Achieving spatial superresolution with engineered spatial modes

Abstract

Abstract Rayleigh’s criterion sets a limit on the minimum separation between two incoherent point sources to be resolved into distinct objects. However, superresolution techniques have been developed to circumvent Rayleigh’s criterion. These techniques mainly deal with single parameter estimation and require prior information about the centroid. Here, we use multi-parameter estimation tools to simultaneously and optimally retrieve information about the centroid and object separation. Collective measurements on photons using two-photon interference followed by spatially resolved detection have significantly improved over direct detection schemes. Following the same approach, we extend the analysis of the two-photon interference protocol to spatially engineered photons having a Pearson type VII profile with arbitrary positive excess kurtosis. We calculate the precision limits in the current measurement scheme as well as the ultimate precision limits based on the quantum Cramer–Rao bound for different spatial modes. We theoretically show that such engineered pulses show enhanced precision with increasing kurtosis in simultaneous estimation of the centroid and object separation compared to a Gaussian amplitude profile. Furthermore, we discuss an experimental setup to realize the proposed superresolution scheme.