Optical wavelet correlator by four-wave mixing via reflection holograms in a bso crystal

A real-time wavelet-matched optical correlator is implemented by using four-wave mixing via reflection gratings. Photorefractive crystals BSO with different thickness are used in the experimental set-up. The square modulus of the Fourier transform of the Mexican-hat wavelet has been utilized to implement the wavelet filtering. The edge enhancement property of the wavelet transform is experimentally demonstrated in this scheme. Several non-binary filters with different dilation factors have been considered for different crystal thicknesses. When proper dilation factors are used, a higher robustness to the noise introduced by the finite crystal depth is obtained. The convenience to use a non-binary filter is experimentally demonstrated.