Improving the observation of spatial quantum correlation of twin beams by means of a sub-pixel symmetry centre retrieval algorithm

We propose a method to improve the observation of spatial quantum correlation of twin beams produced by parametric down-conversion in a non-linear crystal. By applying our post-acquisition algorithm to experimental data we are able to reduce the uncertainty in the determination of the symmetry centre of the signal-idler pattern in the far-field plane, by searching it with sub-pixel accuracy. Reducing the uncertainty leads to an improvement of the observation of spatial quantum correlation of the twin beams. We perform theoretical and numerical investigation in order to test potentialities and limits of our algorithm, and we identify a proper experimental configuration that minimises the problem of symmetry centre uncertainty.