  A tool for representation of the one-dimensional astrometric signal of Gaia
is described and investigated in terms of fit discrepancy and astrometric
performance with respect to number of parameters required. The proposed basis
function is based on the aberration free response of the ideal telescope and
its derivatives, weighted by the source spectral distribution. The influence of
relative position of the detector pixel array with respect to the optical image
is analysed, as well as the variation induced by the source spectral emission.
The number of parameters required for micro-arcsec level consistency of the
reconstructed function with the detected signal is found to be 11. Some
considerations are devoted to the issue of calibration of the instrument
response representation, taking into account the relevant aspects of source
spectrum and focal plane sampling. Additional investigations and other
applications are also suggested.
