We have proved for the first time and proposed an algorithm of unique spatial profile reconstruction of the components
(3)yyyy of complex tensors
(3)(z, ω', ω', −ω, ω) and
(3)(z, 2ω±ω', ±ω', ω, ω), describing four-photon interaction of light waves in a one-dimensionally inhomogeneous plate, whose medium has a symmetry plane my that is perpendicular to its surface. For the media with an additional symmetry axis 2z, 4z, 6z or ∞z that is perpendicular to the plate surface, the proposed method can be used to reconstruct about one-fifth of all independent components of the above tensors.