  Generalizing the original work by Hodges and Blumenthal, we outline a
formalism which allows one, in principle, to reconstruct the potential of the
inflaton field from knowledge of the tensor gravitational wave spectrum or the
scalar density fluctuation spectrum, with special emphasis on the importance of
the tensor spectrum. We provide some illustrative examples of such
reconstruction. We then discuss in some detail the question of whether one can
use real observations to carry out this procedure. We conclude that in
practice, a full reconstruction of the functional form of the potential will
not be possible within the foreseeable future. However, with a knowledge of the
dark matter components, it should soon be possible to combine
intermediate-scale data with measurements of large-scale cosmic microwave
background anisotropies to yield useful information regarding the potential.
