In this paper we characterise 3D optical imaging techniques as 3D linear shift invariant
filtering operations. From the Helmholtz equation that is the basis of scalar diffraction theory we show
that the scattered field, or indeed a holographic reconstruction of this field, can be considered to be the
result of a linear filtering operation applied to a source distribution. We note that if the scattering is
weak, the source distribution is independent of the scattered field and a holographic reconstruction (or
in fact any far-field optical imaging system) behaves as a 3D linear shift invariant filter applied to the
refractive index contrast (which effectively defines the object). We go on to consider tomographic
techniques that synthesise images from recordings of the scattered field using different illumination
conditions. In our analysis we compare the 3D response of monochromatic optical tomography with
the 3D imagery offered by confocal microscopy and scanning white light interferometry (using with
quassi-monochromatic illumination) and explain the circumstances in which these approaches are
equivalent. Finally, we consider the 3D response of polychromatic optical tomography and in
particular the response of spectral optical coherence tomography and scanning white light
interferometry
