  We construct a ${\rm KO}$-valued families index for a class of
$1|1$-dimensional Euclidean field theories. This realizes a conjectured cocycle
map in the Stolz--Teichner program. We further show that a bundle of spin
manifolds leads to a family of partially-defined $1|1$-Euclidean field
theories, yielding a cocycle refinement of the families analytic index. The
methods are chosen with the goal of generalizing to $2|1$-dimensional field
theories, where analogous structures are expected to provide an analytic index
valued in topological modular forms.
