  Spectroastrometry is a technique which has the potential to resolve flux
distributions on scales of milliarcseconds. In this study, we examine the
application of spectroastrometry to binary point sources which are spatially
unresolved due to the observational point spread function convolution. The
technique uses measurements with sub-pixel accuracy of the position centroid of
high signal-to-noise long-slit spectrum observations. With the objects in the
binary contributing fractionally more or less at different wavelengths
(particularly across spectral lines), the variation of the position centroid
with wavelength provides some information on the spatial distribution of the
flux. We examine the width of the flux distribution in the spatial direction,
and present its relation to the ratio of the fluxes of the two components of
the binary. Measurement of three observables (total flux, position centroid and
flux distribution width) at each wavelength allows a unique separation of the
total flux into its component parts even though the angular separation of the
binary is smaller than the observations' point-spread function. This is because
we have three relevant observables for three unknowns (the two fluxes, and the
angular separation of the binary), which therefore generates a closed problem.
This is a wholly different technique than conventional deconvolution methods,
which produce information on angular sizes of the sampling scale.
Spectroastrometry can produce information on smaller scales than conventional
deconvolution, and is successful in separating fluxes in a binary object with a
separation of less than one pixel. We present an analysis of the errors
involved in making binary object spectroastrometric measurements and the
separation method, and highlight necessary observing methodology.
