Near-optimal Quantum Measurement For Locating Two Incoherent Optical Point Sources

On the issue of incoherent point source imaging,the Rayleigh criterion is the most influential measure on the optical imaging resolution in more than a century.The Rayleigh criterion gives a characteristic distance between which two incoherent optical point sources are considered difficult to be distinguished.People have been seeking methods to achieve high resolution when the distances between optical point sources are below the Rayleigh criterion—the sub-Rayleigh region.In fact,one can perform many other measurements on the optical fields in the image place rather than just direct imaging,which measures the intensity distribution of the optical field in the image plane.Recently,using quantum parameter estimation theory,researchers found that direct imaging is far away from the optimal strategy.A method called Spatial-Mode Demultiplexing(SPADE)can optimally estimate the distance between two sources,extracting the maximum Fisher information from the optical field in the image plane.With SPADE,two point sources in the sub-Rayleigh region can also be resolved very well.Despite all these efforts,the(full)SPADE measurement is difficult to be implemented.First,the full SPADE demands to measurement an infinite number of spatial modes.Second,to perform the SPADE measurement,it needs to know the centroid of the two point sources,which is in fact unknown and thus need to be estimation first.However,it has been shown that there exists some simple measurement which is not optimal but near optimal.These simple measurements are significant to the experimental implementation of the SPADE.In this thesis,we will study how to find the simple near-optimal measurement for estimation the locations of incoherent point sources.We first discretize the optical field in the image plane into pixels.Then,we resctrict the measurement in a subset of simple measurements that only distinguish a few spatial modes.We use the gradient descent method to numerically find the optimal measurement in the given subset.We also discuss the characteristics and the properties of theses near-optimal simple measurement as well as their global performance.