Abstract

We propose and demonstrate experimentally a new method based on the spatial entanglement for the absolute calibration of analog detectors. The idea consists on measuring the sub-shot-noise intensity correlation between two branches of parametric down conversion, containing many pairwise correlated spatial modes. We calibrate a scientific CCD camera and a preliminary evaluation of the uncertainty indicates the metrological interest of the method.

© 2010 Optical Society of America

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  2. E. Brambilla, A. Gatti, M. Bache, and L. A. Lugiato, “Simultaneous near-field and far-field spatial quantum correlations in the high-gain regime of parametric down-conversion,” Phys. Rev. A 69, 023802 (2004).
    [CrossRef]
  3. 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] [PubMed]
  4. O. Jedrkievicz, Y.-K Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion,” Phys. Rev. Lett. 93, 243601 (2004).
    [CrossRef]
  5. G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. Ruo-Berchera, “Measurement of sub-shot-noise spatial correlations without background subtraction,” Phys Rev. Lett. 102, 213602 (2009).
    [CrossRef] [PubMed]
  6. G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photon. 4, 227–230 (2010).
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  7. G. Brida, M. Genovese, A. Meda, and I. Ruo Berchera, “Experimental quantum imaging exploiting multi-mode spatial correlation of twin beams,” arXiv:1005.3665v2 [quant-ph].
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    [CrossRef]
  9. T. Ishkakov, M. Chekhova, and G. Leuchs, “Generation and Direct Detection of broadband mesoscopic polarization-squeezed vacuum,” Phys. Rev. Lett. 102, 183602 (2009).
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  11. E. Brambilla, L. Caspani, O. Jedrkiewicz, L. A. Lugiato, and A. Gatti, “High-sensitivity imaging with multi-mode twin beams,” Phys. Rev. A. 77, 053807 (2008).
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    [CrossRef] [PubMed]
  14. B. Y. Zel’dovich and D.N. Klyshko, “Statistics of field in parametric luminescence,” Sov. Phys. JETP Lett. 940–44 (1969).
  15. D. C. Burnham and D. L. Weinberg, “Observation of simultaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).
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  18. V. M. Ginzburg, N. G. Keratishvili, E. L. Korzhenevich, G. V. Lunev, A. N. Penin, and V. I. Sapritsky, “Absolute meter of photodetector quantum efficiency based on the parametric down-conversion effect,” Opt. Eng. 32(11), 2911–2916 (1993).
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  19. A. Migdall, “Correlated-photon metrology without absolute standards,” Phys. Today 1, 41–46 (1999).
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  20. M. Genovese, G. Brida, and C. Novero, “An application of two photons entangled states to quantum metrology,” J. Mod. Opt. 47, 2099-2104 (2000).
  21. G. Brida, S. Castelletto, I. Degiovanni, M. Genovese, C. Novero, and M. L. Rastello, “Toward an accuracy budget in quantum efficiency measurement with parametric fluorescence,” Metrologia 37(5), 629–632 (2000).
