[FPSPACE] Deep Impact focus flaw due to Ball mistake -- newspaper

[William C. Keel]

Bob Christy wrote:

"If we had another "Hubble", would engineers now use a software fix rather
than a physical repair?"

Deconvolution can be a thorny issue in optical astronomy. Its use is
routine in radio interferometry, where life is easier in a couple of
ways.

The problem is basically one of taking smeared flux and putting it back where 
it started in the image, one of the class of "invserve problems". There
is an exact solution, starting from the fact that deconvolution in the
image domain is multiplication in the Fourier domain. This exact
solution, however, has limited use ofr most astronoical applications,
because it requires that the blurring (point-spread function, PSF) be 
precisely known, and that noise in the image not be important (since
noise is amplified along with the higher spatial frequencies in the
image). In radio astronomy, noise is generally not a problem in the
image (it occurs directly in the Fourier domain), and the
PSF can often be calculated from first principles (see a sample
of how well this works at 
http://www.astr.ua.edu/keel/telescopes/nrao.html,
for example. This noise amplification, and measuring the PSF, are the limits 
in optical work. For Hubble, the PSF changes slightly as the telescope 
structure "breathes" (Invar spacing rods and all) each orbit, and changes 
dramatically from point to point in the field of each camera. For planetary 
images with Hubble, Fourier deconvolution often proved adequate, while
other algorithms had to be use for fainter (noisier) targets.
For some problems (measuring exact positions of stars in a globular
clusrer to constrain brightness measures in ground-based image),
they were reliable. However, near the limit, the nonlinear reactrion
of most algorithms to image noise means that real and spurious features
can't be distinguished. The HST PSF at lainch was in fact unusually
amenable to deconvolution, since about 15% of the energy went into
a sharp core with essentially the expected width. This was enough
to anchor some algorithms nicely. They don't work nearly as well for
ground-based long-exposure imagery, since the PSF comnsists of a
single crudely Gaussian blur, which changes from one exposure to the
next and has to be redetermined each time from field stars. High
spatial frequencies (fine detail) are strongly attenuated, so the noise
penalty for gaining more than a factor of about 2 in spatial resolution
is usually prohibitive. (On top of that, for any kind of deconvolutiion,
you have very limited information finer than the pixel sampling, which
can limit some HST imagery because of the tradeoff between pixel
scale and field size).

As an example. here is a deconvolved original HST image of some faint
galaxies:
http://hubblesite.org/newscenter/newsdesk/archive/releases/1992/21/image/a
and here it is (from mult9ipoe colors) after refurbishment, and
without deconvolution:
http://hubblesite.org/newscenter/newsdesk/archive/releases/1996/29/image/a
(the area is just to upper right of the image center in this one).
Some features I thought were artifacts are real, some I thought were
real are artifacts, and there is no comparison in the sensitivity.

There is some petic justice in the fact that adaptive-optics images
look more like old aberrated Hubble images than long-exposure images
from the ground, allowing many of the same kinds of deconvolution.
Summary: for some cetagories of data and subject, deconvolution
can restore nearly the unaberrated image. For others, it can't. The
issues are how precisely known and stable the blur pattern is,
and the signal-to-noise of the data in regions of interest.
(Yes, this rambled on - does it show that I set up one of the
Hubble deconvolution algorithms and wrestled with a Cray on some
of those images???)

Bill Keel