  When there are many observations of an astronomical source - many images with
different dithers, or many spectra taken at different barycentric velocities -
it is standard practice to shift and stack the data, to (for example) make a
high signal-to-noise average image or mean spectrum. Bound-saturating
measurements are made by manipulating a likelihood function, where the data are
treated as fixed, and model parameters are modified to fit the data.
Traditional shifting and stacking of data can be converted into a model-fitting
procedure, such that the data are not modified, and yet the output is the
shift-adjusted mean. The key component of this conversion is a spectral model
that is completely flexible but also a continuous function of wavelength (or
position in the case of imaging) that can represent any signal being measured
by the device after any reasonable translation (or rotation or field
distortion). The benefits of a modeling approach are myriad: The sacred data
never are modified. Noise maps, data gaps, and bad-data masks don't require
interpolation. The output can take the form of an image or spectrum evaluated
on a pixel grid, as is traditional. In addition to shifts, the model can
account for line-spread or point-spread function variations,
world-coordinate-system variations, and calibration or normalization
variations. The noise in the output becomes uncorrelated across neighboring
pixels as the shifts deliver good coverage in some sense. The only cost is a
small increase in computational complexity over that of traditional methods. We
demonstrate the method with a small data example and we provide open source
sample code for re-use.
