  We derive an analytical form of the Schmidt modes of spontaneous parametric
down-conversion (SPDC) biphotons in both Cartesian and polar coordinates. We
show that these correspond to Hermite-Gauss (HG) or Laguerre-Gauss (LG) modes
only for a specific value of their width, and we show how such value depends on
the experimental parameters. The Schmidt modes that we explicitly derive allow
one to set up an optimised projection basis that maximises the mutual
information gained from a joint measurement. The possibility of doing so with
LG modes makes it possible to take advantage of the properties of orbital
angular momentum eigenmodes. We derive a general entropic entanglement measure
using the R\'enyi entropy as a function of the Schmidt number, K, and then
retrieve the von Neumann entropy, S. Using the relation between S and K we show
that, for highly entangled states, a non-ideal measurement basis does not
degrade the number of shared bits by a large extent. More specifically, given a
non-ideal measurement which corresponds to the loss of a fraction of the total
number of modes, we can quantify the experimental parameters needed to generate
an entangled SPDC state with a sufficiently high dimensionality to retain any
given fraction of shared bits.
