Quantum super-resolution imaging: a review and perspective

Abstract

Quantum super-resolution imaging provides a nonlabeling method to surpass the diffraction limit of imaging systems. This technique relies on measurement of the second-order correlation function and usually employs spatially entangled photon sources. We introduce recent methods that achieve spatial resolution enhancement through quantum approaches, particularly the imaging techniques utilizing biphoton states. The fundamental mechanisms are discussed in detail to explain why biphoton states enable super-resolution. Additionally, we introduce multiple algorithms that extract the correlation function from the readings of two-dimensional detectors. Several cases are reviewed to evaluate the advantages and prospects of quantum imaging, along with a discussion of practical developments and potential applications.

Keywords: quantum entanglement; quantum imaging; super-resolution imaging.

Figure 1:

Two-photon diffraction and interference. (a) Simplified schematic of a biphoton diffraction–interference. When biphotons propagate through a double slit, the setup is equivalent to (a). D₁ and D₂ are the photon detectors. Their counts are sent to a coincidence circuit for $G^{\left(2\right)}$ measurement. (b) Diffraction pattern width in the biphoton diffraction experiment. The experimental result does not match the classical diffraction theory. (c) Interference pattern of classical light in the double-slit experiment. (d) Interference pattern of biphotons in the double-slit experiment [40], [41]. Copyright 2001 American Physical Society, 1995 American Physical Society.

Figure 2:

Quantum microscopy by coincidence (QMC). (a) Experimental setup of QMC. The signal beam illuminates the object positioned at the object plane. Both arms are symmetry to ensure the path length of the signal and idler photons are the same. (b) The contrast-to-noise ratios (CNRs) using different methods are evaluated over 10⁵ frames in the presence of stray light. (c) The spatial resolution of classical imaging compared to QMC in relation to the axial z coordinate from the classical focal point. The highest spatial resolutions achieved are 2.9 μm for classical imaging and 1.4 μm for QMC, respectively. Classical imaging (d) and QMC (e) show group 7 (2.76–3.91 μm) of a USAF 1951 resolution target. The images include scale bars of 20 μm and have been normalized [29]. Copyright 2022 Springer Nature.

Figure 3:

Polarization entanglement-enabled quantum holography. (a) Experimental setup. (b) Measurement of the cutoff period of a grating using classical and quantum imaging methods. (c) Holography of phase grating reconstructed using quantum (left) and classical (right) configurations, respectively [33]. Copyright 2021 Springer Nature.

Figure 4:

Optical centroid measurement (OCM). (a) Setup of super-resolution at the Heisenberg limit by OCM. Here, the object is placed in front of the biphoton source. (b) The PSFs measured by the setup in (a) with different light sources. (c) Image captured using the biphoton source. (d) Image captured using a spatially coherent laser at 810 nm. (e) Results of a similar setup with the object behind the biphoton source. The slanted-edge MTFs show that resolution enhancement of OCM is 41 % of the anticipated value $1/\sqrt{2}$ . A USAF resolution target was imaged with both biphoton and uncorrelated light sources. The results demonstrated that the blue MTF curve, corresponding to biphoton illumination, displayed a higher cutoff frequency over that corresponding to the red and green curves, which represent classical imaging configurations and uncorrelated photons. (f) Method of centroid measurement [61], [72]. Copyright 2018 Optical Society of America, 2019 Optical Society of America.

Figure 5:

Quantum imaging by coincidence from entanglement (ICE). (a) Experimental setup. Instead of the wide-field configuration, this setup is based on raster scanning. (b) Classical imaging and ICE of a USAF resolution target. (c) Resolution curve for classical imaging (red) and ICE (blue). Dots represent experimental measurements. (d) Classical and ICE images of carbon fibers embedded in agarose at different depths. Profiles along the yellow dotted lines are plotted in the close-ups to compare the spatial resolutions [65]. Copyright 2024 American Association for the Advancement of Science.