  The dynamic spectrum of a radio pulsar is an in-line digital hologram of the
ionised interstellar medium. It has previously been demonstrated that such
holograms permit image reconstruction, in the sense that one can determine an
approximation to the complex electric field values as a function of
Doppler-shift and delay, but to date the quality of the reconstructions has
been poor. Here we report a substantial improvement in the method which we have
achieved by simultaneous optimisation of the thousands of coefficients that
describe the electric field. For our test spectrum of PSR B0834+06 we find that
the model provides an accurate representation of the data over the full 63 dB
dynamic range of the observations: residual differences between model and data
are noise-like. The advent of interstellar holography enables detailed
quantitative investigation of the interstellar radio-wave propagation paths for
a given pulsar at each epoch of observation; we illustrate this using our test
data which show the scattering material to be structured and highly
anisotropic. The temporal response of the medium exhibits a scattering tail out
to beyond 100 microsec and a pulse arrival time measurement at this frequency
and this epoch of observation would be affected by a mean delay of 15 microsec
due to multipath propagation in the interstellar medium.
