Spatial Coverage (2d):

a. Spatical Coverage has been so far described with a Polygon.
  That is a detailed representation of the sky embraced by a data product.
  But it is not enough.
  It's ok to describe the coverage, eg in order to plot it.
  But what if a user is querying and asking all for products with
  a Field of View bigger than X arcmin ?

b. Typically the coverage of an archived (eg ESO, HST) observation
  is described in terms of a field of view (fov_x, fov_y), a roll angle,
  the coordinates of the pointing associated with a given reference pixel.
  This is ok because a detector shape is approximately rectangluar.
  But it is not enough.
  What if there is severe geometric distorsion (see HST/ACS) ?
  (The rectangular shape of the detector maps to a romboidal shape on the sky.)

  What if the data product is a mosaic of several dithered observations ?
  (Depending on the number of observations and on the offsets, the final
   product will have a very complex shape. )

A more complete Spatial Coverage description is required to satisfy
different points of view.

Hence, Spatial Coverage should contain both a detailed (vectorial)
and a coarse (scalar) representation of the FoV.
The first to be used in a vectorial context (eg plotting, intersecting),
the second in a scalar context (eg, queries):

1)  A Polygon (or other shape)


2) one of the two (or both?):

  i  A representative number indicating the overall Field of View
     (eg FoV_ref_value = sqrt( fov_x**2 + fov_y**2 )

 ii  A rectangular representation of the field of view
     in terms of (fov_x, fov_y, roll_angle, pointing_coords, reference_pixel)
     To be used when (2.i) would be misleading, eg, for very elongated products
     (eg, a la Groth strip). 

Astrometric accuracy:
An overall estimate of the astrometric precision must be given.
It could be as simple as providing the typical astrometric accuracy
of the catalogue used to derive the astrometry of the product,
eg if USNO was used: 0.25 arcsec.
Each vertex in the polygon above is affected by this error.

More complex cases could exist:
suppose a image cutout service returns an image whose pixels come
from two different survey stripes. Different stripes
might have different astrometric accuracies.
Hence the product returned by the image cutout service is characterised
by different astrometric accuracies in different part of the image.
(maybe the cutout service should not provide such images)

Spatial Coverage: List of required quantities

Polygon      (as a list of (eg RA,DEC) pairs, in a given reference frame)
FoV diameter (as a single number, in arcmin)
FoV          (fov_x, fov_y)
Pointing     (WCS, including CRTYPs CRVALs CRPIXs, and Roll Angle)


Spatial Sensitivity:

The Spatial Coverage has to be complemented with the actual description
of the sensitivity (to be discussed in a different chapter).
The idea  being that not the whole FoV is necessarily seen with the
same sensitivity. Within the FoV there will be regions suffering
of vignetting, regions whose S/N is different because the product 
is a mosaic of dithered observations, etc.
But a fairly simple first order approximation might be to include
the upper and lower limits for the flux (eg the saturation level and the
limiting flux at a given S/N level).
The accuracy in the determination of the limiting flux
is to be provided, and it depends on other quantities like the ZeroPoint
of the image (usually estimated using standard stars), and the AirMass
for a ground-based observatory. Such accuracy
is the Photometric accuracy, and could be (first order) just a number
in flux or magnitude units.

Spatial Sensitivity: List of required quantities

Flux Lower Limit (saturation)
Flux Upper Limit (limiting flux/magnitude)
Photometric info (zeropoint, airmass)
Photometric accuracy 


Spatial Resolution & Sampling:

Light is collected by a telescope, after having or not passed through
the atmosphere, and focused onto a detector. The dector is then read out.

Such apparently simple process brings into our game various distorsions
and effects.

 
     i.- Seeing (atmospheric) 

         Usually monitored by the observatory (DIMM seeing).
         Typically provided as an avg value, sometimes with an error:
         (AvgSeeing, ErrSeeing)


    ii.- Instrumental Point Spread Function (IPSF)

         Ideally the IPSF would be the Airy PSF {1.22*Lambda/D}
         Sometimes, the PSF is position dependent -> IPSF=IPSF(x,y)



   iii.- Pixel Response Function (also position dependent -> PRF(x,y)) 


    iv.- Sampling on a equally-spaces grid
         The grid is characterised by the pixel scale, which depends
         on the focal length and the phisical pixel dimensions,
         and it is usually given in seconds of arc:
         pixel scale := (px,py) (the X and Y sizes might differ)


     v.- the readout process might rebin the pixels, hence introducing
         an effect in both the pixel scale, and in the signal to noise ratio.


The Spatial Resolution (sometimes refered to as the Quality of the image)
could be described by providing a single quantity: the FWHM measured onto
the data product, which is the covolution of the various
above-mentioned components.
Usually, the following heuristic formula is used:

         FWHM = sqrt( Seeing**2 + IPSF**2 + [ (px+py)/2 ]**2 )
              = sqrt( Seeing**2 + (1.22*Lambda/D)**2 + [ (px+py)/2 ]**2 )

A real world example, the HST/WFPC2 case (no seeing in space):

         FWHM = sqrt( pixel_scale**2 + (1.22*Lambda/D)**2 )

which is ok since the FWHM does not vary that much within the FoV.

More generically, a first order approximation would be to provide
the usual triplet (loValue, refValue, hiValue) to describe the PSF.


The Sampling can be described by providing the pixel scales (px,py),
the actual number of pixels in both X and Y (eg, NAXIS1, NAXIS2),  
and the ration between the Spatial Resolution FWHM and the pixel scale
to know whether the image is undersampled or not.
Electronic rebinning is also to be provided.


Spatial Resolution & Sampling: List of required quantities

Seeing
ErrSeeing
PSF_FWHM        (loValue, refValue, hiValue) [wavelength and position dependent]

Sampling (aka Detector grid):
   Original pixel scales (px,py)
   Binning Factor        (electronic, eg 1x1, 2x2, etc)
   Bin Size              (product of pixel scale and binning factor)
   Numbero of Bins       (naxis1, naxis2)


Conclusions

All in all, by considering both the Spatial Coverage/Sensitivity,
Resolution and Sampling, the first order approximation required quantities
to be included in the model are:

Polygon      (as a list of (eg RA,DEC) pairs, in a given reference frame)
                -> other shapes can be considered of course
CoordinateSystem   (CRTYPs)        { for transformation (x,y) -> (skyCoords) }
CoordinatePointing (CRVALs)        { for transformation (x,y) -> (skyCoords) }
CoordinateDetector (CRPIXs)        { for transformation (x,y) -> (skyCoords) }
Roll Angle                         { for transformation (x,y) -> (skyCoords) }
FoV diameter (as a single number, in arcmin)            { for query purposes }
Aperture     (fov_x, fov_y)                             { for query purposes }
Astrometric accuracy (single number, in arcsec)       { for characterisation }
Seeing                                                { for characterisation }
ErrSeeing                                             { for characterisation }
PSF_FWHM     (loValue, refValue, hiValue) [wavelength and position dependent]
                                                      { for characterisation }
Binning Factor     (electronic, eg 1x1, 2x2, etc)      { for S/N computation }
Bin Size           (product of pixel scale and binning factor)
Numbero of Bins    (naxis1, naxis2)
Flux Upper Limit   (the saturation level)
Flux Lower Limit   (the limiting flux/magnitude)
Photometric info   (zeropoint, airmass)
Photometric accuracy (in delta magnitudes in the optical, better in flux)

A more detailed description would include various position and wavelength
dependent quantities:
PSF,
PRF,
Sensitiviy maps,
Exposure maps
etc.