to 1".
>  
>
The problem with R-L and similar deconvolution algorithms is that they 
are non-linear, so for a given number of iterations, the degree of FWHM 
shrinkage depends on the S/N of the star to begin with. Brighter (but 
non-saturated) stars will show a lot more improvement than fainter stars 
and faint extended structures. This is because the engine of the 
deconvolution is a probability concept such as "maximum likelihood" (in 
the case of R-L) or "maximum entropy" (in the case of ...well the 
Maximum Entropy Method [MEM], obviously). The algorithms are designed 
with a certain inertia built in, a resistance to change the image at 
each iteration unless the probability warrants it. A source with high 
signal and low noise will be able to more quickly "persuade" the 
algorithm of the likelihood or entropy of its underlying sharp 
structure, than a faint source whose claims to equal sharpness just 
can't be trusted because of its noise. In probability terms, a noisier 
source is consistent with a wider variety of spatial shapes and 
intensities, so it is not possible to assign its photons into a tighter 
spot with any high degree of confidence that this really represents the 
underlying unblurred image.

So the upshot of deconvolution is that afterwards, some stars will be 
sharper than others. There will no longer be a common FWHM (i.e. a 
common PSF) for all objects in the field. It is possible to iterate so 
much that the bright stars end up with virtually all their light piled 
into a single pixel, but this is not real resolution, because they are 
now so undersampled that their spatial information has actually been lost.

So the more meaningful way to measure FWHM after deconvolution is to do 
it for the fainter stars.

Ray "a believer in carefully applied deconvolution since 1994" Butler

PS - important tip for deconvolution novices: subtract the constant 
background intensity level of the image first. This will reduce the 
appearance of "holes" around the brighter objects. It is even better if 
you can tell the algorithm how much background you subtracted, so that 
it can take account of it in determining the true S/N at each pixel, but 
perhaps not all implementations support that feature.

-- 
Dr. Ray Butler
Lecturer, Physics Department & Computational Astrophysics Laboratory,
National University of Ireland - Galway, 
University Road, Galway, Ireland. 
Web: www.nuigalway.ie/physics/ 	Email: ray.butler-AT-nuigalway.ie 
Tel: +353-91-493788 		FAX: +353-91-494584

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