Algorithm

Imaging will be performed by illuminating an object with multi-photon quantum states of light and detecting the scattered light with a single photon detector array. High order spatial correlation functions are thus accessible and will allow to reconstruct the object with a resolution higher than the one imposed by classical optics. Because multi-photon states will be detected at high frame rate, the amount of data to process will become very large. Therefore, optimized algorithms will be developed in order to extract the image with the highest possible resolution from the set of available data.

The algorithm itself will be based on fitting the measured correlation function with a linear combination of correlation functions obtained by measuring/modeling correlation functions for a set of known elementary images (patterns), which reduces the problem of image reconstruction to a constrained linear inversion,

where coefficients x describe the respective weight of the elementary images in the superposition. This fitting would be optimized with respect to minimization of the distance between the measured and predicted correlation functions taking into account minimization of amount of taken/processed data. Minimization of the data to process is crucial when processing results of measurement of the higher-order correlation functions. Possible statistical and systematic errors will be accounted for in the procedure

The development of the algorithm will be closely accompanied by corresponding quantum imaging experiments, which, in a first step, involve entangled two-photon states generated by spontaneous parametric down-conversion; Spatial correlations between the two photons can then be measured by means of a second-order correlation function and the resulting data serves as a test bed for the algorithms. Finally, the extension of the imaging reconstruction algorithm to N-photon correlations will be experimentally supported by the use of a source providing entangled N-photon states.