Abstract

The spatial resolution of an optical system is limited by diffraction. Various schemes have been proposed to achieve resolution enhancement by employing either a scanning source/detector configuration or a two-photon response of the object. Here, we experimentally demonstrate a full-field resolution-enhancing scheme, based on the centroid estimation of spatially quantum-correlated biphotons. Our standard-quantum-limited scheme is able to image a general non-fluorescing object, using low-energy and low-intensity infrared illumination (i.e., with <0.001 photon per pixel per frame at 710 nm), achieving 41% of the theoretically available resolution enhancement. Images of real-world objects are shown for visual comparison, in which the classically bound resolution is surpassed using our technically straightforward quantum-imaging scheme.

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References

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2018 (2)

I. Gyongy, N. Calder, A. Davies, N. A. W. Dutton, R. R. Duncan, C. Rickman, P. Dalgarno, and R. K. Henderson, “A 256x256, 100-kfps, 61% fill-factor SPAD image sensor for time-resolved microscopy applications,” IEEE Trans. Electron Dev. 65, 547–554 (2018).
[Crossref]

M. Unternährer, B. Bessire, L. Gasparini, M. Perenzoni, and A. Stefanov, “Super-resolution quantum imaging at the Heisenberg limit,” Optica 5, 1150–1154 (2018).
[Crossref]

2017 (3)

2016 (3)

J. Schneeloch and J. C. Howell, “Introduction to the transverse spatial correlations in spontaneous parametric down-conversion through the biphoton birth zone,” J. Opt. 18, 053501 (2016).
[Crossref]

M. Genovese, “Real applications of quantum imaging,” J. Opt. 18, 073002 (2016).
[Crossref]

A. Avella, I. Ruo-Berchera, I. P. Degiovanni, G. Brida, and M. Genovese, “Absolute calibration of an EMCCD camera by quantum correlation, linking photon counting to the analog regime,” Opt. Lett. 41, 1841–1844 (2016).
[Crossref]

2015 (3)

E. Lantz, S. Denis, P.-A. Moreau, and F. Devaux, “Einstein-Podolsky-Rosen paradox in single pairs of images,” Opt. Express 23, 26472–26478 (2015).
[Crossref]

D.-Q. Xu, X.-B. Song, H.-G. Li, D.-J. Zhang, H.-B. Wang, J. Xiong, and K. Wang, “Experimental observation of sub-Rayleigh quantum imaging with a two-photon entangled source,” Appl. Phys. Lett. 106, 171104(2015).
[Crossref]

P. A. Morris, R. S. Aspden, J. E. C. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons,” Nat. Commun. 6, 5913 (2015).
[Crossref]

2014 (3)

D. Gatto Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Ruo-Berchera, P. Olivero, I. P. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113, 143602 (2014).
[Crossref]

L. A. Rozema, J. D. Bateman, D. H. Mahler, R. Okamoto, A. Feizpour, A. Hayat, and A. M. Steinberg, “Scalable spatial superresolution using entangled photons,” Phys. Rev. Lett. 112, 223602 (2014).
[Crossref]

Y. Zhai, F. E. Becerra, J. Fan, and A. Migdall, “Direct measurement of sub-wavelength interference using thermal light and photon-number-resolved detection,” Appl. Phys. Lett. 105, 101104 (2014).
[Crossref]

2013 (3)

O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch, and D. Oron, “Superresolution microscopy with quantum emitters,” Nano Lett. 13, 5832–5836 (2013).
[Crossref]

J.-M. Cui, F.-W. Sun, X.-D. Chen, Z.-J. Gong, and G.-C. Guo, “Quantum statistical imaging of particles without restriction of the diffraction limit,” Phys. Rev. Lett. 110, 153901 (2013).
[Crossref]

J.-E. Oh, Y.-W. Cho, G. Scarcelli, and Y.-H. Kim, “Sub-Rayleigh imaging via speckle illumination,” Opt. Lett. 38, 682–684 (2013).
[Crossref]

