  We compute both extrinsic (lensing) and intrinsic contributions to the
(galaxy-)density-ellipticity correlation function, the latter done using
current analytic theories of tidal alignment. The gravitational lensing
contribution has two components: one is analogous to galaxy-galaxy lensing and
the other arises from magnification bias -- that gravitational lensing induces
a modulation of the galaxy density as well as ellipticity. On the other hand,
the intrinsic alignment contribution vanishes, even after taking into account
source clustering corrections, which suggests the density-ellipticity
correlation might be an interesting diagnostic in differentiating between
intrinsic and extrinsic alignments. {\it However}, an important assumption,
commonly adopted by current analytic alignment theories, is the Gaussianity of
the tidal field. Inevitable non-Gaussian fluctuations from gravitational
instability induces a non-zero intrinsic density-ellipticity correlation, which
we estimate. We also argue that non-Gaussian contributions to the intrinsic
{\it ellipticity-ellipticity} correlation are often non-negligible. This leads
to a linear rather than, as is commonly assumed, quadratic scaling with the
power spectrum on sufficiently large scales. Finally, we estimate the
contribution of intrinsic alignment to low redshift galaxy-galaxy lensing
measurements (e.g. SDSS), due to the partial overlap between foreground and
background galaxies: the intrinsic contamination is about 10 - 30 % at 10'.
Uncertainties in this estimate are discussed.
