Subject: 20 Astrometric Questions

From: Dave Monet

Submitted: Fri, 11 Apr 2003 11:19:26 -0700

Message number: 105 (previous: 104, next: 106 up: Index)

Given the current trend for Gatesification of Requirements Documents,
let me ask the following 20 Questions in an attempt to define the
astrometric task.  This doesn't replace a Requirements Document,
but perhaps it will help focus our thoughts on what is involved, and what
questions can be answered before we commit to algorithms, pipelines,
and surveys.  Fire away!  There is nothing that you can say that compares
with the damage being inflicted by my own organization.

  1) What is the astrometric accuracy floor under ideal circumstances?
  2) How does the accuracy degrade with short exposure time?
  3) How does the accuracy vary with field size?

    (I sent around a message based on CFHT Megacam data, but it would
     be nice to get similar short exposure data for different sites
     and/or different nights at the same site.  In particular, it
     is important to understand if image FWHM and the short exposure
     astrometric accuracy were correlated, and even more important to
     test if there are other parameters (wind over trees, etc.) that
     might influence the astrometric accuracy.  I have taken an action
     to chat up various observatory directors in search of a few minutes
     of T&E time to get such data.  Volunteers (i.e., those with access
     to large aperture, large FOV systems with a few extra minutes)
     are welcome, too.)

   4) How does astrometric accuracy degrade with field crowding in
      the pixel-based frame, and is processing these data appropriate
      given the observing cadence?
   5) What are the astrometric requirements for the difference image,
      and who is responsible for them?
   6) What are the astrometric requirements for the accumulated (deep)
      image and who is responsible for them?

     (Obviously, I am frightened by the whole process of warping,
      repixelization, subtraction, and accumulation.  DCR is at least
      one of the problems involved, but others might be as simple as
      finding algorithms that preserve 1 or 10 or ?? millipixel accuracy.
      However, if the baseline cadence renders all fields hopelessly
      confused, then some sort of compromise is needed.  I need to
      think about what sort of data are needed, and then figure out
      if these data have been taken for other projects.  Off the top
      of my head, I have no idea what the Milky Way looks like at R=26.)

   7) Is the best centroiding algorithm the same as that used
      by the pipeline?

     (Historically, the best centroiding algorithms concentrate
      in the portion of the image wherein the brightness gradient
      is largest.  In the Gaussian approximation, this is typically
      in the range of 0.5 to 3.0 sigmas.  Most photometric algorithms
      match the PSF in the outer wings since the total flux is
      significant even if the SNR in a single pixel is low.
      Perhaps the pipeline needs to implement a separate algorithm
      for the measurement of the centroid.)

   8) Can we use reference galaxies instead of reference stars?

     (We want absolute parallaxes and proper motions, and
      there should be lots of galaxies to choose from.  Can a subset
      with a reasonable range of color and shape (reasonably round
      ellipticals) be isolated, and what is the astrometric penalty
      for using these?)

   9) Are the DCR models correct, and are there warping schemes that
      can accommodate DCR?

     (Differential Color Refraction appears to put serious limitations
      on the fidelity of the accumulated and difference images.  A
      sanity check of watching fields rise and set would be useful
      but the real task is developing a local warping that depends
      on color and the circumstances of the observation that can be
      combined with the algorithms of (5) and (6) to yield a better
      result.  Of course, if the size of the DCR is small compared to
      the requirements, or if hour angle imitations are introduced
      into the observing cadence, then this point is moot.)

  10) Who maintains the pixel-based catalog?
  11) What is the latency of the pixel-based catalog?
  12) Does any other task need the pixel-based catalog?

     (If real astrometry comes from the pixel-based catalog, then
      somebody must be in charge of accumulating the data,
      indexing it every once in a while, and making it available.
      If this is an "astrometry-only" task, then monthly (or
      similarly slow) latency is probably acceptable, and only
      the most minimal of access paths are needed.  I suspect
      that other precision tasks such as millimagnitude photometry
      need the pixel-based catalog.  These need to be identified
      and their needs accommodated.)

  13) Do the pixels last long enough for enhanced processing?

     (In some cases, multi-object fitting might alleviate the
      crowding problem.  This seems to be outside the normal
      pipeline task, but many astrometric objects can be
      identified, and the proper multi-object fitting template
      prepared in advance or on the basis of a few observations.
      This knowledge can be used to do enhanced processing on
      the image data during the interval after the real-time
      pipeline runs but before the pixels are deleted.)

  14) Are there fast algorithms for taking the Fourier transform
      of unequally spaced data?
  15) Can filters optimized for detecting Keplerian motion in the
      Fourier coefficients be developed?

     (Proper motion and parallax are fit using simple least squares
      assuming that the parallax factors have been computed from
      the circumstances of the observation.  Keplerian motion
      is tough to process in (x,y) as a function of time, but is
      very well understood in the transform domain.  Unfortunately,
      FFT algorithms require equal sampling in time, and this is
      not possible, so efficient algorithms for unequally spaced
      data are needed.)

  16) Can useful astrometric data be produced from cadence+filter
      combinations used by other programs?

     (It appears that the Solar System cadence will involve wider
      filters and larger zenith distances than the nominal astrometric
      cadence.  Should we try to do astrometry with these data?
      The medium and deep surveys will provide extra data on smaller
      areas of sky.  Will we get better astrometry from these, and
      are there astrometric projects that can use the combination
      of smaller area and improved accuracy?)

  17) What historical catalogs and archives of astrometric data
      need to be prepared (digitized, characterized, put in a database,
      etc.) to extend the scientific impact of the survey?

     (Historical catalogs, catalog from other wavelengths, etc., need
      to be identified, collected, and organized, and this activity
      should be completed before the survey starts.)

  18) What astrometric products should trigger e-mail or other rapid
      dissemination paths?

     (If the expected accuracy is realized, we will get decent (10%
      error) parallaxes for all objects within 10pc given 6 months
      of data.  Hence, there will be a rolling window during the first
      year wherein each lunation will produce a list of nearby
      objects, and this list may be of interest to a wider community.
      Perhaps there is interest in rapid delivery of lists of
      high proper motion objects, objects with peculiar DCR motions,
      or even with preliminary evidence for wiggles.)

  19) How do we do the astrometric tie between the bright sky
      and the faint sky?

     (GAIA might do this for us, but it is at least a decade away.
      Hipparcos quits at about 10, and the survey will saturate
      between 16 and 18.  There are lots of interesting stars
      in this missing magnitude range.  I have proposed adding an
      ND survey for astrometry during bright time, but this has
      been met with laughter.  How else do we do this task since
      it appears to be necessary for the discussion of completeness, etc.)

  20) Who (other than USNO) is interested in the "inversion problem"
      of taking the relative measures and solving for an improved
      astrometric catalog containing (RA, Dec, motion, parallax, and
      wiggles)?

     (This is the Grand Prize, but very few groups other than USNO
      have the expertise or interest in doing a fit of 10e10 objects
      over 3pi steradians.)

-Dave

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