2012 (3)

M. Edgar, D. Tasca, F. Izdebski, R. Warburton, J. Leach, M. Agnew, G. Buller, R. Boyd, and M. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3, 984 (2012).
[Crossref]

X. Zhang, T. Kashti, D. Kella, T. Frank, D. Shaked, R. Ulichney, M. Fischer, and J. P. Allebach, “Measuring the modulation transfer function of image capture devices: what do the numbers really mean?” Proc. SPIE 8293, 829307 (2012).
[Crossref]

O. Schwartz and D. Oron, “Improved resolution in fluorescence microscopy using quantum correlations,” Phys. Rev. A 85, 033812 (2012).
[Crossref]

2011 (1)

H. Shin, K. W. C. Chan, H. J. Chang, and R. W. Boyd, “Quantum spatial superresolution by optical centroid measurements,” Phys. Rev. Lett. 107, 083603 (2011).
[Crossref]

2010 (5)

G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4, 227–230(2010).
[Crossref]

F. Guerrieri, L. Maccone, F. N. C. Wong, J. H. Shapiro, S. Tisa, and F. Zappa, “Sub-Rayleigh imaging via $N$-photon detection,” Phys. Rev. Lett. 105, 163602 (2010).
[Crossref]

L. Schermelleh, R. Heintzmann, and H. Leonhardt, “A guide to super-resolution fluorescence microscopy,” J. Cell Biol. 190, 165–175 (2010).
[Crossref]

B. Huang, H. Babcock, and X. Zhuang, “Breaking the diffraction barrier: super-resolution imaging of cells,” Cell 143, 1047–1058 (2010).
[Crossref]

S. Walborn, C. Monken, S. Pádua, and P. Souto Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep. 495, 87–139 (2010).
[Crossref]

2009 (2)

V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A 79, 013827 (2009).
[Crossref]

M. Tsang, “Quantum imaging beyond the diffraction limit by optical centroid measurements,” Phys. Rev. Lett. 102, 253601 (2009).
[Crossref]

2008 (1)

J.-L. Blanchet, F. Devaux, L. Furfaro, and E. Lantz, “Measurement of sub-shot-noise correlations of spatial fluctuations in the photon-counting regime,” Phys. Rev. Lett. 101, 233604 (2008).
[Crossref]

2005 (2)

Y.-H. Zhai, X.-H. Chen, D. Zhang, and L.-A. Wu, “Two-photon interference with true thermal light,” Phys. Rev. A 72, 043805 (2005).
[Crossref]

B. E. A. Saleh, M. C. Teich, and A. V. Sergienko, “Wolf equations for two-photon light,” Phys. Rev. Lett. 94, 223601 (2005).
[Crossref]

2004 (1)

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science 306, 1330–1336 (2004).
[Crossref]

2002 (1)

2000 (1)

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).
[Crossref]

1998 (1)

E. Samei, M. J. Flynn, and D. A. Reimann, “A method for measuring the presampled MTF of digital radiographic systems using an edge test device,” Med. Phys. 25, 102–113 (1998).
[Crossref]

1995 (3)

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon ‘ghost’ interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[Crossref]

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429–R3432 (1995).
[Crossref]

S. W. Hell and M. Kroug, “Ground-state-depletion fluorescence microscopy: a concept for breaking the diffraction resolution limit,” Appl. Phys. B 60, 495–497 (1995).
[Crossref]

1994 (1)

1985 (1)

C. K. Hong and L. Mandel, “Theory of parametric frequency down conversion of light,” Phys. Rev. A 31, 2409–2418 (1985).
[Crossref]

1968 (1)

D. A. Kleinman, “Theory of optical parametric noise,” Phys. Rev. 174, 1027–1041 (1968).
[Crossref]

1896 (1)

F. R. S. Lord Rayleigh, “XV. On the theory of optical images, with special reference to the microscope,” Lond. Edinb. Dublin Philos. Mag. J. Sci. 42, 167–195 (1896).
[Crossref]

1873 (1)

E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikrosk. Wahrnehmung,” Arch. f. mikrosk. Anatomie 9, 413–418 (1873).
[Crossref]

Abbe, E.

