  We present the first experimental study of the electric field distributions
E_N of a three-dimensional (3D) microwave chaotic rough billiard with the
translational symmetry. The translational symmetry means that the cross-section
of the billiard is invariant under translation along z direction. The 3D
electric field distributions were measured up to the level number N = 489. In
this way the experimental spatial correlation functions C_{N,p}(x,s) ~ <
E_{N,p}(x+1/2*s) E_{N,p}^(*)(x - 1/2*s)> were found and compared with the
theoretical ones. The experimental results for higher two-dimensional level
number N_{|} appeared to be in good agreement with the theoretical predictions.
