Quantum-statistical analysis of superresolution for optical systems with circular symmetry

We present a detailed quantum-statistical analysis of superresolution for optical systems with circular symmetry based on our previous paper [Opt. Commun. 264, 9 (2006)].We consider as example an imaging system with two Fourier lenses; however, our approach can be easily generalized for more complex paraxial systems with circular symmetry. We present an original and very effective algorithm for numerical evaluation of the circular prolate spheroidal functions, which are the eigenmodes of our system. We investigate in detail the two-dimensional reconstruction point-spread function and provide examples of superresolution for rotationally symmetric and angularly dependent objects. Finally, we investigate the role of the local quantum fluctuations in the superresolution process and evaluate the local noise figure for the reconstruction process.