E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikrosk. Wahrnehmung,” Arch. f. mikrosk. Anatomie 9, 413–418 (1873).
[Crossref]

Abouraddy, A. F.

Abrams, D. S.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).
[Crossref]

Agnew, M.

M. Edgar, D. Tasca, F. Izdebski, R. Warburton, J. Leach, M. Agnew, G. Buller, R. Boyd, and M. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3, 984 (2012).
[Crossref]

Allebach, J. P.

X. Zhang, T. Kashti, D. Kella, T. Frank, D. Shaked, R. Ulichney, M. Fischer, and J. P. Allebach, “Measuring the modulation transfer function of image capture devices: what do the numbers really mean?” Proc. SPIE 8293, 829307 (2012).
[Crossref]

Aspden, R. S.

P. A. Morris, R. S. Aspden, J. E. C. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons,” Nat. Commun. 6, 5913 (2015).
[Crossref]

Avella, A.

Babcock, H.

B. Huang, H. Babcock, and X. Zhuang, “Breaking the diffraction barrier: super-resolution imaging of cells,” Cell 143, 1047–1058 (2010).
[Crossref]

Bateman, J. D.

L. A. Rozema, J. D. Bateman, D. H. Mahler, R. Okamoto, A. Feizpour, A. Hayat, and A. M. Steinberg, “Scalable spatial superresolution using entangled photons,” Phys. Rev. Lett. 112, 223602 (2014).
[Crossref]

Becerra, F. E.

Y. Zhai, F. E. Becerra, J. Fan, and A. Migdall, “Direct measurement of sub-wavelength interference using thermal light and photon-number-resolved detection,” Appl. Phys. Lett. 105, 101104 (2014).
[Crossref]

Bell, J. E. C.

P. A. Morris, R. S. Aspden, J. E. C. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons,” Nat. Commun. 6, 5913 (2015).
[Crossref]

Bessire, B.

Blanchet, J.-L.

J.-L. Blanchet, F. Devaux, L. Furfaro, and E. Lantz, “Measurement of sub-shot-noise correlations of spatial fluctuations in the photon-counting regime,” Phys. Rev. Lett. 101, 233604 (2008).
[Crossref]

Boreman, G. D.

G. D. Boreman, Modulation Transfer Function in Optical and Electro-Optical Systems (SPIE, 2001).

Boto, A. N.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).
[Crossref]

Boyd, R.

M. Edgar, D. Tasca, F. Izdebski, R. Warburton, J. Leach, M. Agnew, G. Buller, R. Boyd, and M. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3, 984 (2012).
[Crossref]

Boyd, R. W.

P. A. Morris, R. S. Aspden, J. E. C. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons,” Nat. Commun. 6, 5913 (2015).
[Crossref]

H. Shin, K. W. C. Chan, H. J. Chang, and R. W. Boyd, “Quantum spatial superresolution by optical centroid measurements,” Phys. Rev. Lett. 107, 083603 (2011).
[Crossref]

Braunstein, S. L.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).
[Crossref]

Brida, G.

A. Avella, I. Ruo-Berchera, I. P. Degiovanni, G. Brida, and M. Genovese, “Absolute calibration of an EMCCD camera by quantum correlation, linking photon counting to the analog regime,” Opt. Lett. 41, 1841–1844 (2016).
[Crossref]

D. Gatto Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Ruo-Berchera, P. Olivero, I. P. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113, 143602 (2014).
[Crossref]

G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4, 227–230(2010).
[Crossref]

Buller, G.

