  In this paper we develop the foundations for microlocal analysis on
supermanifolds. Making use of pseudodifferential operators on supermanifolds as
introduced by Rempel and Schmitt, we define a suitable notion of super
wavefront set for superdistributions which generalizes Dencker's polarization
sets for vector-valued distributions to supergeometry. In particular, our super
wavefront sets detect polarization information of the singularities of
superdistributions. We prove a refined pullback theorem for superdistributions
along supermanifold morphisms, which as a special case establishes criteria
when two superdistributions may be multiplied. As an application of our
framework, we study the singularities of distributional solutions of a
supersymmetric field theory.