    [CrossRef]
  22. G. Brida, M. Chekhova, M. Genovese, M. Gramegna, L. Krivitsky, and M. L. Rastello, “Single-Photon detectors calibration by means of conditional polarization rotation,” J. Opt. Soc. Am. B 22, 488–492 (2005).
    [CrossRef]
  23. G. Brida, M. Genovese, and M. Gramegna, “Twin-Photon techniques for photo-detector calibration,” Laser Phys. Lett. 3, 115–123 (2006)
    [CrossRef]
  24. A. V. Sergienko and A. N. Penin, “Absolute calibration of analog photodetectors using biphotonic fields,” Sov. Tech. Phys. Lett. 12, 328–329 (1986).
  25. G. Brida, M. Chekhova, M. Genovese, A. Penin, and I. Ruo-Berchera, “The possibility of absolute calibration of analog detectors by using parametric down-conversion: a systematic study,” J. Opt. Soc. Am. B 23, 2185–2193 (2006).
    [CrossRef]
  26. I. Ruo Berchera, “Theory of PDC in a continuous variables framework and its applications to the absolute calibration of photo-detectors,” Adv. Sci. Lett. 2, 407–429 (2009).
    [CrossRef]
  27. G. Brida, M. Chekhova, M. Genovese, and I. Ruo-Berchera, “Analysis of the possibility of analog detectors calibration by exploiting Stimulated Parametric Down Conversion,” Opt. Express 1612550–12558 (2008).
    [CrossRef] [PubMed]
  28. G. Brida, M. Chekhova, M. Genovese, M. L. Rastello, and I. Ruo Berchera, “Absolute calibration of Analog Detector using Stimulated Parametric Down Conversion,” J. Mod. Opt. 56(2–3), 401–408 (2009).
    [CrossRef]
  29. M. Lindenthal and J. Kofler, “Measuring of the absolute photodetection efficiency using photon number correlations,” Appl. Opt. 45(24), 6059–6064 (2006).
    [CrossRef]
  30. T. S. Iskhakov, E. D. Lopaeva, A. N. Penin, G. O. Rytikov, and M. V. Chekhova, “Two methods for detecting nonclassical correlations in parametric scattering of light,” JETP Lett. 88(10), 660-664 (2008).
    [CrossRef]
  31. J. Zwinkels, E. Ikonen, N. Fox, G. Ulm, and M. L. Rastello, “Photometry, radiometry and the candela: evolution in the classical and quantum world,” Metrologia, to appear.
  32. G. Brida, M. Genovese, A. Meda, E. Predazzi, and I. Ruo Berchera, “Systematic study of the PDC speckle structure for quantum imaging applications,” Int. Journ. Quantum Inf. 7, 139–147 (2009).
    [CrossRef]
  33. G. Brida, M. Genovese, A. Meda, E. Predazzi, and I. Ruo Berchera, “Tailoring PDC speckle structure,” J. Mod. Opt. 56, 201–208 (2009).
    [CrossRef]
  34. I. N. Agafonov, M. V. Chekhova, and G. Leuchs, “Two-Color Bright Squeezed Vacuum,” arXiv:0910.4831.
  35. The order of magnitude in our experiment is estimable as large as 2η+MtotV (μ)/μ =V (<Ns +Ni>)/<Ns +Ni>∼ 5·103 (see Tab. 1, first two columns). It is four order of magnitude larger than the excess noise due to the thermal fluctuations.
  36. “Guide to the expression of uncertainty in measurement (GUM),” ISO/IEC Guide 98:1995.
  37. O. Jedrkiewicz, P. Di Trapani, Y. Jiang, S. Minardi, A. Mosset, E. Lantz, and F. Devaux, “Retrieval of spatial shot-noise in the full dynamic range of calibrated CCD cameras,” Eur. Phys. J. D 22, 521–526 (2003).
    [CrossRef]

