In the past, the rainbow schlieren deflectometry technique has been employed to obtain scalar measurements in non-reacting and reacting laminar steady or unsteady flows. The technique has been limited to laminar flows because the path integrated beam deflection angle data must be de-convulated to obtain the local flow properties. In this study, a cross beam approach, whereby two orthogonal beams are employed is explored for statistical measurements in turbulent flows. The theoretical framework of the cross beam correlation technique requiring assumptions of homogeneous and isotropic turbulence is presented. The workability of the technique is verified using numerical simulations of an unsteady laminar helium-air jet.