M. Edgar, D. Tasca, F. Izdebski, R. Warburton, J. Leach, M. Agnew, G. Buller, R. Boyd, and M. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3, 984 (2012).
[Crossref]

Calder, N.

I. Gyongy, N. Calder, A. Davies, N. A. W. Dutton, R. R. Duncan, C. Rickman, P. Dalgarno, and R. K. Henderson, “A 256x256, 100-kfps, 61% fill-factor SPAD image sensor for time-resolved microscopy applications,” IEEE Trans. Electron Dev. 65, 547–554 (2018).
[Crossref]

Chan, K. W. C.

H. Shin, K. W. C. Chan, H. J. Chang, and R. W. Boyd, “Quantum spatial superresolution by optical centroid measurements,” Phys. Rev. Lett. 107, 083603 (2011).
[Crossref]

Chang, H. J.

H. Shin, K. W. C. Chan, H. J. Chang, and R. W. Boyd, “Quantum spatial superresolution by optical centroid measurements,” Phys. Rev. Lett. 107, 083603 (2011).
[Crossref]

Chen, X.-D.

J.-M. Cui, F.-W. Sun, X.-D. Chen, Z.-J. Gong, and G.-C. Guo, “Quantum statistical imaging of particles without restriction of the diffraction limit,” Phys. Rev. Lett. 110, 153901 (2013).
[Crossref]

Chen, X.-H.

Y.-H. Zhai, X.-H. Chen, D. Zhang, and L.-A. Wu, “Two-photon interference with true thermal light,” Phys. Rev. A 72, 043805 (2005).
[Crossref]

Cho, Y.-W.

Cui, J.-M.

J.-M. Cui, F.-W. Sun, X.-D. Chen, Z.-J. Gong, and G.-C. Guo, “Quantum statistical imaging of particles without restriction of the diffraction limit,” Phys. Rev. Lett. 110, 153901 (2013).
[Crossref]

Dalgarno, P.

I. Gyongy, N. Calder, A. Davies, N. A. W. Dutton, R. R. Duncan, C. Rickman, P. Dalgarno, and R. K. Henderson, “A 256x256, 100-kfps, 61% fill-factor SPAD image sensor for time-resolved microscopy applications,” IEEE Trans. Electron Dev. 65, 547–554 (2018).
[Crossref]

Davies, A.

I. Gyongy, N. Calder, A. Davies, N. A. W. Dutton, R. R. Duncan, C. Rickman, P. Dalgarno, and R. K. Henderson, “A 256x256, 100-kfps, 61% fill-factor SPAD image sensor for time-resolved microscopy applications,” IEEE Trans. Electron Dev. 65, 547–554 (2018).
[Crossref]

Degiovanni, I. P.

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L. A. Rozema, J. D. Bateman, D. H. Mahler, R. Okamoto, A. Feizpour, A. Hayat, and A. M. Steinberg, “Scalable spatial superresolution using entangled photons,” Phys. Rev. Lett. 112, 223602 (2014).
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L. Schermelleh, R. Heintzmann, and H. Leonhardt, “A guide to super-resolution fluorescence microscopy,” J. Cell Biol. 190, 165–175 (2010).
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J. Schneeloch and J. C. Howell, “Introduction to the transverse spatial correlations in spontaneous parametric down-conversion through the biphoton birth zone,” J. Opt. 18, 053501 (2016).
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O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch, and D. Oron, “Superresolution microscopy with quantum emitters,” Nano Lett. 13, 5832–5836 (2013).
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O. Schwartz and D. Oron, “Improved resolution in fluorescence microscopy using quantum correlations,” Phys. Rev. A 85, 033812 (2012).
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F. Guerrieri, L. Maccone, F. N. C. Wong, J. H. Shapiro, S. Tisa, and F. Zappa, “Sub-Rayleigh imaging via $N$-photon detection,” Phys. Rev. Lett. 105, 163602 (2010).
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L. A. Rozema, J. D. Bateman, D. H. Mahler, R. Okamoto, A. Feizpour, A. Hayat, and A. M. Steinberg, “Scalable spatial superresolution using entangled photons,” Phys. Rev. Lett. 112, 223602 (2014).
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J.-M. Cui, F.-W. Sun, X.-D. Chen, Z.-J. Gong, and G.-C. Guo, “Quantum statistical imaging of particles without restriction of the diffraction limit,” Phys. Rev. Lett. 110, 153901 (2013).
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Supplementary Material (1)