2010 (1)

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

2009 (6)

G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. Ruo-Berchera, “Measurement of sub-shot-noise spatial correlations without background subtraction,” Phys Rev. Lett. 102, 213602 (2009).
[CrossRef] [PubMed]

T. Ishkakov, M. Chekhova, and G. Leuchs, “Generation and Direct Detection of broadband mesoscopic polarization-squeezed vacuum,” Phys. Rev. Lett. 102, 183602 (2009).
[CrossRef]

I. Ruo Berchera, “Theory of PDC in a continuous variables framework and its applications to the absolute calibration of photo-detectors,” Adv. Sci. Lett. 2, 407–429 (2009).
[CrossRef]

G. Brida, M. Chekhova, M. Genovese, M. L. Rastello, and I. Ruo Berchera, “Absolute calibration of Analog Detector using Stimulated Parametric Down Conversion,” J. Mod. Opt. 56(2–3), 401–408 (2009).
[CrossRef]

G. Brida, M. Genovese, A. Meda, E. Predazzi, and I. Ruo Berchera, “Systematic study of the PDC speckle structure for quantum imaging applications,” Int. Journ. Quantum Inf. 7, 139–147 (2009).
[CrossRef]

G. Brida, M. Genovese, A. Meda, E. Predazzi, and I. Ruo Berchera, “Tailoring PDC speckle structure,” J. Mod. Opt. 56, 201–208 (2009).
[CrossRef]

2008 (5)

T. S. Iskhakov, E. D. Lopaeva, A. N. Penin, G. O. Rytikov, and M. V. Chekhova, “Two methods for detecting nonclassical correlations in parametric scattering of light,” JETP Lett. 88(10), 660-664 (2008).
[CrossRef]

G. Brida, M. Chekhova, M. Genovese, and I. Ruo-Berchera, “Analysis of the possibility of analog detectors calibration by exploiting Stimulated Parametric Down Conversion,” Opt. Express 1612550–12558 (2008).
[CrossRef] [PubMed]

V. Boyer, A. M. Marino, and P. D. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett. 100, 143601 (2008).
[CrossRef] [PubMed]

E. Brambilla, L. Caspani, O. Jedrkiewicz, L. A. Lugiato, and A. Gatti, “High-sensitivity imaging with multi-mode twin beams,” Phys. Rev. A. 77, 053807 (2008).
[CrossRef]

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] [PubMed]

2007 (2)

M. Bondani, A. Allevi, G. Zambra, M. Paris, and A. Andreoni, “Sub-shot-noise photon-number correlation in a mesoscopic twin beam of light,” Phy. Rev. A 76, 013833 (2007).
[CrossRef]

S. Polyakov and A. Migdall, “High accuracy verification of a correlated-photon- based method for determining photoncounting detection efficiency,” Opt. Express 15(4), 1390–1407 (2007).
[CrossRef] [PubMed]

2006 (3)

G. Brida, M. Chekhova, M. Genovese, A. Penin, and I. Ruo-Berchera, “The possibility of absolute calibration of analog detectors by using parametric down-conversion: a systematic study,” J. Opt. Soc. Am. B 23, 2185–2193 (2006).
[CrossRef]

M. Lindenthal and J. Kofler, “Measuring of the absolute photodetection efficiency using photon number correlations,” Appl. Opt. 45(24), 6059–6064 (2006).
[CrossRef]

G. Brida, M. Genovese, and M. Gramegna, “Twin-Photon techniques for photo-detector calibration,” Laser Phys. Lett. 3, 115–123 (2006)
[CrossRef]

2005 (2)

2004 (2)

O. Jedrkievicz, Y.-K Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion,” Phys. Rev. Lett. 93, 243601 (2004).
[CrossRef]

E. Brambilla, A. Gatti, M. Bache, and L. A. Lugiato, “Simultaneous near-field and far-field spatial quantum correlations in the high-gain regime of parametric down-conversion,” Phys. Rev. A 69, 023802 (2004).
[CrossRef]

2003 (1)

O. Jedrkiewicz, P. Di Trapani, Y. Jiang, S. Minardi, A. Mosset, E. Lantz, and F. Devaux, “Retrieval of spatial shot-noise in the full dynamic range of calibrated CCD cameras,” Eur. Phys. J. D 22, 521–526 (2003).
[CrossRef]

2000 (2)

M. Genovese, G. Brida, and C. Novero, “An application of two photons entangled states to quantum metrology,” J. Mod. Opt. 47, 2099-2104 (2000).

G. Brida, S. Castelletto, I. Degiovanni, M. Genovese, C. Novero, and M. L. Rastello, “Toward an accuracy budget in quantum efficiency measurement with parametric fluorescence,” Metrologia 37(5), 629–632 (2000).
[CrossRef]

1999 (1)

A. Migdall, “Correlated-photon metrology without absolute standards,” Phys. Today 1, 41–46 (1999).
[CrossRef]

1993 (1)

V. M. Ginzburg, N. G. Keratishvili, E. L. Korzhenevich, G. V. Lunev, A. N. Penin, and V. I. Sapritsky, “Absolute meter of photodetector quantum efficiency based on the parametric down-conversion effect,” Opt. Eng. 32(11), 2911–2916 (1993).
[CrossRef]

1986 (1)

A. V. Sergienko and A. N. Penin, “Absolute calibration of analog photodetectors using biphotonic fields,” Sov. Tech. Phys. Lett. 12, 328–329 (1986).

