Optimal Size of Spectrograph Pixels for Galaxy Surveys
Santiago Arribas computed the relative S/N of point sources when varying the pixel size
for a give exposure time. From this, he computed a optimal pixel
size for an isolated spectrum by maximizing its s/n.
For a galaxy survey, a lower s/n on each spectrum
might be acceptable if spectra of a larger number of galaxies
can be taken. The choice of the pixel size has therefore to take into
account the resulting field of view.
If high redshift galaxies are significantly larger than the NGST PSF,
the signal will increase faster for larger slit widths than in the case
of point sources. This factor will also favor larger pixel sizes.
larger pixel sizes is the final extension of galaxies.
The purpose
of this analysis it to investigate the trade-off between field of view
and s/n per spectrum for a galaxy survey, using observed galaxy densities
and galaxy sizes derived from the HDF.
In the analysis of the crowding of spectra on the detector,
the sources are still assumed to be point sources. Different models for
the galaxy density are used.
In the analysis of the galaxy sizes, the slit losses for
HDF galaxies as a function of magnitude is computed. In addition, the impact
of galaxies not be centered in the slit is investigated. This turns out
to be a very small effect.
The results are summarized in the following plot which compares the
"figure of merit" for the case of a single unresolved galaxy with Kab=27, a
27 Kab magnitude limited survey of high redshift galaxies assumed to
be unresolved, and the
same survey assuming the galaxies are of similar sizes and shapes as
the faintest HDF galaxies. It can be seen that a spectrograph optimized for
galaxy surveys has pixels about twice the size as one optimized for s/n of
a single spatially unresolved spectrum.
