Quantum-limited estimation of the axial separation of two incoherent point sources

Yiyu Zhou, Jing Yang, Jeremy D. Hassett, Seyed Mohammad Hashemi Rafsanjani, Mohammad Mirhosseini, A. Nick Vamivakas, Andrew N. Jordan, Zhimin Shi, Robert W. Boyd

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


Improving axial resolution is crucial for three-dimensional optical imaging systems. Here we present a scheme of axial superresolution for two incoherent point sources based on spatial mode demultiplexing. A radial mode sorter is used to losslessly decompose the optical fields into a radial mode basis set to extract the phase information associated with the axial positions of the point sources. We show theoretically and experimentally that, in the limit of a zero axial separation, our scheme allows for reaching the quantum Cramér-Rao lower bound and thus can be considered as one of the optimal measurement methods. Unlike other superresolution schemes, this scheme does not require either activation of fluorophores or sophisticated stabilization control. Moreover, it is applicable to the localization of a single point source in the axial direction. Our demonstration can be useful for a variety of applications such as far-field fluorescence microscopy.

Original languageEnglish (US)
Article number355468
Pages (from-to)534-541
Number of pages8
Issue number5
StatePublished - May 20 2019

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics


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