1981 (1)

A. A. Malygin, A. N. Penin, and A. V. Sergienko, “Absolute calibration of the sensitivity of photodetectors using a two-photon field,” Sov. Phys. JETP Lett. 33, 477–480 (1981).

1980 (1)

D. N. Klyshko, “Use of two-photon light for absolute calibration of photoelectric detectors,” Sov. J. Quantum Electron. 10, 1112–1116 (1980).
[CrossRef]

1970 (1)

D. C. Burnham and D. L. Weinberg, “Observation of simultaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).
[CrossRef]

1969 (1)

B. Y. Zel’dovich and D.N. Klyshko, “Statistics of field in parametric luminescence,” Sov. Phys. JETP Lett. 940–44 (1969).

Allevi, A.

M. Bondani, A. Allevi, G. Zambra, M. Paris, and A. Andreoni, “Sub-shot-noise photon-number correlation in a mesoscopic twin beam of light,” Phy. Rev. A 76, 013833 (2007).
[CrossRef]

Andreoni, A.

M. Bondani, A. Allevi, G. Zambra, M. Paris, and A. Andreoni, “Sub-shot-noise photon-number correlation in a mesoscopic twin beam of light,” Phy. Rev. A 76, 013833 (2007).
[CrossRef]

Bache, M.

O. Jedrkievicz, Y.-K Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion,” Phys. Rev. Lett. 93, 243601 (2004).
[CrossRef]

E. Brambilla, A. Gatti, M. Bache, and L. A. Lugiato, “Simultaneous near-field and far-field spatial quantum correlations in the high-gain regime of parametric down-conversion,” Phys. Rev. A 69, 023802 (2004).
[CrossRef]

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] [PubMed]

Bondani, M.

M. Bondani, A. Allevi, G. Zambra, M. Paris, and A. Andreoni, “Sub-shot-noise photon-number correlation in a mesoscopic twin beam of light,” Phy. Rev. A 76, 013833 (2007).
[CrossRef]

Boyer, V.

V. Boyer, A. M. Marino, and P. D. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett. 100, 143601 (2008).
[CrossRef] [PubMed]

Brambilla, E.

E. Brambilla, L. Caspani, O. Jedrkiewicz, L. A. Lugiato, and A. Gatti, “High-sensitivity imaging with multi-mode twin beams,” Phys. Rev. A. 77, 053807 (2008).
[CrossRef]

O. Jedrkievicz, Y.-K Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion,” Phys. Rev. Lett. 93, 243601 (2004).
[CrossRef]

E. Brambilla, A. Gatti, M. Bache, and L. A. Lugiato, “Simultaneous near-field and far-field spatial quantum correlations in the high-gain regime of parametric down-conversion,” Phys. Rev. A 69, 023802 (2004).
[CrossRef]

Brida, G.

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

G. Brida, M. Chekhova, M. Genovese, M. L. Rastello, and I. Ruo Berchera, “Absolute calibration of Analog Detector using Stimulated Parametric Down Conversion,” J. Mod. Opt. 56(2–3), 401–408 (2009).
[CrossRef]

G. Brida, M. Genovese, A. Meda, E. Predazzi, and I. Ruo Berchera, “Tailoring PDC speckle structure,” J. Mod. Opt. 56, 201–208 (2009).
[CrossRef]

G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. Ruo-Berchera, “Measurement of sub-shot-noise spatial correlations without background subtraction,” Phys Rev. Lett. 102, 213602 (2009).
[CrossRef] [PubMed]

