Abstract

Superresolution fluorescence microscopy and compressed sensing work for sparse point sources. But what if we cannot control the sources, such as stars or exoplanets, and they are closer to one another than the diffraction limit? Using a shot-noise model and parameter-estimation theory, I derive fundamental limits to direct imaging in this subdiffraction regime, demonstrating that the moments of the source distribution are the natural parameters to estimate in this case [1]. I further show that an optical spatial-mode demultiplexing (SPADE) technique can estimate the second and higher moments much more accurately than direct imaging can fundamentally do [1,2]. The recent breakthrough discovery on two-point resolution [3] can be regarded as a special case. Realizable with linear optics and photon counting, SPADE is expected to benefit both fluorescence microscopy and astronomy.

References:
[1] M. Tsang, "Subdiffraction incoherent optical imaging via spatial-mode demultiplexing," New Journal of Physics 19, 023054 (2017).
[2] M. Tsang, "Subdiffraction incoherent optical imaging via spatial-mode demultiplexing: semiclassical treatment," e-print arXiv:1703.08833.
[3] M. Tsang, R. Nair, and X.-M. Lu, "Quantum Theory of Superresolution for Two Incoherent Optical Point Sources," Physical Review X 6, 031033 (2016).