  In three-dimensional systems of the Ising universality class the ratio of
correlation length amplitudes for the high- and low-temperature phases is a
universal quantity. Its field theoretic determination apart from the
$\epsilon$-expansion represents a gap in the existing literature. In this
article we present a method, which allows to calculate this ratio by
renormalized perturbation theory in the phases with unbroken and broken
symmetry of a one-component $\phi^4$-theory in fixed dimensions $D=3$. The
results can be expressed as power series in the renormalized coupling constant
of either of the two phases, and with the knowledge of their fixed point values
numerical estimates are obtainable. These are given for the case of a two-loop
calculation.
