Strings in Twistor Superspace and Mirror Symmetry

We obtain the super-Landau-Ginzburg mirror of the A-twisted topological sigma model on a twistor superspace -- the quadric in CP^{3|3} x CP^{3|3} which is a Calabi-Yau supermanifold. We show that the B-model mirror has a geometric interpretation. In a particular limit for one of the Kaehler parameters of the quadric, we show that the mirror can be interpreted as the twistor superspace CP^{3|4}. This agrees with the recent conjecture of Neitzke and Vafa proposing a mirror equivalence between the two twistor superspaces.