Parallel spatial intensity correlations to decode random frequency-downconverted images

We record frequency-downconverted images that are chaotic, as they are obtained in a chi((2)) crystal from the interaction of two pulsed pseudo-thermal fields of which the one at the higher frequency encountered the imaged object. Spatial correlations of the intensity fluctuations in these chaotic images with the intensity of a single spatial Fourier component of the low-frequency input field, allow image retrieval if the number of records on which the ensemble-averages are calculated is suitably large. When it is too small to achieve a satisfactory result, we show that computing the correlations in parallel with different components of the low-frequency input field, shifting the correlation maps according to a rule suggested by 3D phase-matching, and averaging them, leads to the recovery of the downconverted image. The method can be used for secure and fast image transmission.