Spectroscopic calibrations are complex, with added complexity from the multislit nature of DEIMOS. We assume multislit throughout; longslit is a special case of multislit.
This chapter deals with these elements:
to describe the x-distortion pattern.
0.25
pixel or better. We assume the form:
where the subscripts o and a denote derivation from the individual
observation or from the database archive, respectively.
We assume the spectra have already been x-rectified or straightened.
This functional form
describes the wavelength dependence for across an image; note that between
slitlets there will be a discontinuity in
the coefficient functions p(x), q(x), r(x), s(x), t(x),.
The general form requires knowledge of p, q, r, s, t as functions of
as well.
cm 
Å .
Wavelength Calibration:
Internal arcs lamps cannot be used to precisely wavelength calibrate spectra on the sky for these reasons:
However, spectra on the sky (particularly in the blue) will not always
include enough night sky lines of sufficient S/N to provide
a satisfactory wavelength solution. A hybrid calibration
-- using internal lamps for higher order terms and night sky lines for
lower-order terms --
is probably the most practical method to overcome these difficulties.
In practice, we propose that the coefficients r, s, t can be obtained
from internal arc spectra (and maintained in the database for pipeline
mode), and only the zeropoint and scale (p, q) come directly from the
science images using night sky lines. Our goal by this method is
px.
The coefficients are measured for each grating using a set of
``line-of-slitlets''
(LOS) masks to provide a grid of positions in the MF/SMCS. Spectra are
obtained and measured for each slit through a sequence of grating tilts.
For each grating, this gives a set of coefficients on a representative
grid in grating tilt ( 
) and slitmask coordinates (X,Y), that is,
Note that, once x-rectified, there is a one-to-one correspondence between
X and x
.
There are two options for database storage. First, the actual 3-D data cubes
(one per grating) can be stored. For reasonable values of gratings (5),
LOS masks (8), slits per mask (100) and grating tilts (12), this means
storing five data cubes of 9600 numbers each, or 48000 numbers total.
To retrieve coeeficients would involve interpolating in the appropriate
data cube.
The second method is to fit each data cube with an interpolating function
of the form:
For five interpolating functions with 13 coefficients each, we need
to store only 65 numbers per grating, or 325 numbers total for five gratings.
The actual number of coefficients needed is TBD.
Flux Calibration: The grating introduces an additional degree of complexity, partially by introducing an occasional vignetting that depends on grating tilt, but most importantly because the camera will now vignette some of the incoming beams. The vignetting at the grating itself, however, will affect absolute but not relative flux calibration, as the light is not yet dispersed. Furthermore, the camera vignetting is a function of the grating reflection angle only, and it does not matter if that angle is a result of dispersion, slitlet location, or both. For this reason, we can use continuous spectra of a line-of-holes (LOH) mask to map out the camera vignetting sufficient for relative flux calibration.
Here is a summary of the various components to spectral flux calibration:
)
grating at large tilts. Measurement TBD.
(here, ``a'' refers
to ``arc spectrum'');
for each object spectrum,
assuming 
from previous fits.
grid.
from information in the database .
Night sky lines (or internal arc at same position/time) are used to solve
for specific , assuming r, s, t from above.
Image is remapped onto a specified grid.
The database will contain a current x-distortion map;
for each grating, a 3-D table of coefficients that can
be interpolated to specific values at a given (x,y) and
or interpolating functions for each grating to provide the same values;
[flux cal info, TDB].
The database will also contain certain supplemental information:
Required Hardware:
. Place in a 3-D table
for each grating and tilt (240000 coefficients total).
for each grating.
Instrument-control scripts and instructions to create the database products listed above will be required.
As stated earlier, for flux calibration there is a need for a continuum light source of constant spectral shape.
We need to discuss the effect of spatial distortion (different scales throughout the image) on flux calibration. If the distortion is mapable, there is no problem correcting the data for this.
We have not described slit functions (variations in throughput due to irregularities in the slit shape). These must be mapped by the user for each mask, and will be sensitive to plate scale changes, but their measurement and removal is not expected to be a problem. Current milling practices appear to reduce variations along the slit to less than about 1%.