Holographic properties of the second-harmonic cross correlation of object and reference optical wave fields

We show that second-harmonic cross correlation of the optical field that propagates from an illuminated object with the illuminating field is a process that shares many features with holography. The wave fronts of the double-frequency field are able to reconstruct holographic images of the object whose dimensions and position can be calculated by use of the holographic formalism. Our theory fits the experimental results obtained by use of a Q-switched Nd:YAG laser as the illuminating source and a thin β-barium borate crystal in a noncollinear type I phase-matching geometry for cross correlation.