Fri May 16th - Moon Room - 2:00pm
The Sky Pixelization Algorithm - How Should Pan-STARRS Sample the Sky?
Discussion leader: Nick Kaiser

In the existing pipelines the part of the sky observed is usually
mapped to a single tangent plane, the size of this plane being
generally similar to the field size at CFHT or SUBARU.  This tangent
plane is then covered with a rectangular grid of slightly overlapping
image. This is motivated by computation convenience: it allows one
to deal with generally non-rectangular data boundaries; using
rectangular units allows one to use the FFT for smoothing, and
using a grid of small units avoids problems with FFT costs for very
large images, and, finally, it admits parallelization.  The other
main design factor is the sampling rate (inverse area per pixel).

Pan-STARRS will cover 3/4 of the sky, so the the simplest modification
would be to cover the sky with a set of slightly overlapping tangent
planes.  The fundamental requirements of of the sky-pixelization
algorithm are that it should allow creation, updating and retrieval
of image data (a representation of the sky surface brightness)
efficiently.  Support for efficient smoothing and other image
processing tasks is required. Within this framework the design
questions include:

1) What sort of tesselation of the sky into tangent planes should
one use? Various hierarchical schemes exist (please consult references
below and forward any similar stuff you find to the exploder).
What are their pros and cons?  What software is available? How
reliable/maintainable is it?  Should we aim to be backward compatible
with e.g. SDSS?  How large should the tangent planes be? How much
overlap, if any, is desirable?

2) Should the tangent planes be large, and broken up into rectangular
chunks? If so, how large is too large?  What type of projection
should be used?  Stereographic?

3) Or should the tangent plane size be taken to be the same as the
fundamental image chunk size? If so, what size should the tangent
planes be? Does this require too much overlap to reconcile with
the use of rectangular rasters?

3) What should the sky-pixel sampling rate be?  Are simple
considerations of e.g. point source photometry, astrometry figures
of merit adequate?

4) More radically, one might eschew the arguably ungainly concept
of overlapping tangent planes altogether and simply follow the
hierarchy down to the pixel level.  After all, many of the schemes
available boast efficient data retrieval and fast spherical transforms
(that can be used for smoothing).  Is this at all plausible?

I will try to open up the discussion on this topic this Friday,
but do not promise any answers.  The goal here is to establish
where consensus exists, if anywhere, and then to set out what is
required to resolve outstanding issues.

I have probably overlooked some important questions - please
circulate omissions.  I encourage you to take a look at what's
around and make your own assessment. One useful reference to various
tesselation schemes can be found at the Healpix site.
http://www.eso.org/science/healpix/content/HEALPix_Documentation_html/intronode3.
htm
It gives references to  Driscoll & Healy (1994), Muciaccia, Natoli
& Vittorio (1998) Baumgardner & Frederickson (1985), Tegmark (1996)
, Saff & Kuijlaars (1997), Crittenden & Turok (1998)  Szalay &
Brunner (1998)  (Grski (1999)).  Enjoy!  BTW, If you pick any of
these papers, please e-mail the URL or the .pdf and I'll post.

http://www.sdss.jhu.edu/htm/index.html#desc
describes the SDSS sccheme http://www.fftw.org/benchfft/results/
shows the (large) deviations from N * log(N) scaling for
state-of-the art FFT codes.

http://fits.cv.nrao.edu/documents/wcs/wcs.html describes the various
possible projections of the sphere onto tangent planes.

The point source figure of merit was discussed in
http://pan-starrs.ifa.hawaii.edu/project/people/kaiser/efficiency_notes/
related results can be found at
http://pan-starrs.ifa.hawaii.edu/project/people/kaiser/pipeline

Nick