Abstract: 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) = were found and compared with the theoretical ones. The experimental results appeared to be in good agreement with the theoretical predictions. We also found the dependence of the number of nodal domains lying on the cross-sectional planes of the cavity on the two-dimensional level number. Nodal domains are regions where a wave function has a definite sign. The experimental result are compared with the predictions of percolation theory.