Frank,
I see now that resolution is not cleanly described as a probability
function on the pixels,
since it is a rough description of the PSF which was convolved with the
perfect image to create the observed image. There are varying degrees
of descriptions for the PSF:
1) A FWHM for each axis. Mention of whether to use a Gaussian or an
Airy disk would be nice.
2) Same as 1 but different values for different parts of the 4DBin Object. 3) A 4D PSF. this would probably be a URL to a 4DBin Object 4) Same as 3 but a different PSF for different parts of the 4DBin Object.
The cross-talk that I mention could be handled somewhat like the resolution. It is different however, because in this case it is a function of the location on the pixel. A cusp centered on a pixel will blur less than a cusp centered near the edge of the pixel. PSF convolution does not work that way.
Ed
PS - I have to run off to the Cambridge meeting right now. Still to
come, how to put the
list of describing elements of the 4DBin object into XML.
Frank Valdes wrote:
>My offhand comment about filters and resolution is somewhat confusing even
>to me. Thinking a little more precisely what you have is
>
> P(i|x,y,e,t) - prob. of detecting a photon in bin i given (x,y,e,t)
>
>The mapping to index space is where the instrumental characteristics enter.
>This function is not very practical. Instead one would integrate over
>a bin j to get
>
> P(i|j) - prob. of detecting a photon in bin i given it should fall in bin j
>
>If the indexing scheme for the bins is ordinal then this would take the form
>of a sparse matrix. It would only be diagonal for bins with one
>parameter varying.
>
>Even this is probaby too general for a simple data model. A simpler
>definition, which is close to how resolution is typically described in
>image and spectral data, is to define "resolution" bins. It would use
>the same method used to describe the widths of the bins in the
>continuous parameter space but define a probability (say 95%) that a
>photon with parameter values corresponding to the center of the bin (or
>with any value within the bin) is counted within the resolution bin.
>The exact definition TBD. These resolution bins may or may not
>overlap.
>
>Some more food for thought,
>Frank
>
>
>
Received on 2003-05-13Z19:55:06