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"Achieving Quantum Limited 3D Optical Super-resolution by Classical Measurements"

Dr. Zhixian Yu
University of New Mexico


Lord Rayleigh's criterion for resolution of two incoherent point sources has been the most widely accepted criterion in optics since its formulation in 1879. Despite very influential, his criterion developed for the human eye as the main detector is not a fundamental limit. A more accurate approach to optical resolution can be formulated in terms of the Fisher information (FI) and the associated Cramer-Rao bound. For direct imaging, which records the light intensity but discards information about the phase in the image plane, FI drops quadratically with the source-pair separation. In consequence, the variance of any biased estimator based on these intensity measurements diverges, giving rise to the so-called Rayleigh's curse [1]. I will discuss a recent wave of paradigm-shifting research on the super-resolution of a pair of incoherent point sources, with quantum Fisher information (QFI) revealing the ultimate lower bound on the estimation error of the source-pair transverse separation [1]. I will extend the previous work to full three-dimensional (3D) super-resolution [2,3] and show that the QFI for estimating the full 3D source pair separation vector is strictly a constant. Surprisingly, as I will also show, one can achieve this bound in certain limits in all 3D with purely classical phase-sensitive measurements [2,3] that are not standard image based, but rather utilize coherent projections of the optical wavefront. Phase does matter, even when it comes to making good images of incoherent objects.

[1] M. Tsang, R. Nair, and X.-M. Lu, Quantum Theory of Superresolution for Two Incoherent Optical Point Sources, Phys. Rev. X 6, 031033 (2016).
[2] Z. Yu and S. Prasad, Quantum Limited Superresolution of an Incoherent Source Pair in Three Dimensions, Phys. Rev. Lett 121, 180504 (2018).
[3] S. Prasad and Z. Yu, Quantum-limited Superlocalization and Superresolution of a source pair in three dimensions, Phys. Rev. A 99, 022116 (2019).

Tuesday, April 23, 2019
IQSE Seminar Room, 12:00 Noon
(578 MPHY)

Institute for Quantum Science and Engineering
Texas A&M University

Sandwich lunch to be served at 11:30 a.m.

Host: Dr. Marlan Scully