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Figures (4)

Fig. 1.
Fig. 1. Experimental setup. The optics of our resolution-enhanced imaging scheme consists of a source of spatially correlated photons (labeled as “biphoton illumination”), an object, a non-ideal imaging system (in our case, an NA-limited system), and a single-photon sensitive EMCCD camera. The planes of the crystal and of the object are imaged onto the plane of the detector. An aperture placed in the far field of both the crystal and the object is used to tune the diffraction limit of the non-ideal imaging system.
Fig. 2.
Fig. 2. Centroid estimation of biphotons. Within a 3×3 pixel kernel and a two-pixel-wide safety margin, 11 out of 12 biphotons are detected: four skew as shown in (a); four long range as shown in (b); and three short range as shown in (c). Vertically adjacent events that may be affected by the camera’s charge smearing artifact, as well as interlinked events, are rejected, as shown in (e). A resolution-enhanced image is obtained when the object (represented by a slanted white bar) is illuminated by spatially correlated light, and the detected events are processed by our biphoton-finding algorithm, as shown in (d). In the case of spatially uncorrelated light, the meaningless centroid positions of the accidentally detected event pairs return an unimproved image of the object, as represented in (e). The classical imaging scheme represented in (f) is obtained by averaging all of the binary detected events, producing an unimproved image of the object, which is, however, affected by high-background intensity, as there is no rejection of noise events.
Fig. 3.
Fig. 3. Demonstration and quantification of resolution enhancement via slanted-edge MTF. The resolution of our centroid-estimation imaging scheme using biphoton illumination (blue MTF) is compared against the resolution of an equivalent classical imaging scheme (red MTF). As a test, we apply our centroid estimation to uncorrelated light (green MTF) and verify that the resolution is the same as for the classical case, confirming that the resolution enhancement of our scheme is linked to the presence of spatially correlated biphotons. The theoretical curve (black MTF) represents the full 1/2 standard-quantum-limit resolution enhancement with respect to the narrowing of the PSF, here not achieved due to the limited performance of the EMCCD and the non-perfect detection of event pairs of our biphoton-finding algorithm. Shot noise in the pixel intensities causes the noise floor of the centroid-estimated MTF curves (blue and green curves) to be greater than the noise floor of the classical simple average of all events MTF (red curve). The error bars were computed over 10 datasets, each comprising 106.
Fig. 4.
Fig. 4. Image comparison for real-world objects. The wing of a fly (a) and a bundle of glass fibers (b) were imaged using both the single average of all frames (top row, red frames) and our centroid estimation of biphotons (bottom row, blue frames). The size bar at the bottom right applies to all reconstructed images. The insets show features that appear to be sharper using our centroid estimation of biphotons, as confirmed by the plotted intensity cross sections for the insect’s wing (bottom left) and the glass fiber (bottom right). The horizontal streak lines are due to the uneven response of some regions of the EMCCD chip and to charge smearing. These effects, which are usually negligible at higher photon fluxes, become more evident when many thousands of photon-sparse frames are averaged together.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

Var(δXs)=Var(δXi)=(σPSF)2.
δXc=δXs+δXi2.
r=Var(δXc)=Var(δXs+δXi2)=Var(δXs+δXi)2.
r=Var(δXs+δXi)2=Var(δXs)+Var(δXi)2=σPSF2.