  In a previous paper we described a method of estimating the
single-measurement bias to be expected in astrometric observations of targets
in crowded fields with the future Space Interferometry Mission (SIM). That
study was based on a simplified model of the instrument and the measurement
process involving a single-pixel focal plane detector, an idealized
spectrometer, and continuous sampling of the fringes during the delay scanning.
In this paper we elaborate on this ``instrument model'' to include the
following additional complications: spectral dispersion of the light with a
thin prism, which turns the instrument camera into an objective prism
spectrograph; a multiple-pixel detector in the camera focal plane; and, binning
of the fringe signal during scanning of the delay. The results obtained with
this improved model differ in small but systematic ways from those obtained
with the earlier simplified model. We conclude that it is the pixellation of
the dispersed fringes on the focal plane detector which is responsible for the
differences. The improved instrument model described here suggests additional
ways of reducing certain kinds of confusion, and provides a better basis for
the evaluation of instrumental effects in the future.
