  The double-detonation explosion model has been considered a candidate for
explaining astrophysical transients with a wide range of luminosities. In this
model, a carbon-oxygen white dwarf star explodes following detonation of a
surface layer of helium. One potential signature of this explosion mechanism is
the presence of unburned helium in the outer ejecta, left over from the surface
helium layer. In this paper we present simple approximations to estimate the
optical depths of important He I lines in the ejecta of double-detonation
models. We use these approximations to compute synthetic spectra, including the
He I lines, for double-detonation models obtained from hydrodynamical explosion
simulations. Specifically, we focus on photospheric-phase predictions for the
near-infrared 10830 \AA~and 2 $\mu$m lines of He I. We first consider a double
detonation model with a luminosity corresponding roughly to normal SNe Ia. This
model has a post-explosion unburned He mass of 0.03 $M_{\odot}$ and our
calculations suggest that the 2 $\mu$m feature is expected to be very weak but
that the 10830 \AA~feature may have modest opacity in the outer ejecta.
Consequently, we suggest that a moderate-to-weak He I 10830 \AA~feature may be
expected to form in double-detonation explosions at epochs around maximum
light. However, the high velocities of unburned helium predicted by the model
($\sim 19,000$~km~s$^{-1}$) mean that the He I 10830 \AA~feature may be
confused or blended with the C I 10690~\AA~line forming at lower velocities. We
also present calculations for the He I 10830 \AA~and 2 $\mu$m lines for a lower
mass (low luminosity) double detonation model, which has a post-explosion He
mass of 0.077 $M_{\odot}$. In this case, both the He I features we consider are
strong and can provide a clear observational signature of the double-detonation
mechanism.
