  Subject of this paper are intrinsic ellipticity correlations between
galaxies, their statistical properties, their observability with future surveys
and their interference with weak gravitational lensing measurements. Using an
angular momentum-based, quadratic intrinsic alignment model we derive
correlation functions of the ellipticity components and project them to yield
the four non-zero angular ellipticity spectra $C^\epsilon_E(\ell)$,
$C^\epsilon_B(\ell)$, $C^\epsilon_C(\ell)$ and $C^\epsilon_S(\ell)$ in their
generalisation to tomographic surveys. For a Euclid-like survey, these spectra
would have amplitudes smaller than the weak lensing effect on nonlinear
structures, but would constitute an important systematic. Computing estimation
biases for cosmological parameters derived from an alignment-contaminated
survey suggests biases of $+5\sigma_w$ for the dark energy equation of state
parameter $w$, $-20\sigma_{\Omega_m}$ for the matter density $\Omega_m$ and
$-12\sigma_{\sigma_8}$ for the spectrum normalisation $\sigma_8$. Intrinsic
alignments yield a signal which is easily observable with a survey similar to
Euclid: While not independent, significances for estimates of each of the four
spectra reach values of tens of $\sigma$ if weak lensing and shape noise are
considered as noise sources, which suggests relative uncertainties on alignment
parameters at the percent level.

Cosmology and Nongalactic Astrophysics