G. Brida, M. Genovese, A. Meda, E. Predazzi, and I. Ruo Berchera, “Systematic study of the PDC speckle structure for quantum imaging applications,” Int. Journ. Quantum Inf. 7, 139–147 (2009).
[CrossRef]

G. Brida, M. Chekhova, M. Genovese, and I. Ruo-Berchera, “Analysis of the possibility of analog detectors calibration by exploiting Stimulated Parametric Down Conversion,” Opt. Express 1612550–12558 (2008).
[CrossRef] [PubMed]

G. Brida, M. Genovese, and M. Gramegna, “Twin-Photon techniques for photo-detector calibration,” Laser Phys. Lett. 3, 115–123 (2006)
[CrossRef]

G. Brida, M. Chekhova, M. Genovese, A. Penin, and I. Ruo-Berchera, “The possibility of absolute calibration of analog detectors by using parametric down-conversion: a systematic study,” J. Opt. Soc. Am. B 23, 2185–2193 (2006).
[CrossRef]

G. Brida, M. Chekhova, M. Genovese, M. Gramegna, L. Krivitsky, and M. L. Rastello, “Single-Photon detectors calibration by means of conditional polarization rotation,” J. Opt. Soc. Am. B 22, 488–492 (2005).
[CrossRef]

G. Brida, S. Castelletto, I. Degiovanni, M. Genovese, C. Novero, and M. L. Rastello, “Toward an accuracy budget in quantum efficiency measurement with parametric fluorescence,” Metrologia 37(5), 629–632 (2000).
[CrossRef]

M. Genovese, G. Brida, and C. Novero, “An application of two photons entangled states to quantum metrology,” J. Mod. Opt. 47, 2099-2104 (2000).

Burnham, D. C.

D. C. Burnham and D. L. Weinberg, “Observation of simultaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).
[CrossRef]

Caspani, L.

G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. Ruo-Berchera, “Measurement of sub-shot-noise spatial correlations without background subtraction,” Phys Rev. Lett. 102, 213602 (2009).
[CrossRef] [PubMed]

E. Brambilla, L. Caspani, O. Jedrkiewicz, L. A. Lugiato, and A. Gatti, “High-sensitivity imaging with multi-mode twin beams,” Phys. Rev. A. 77, 053807 (2008).
[CrossRef]

Castelletto, S.

G. Brida, S. Castelletto, I. Degiovanni, M. Genovese, C. Novero, and M. L. Rastello, “Toward an accuracy budget in quantum efficiency measurement with parametric fluorescence,” Metrologia 37(5), 629–632 (2000).
[CrossRef]

Chekhova, M.

Chekhova, M. V.

T. S. Iskhakov, E. D. Lopaeva, A. N. Penin, G. O. Rytikov, and M. V. Chekhova, “Two methods for detecting nonclassical correlations in parametric scattering of light,” JETP Lett. 88(10), 660-664 (2008).
[CrossRef]

Degiovanni, I.

G. Brida, S. Castelletto, I. Degiovanni, M. Genovese, C. Novero, and M. L. Rastello, “Toward an accuracy budget in quantum efficiency measurement with parametric fluorescence,” Metrologia 37(5), 629–632 (2000).
[CrossRef]

Devaux, F.

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] [PubMed]

O. Jedrkiewicz, P. Di Trapani, Y. Jiang, S. Minardi, A. Mosset, E. Lantz, and F. Devaux, “Retrieval of spatial shot-noise in the full dynamic range of calibrated CCD cameras,” Eur. Phys. J. D 22, 521–526 (2003).
[CrossRef]

Di Trapani, P.

O. Jedrkievicz, Y.-K Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion,” Phys. Rev. Lett. 93, 243601 (2004).
[CrossRef]

O. Jedrkiewicz, P. Di Trapani, Y. Jiang, S. Minardi, A. Mosset, E. Lantz, and F. Devaux, “Retrieval of spatial shot-noise in the full dynamic range of calibrated CCD cameras,” Eur. Phys. J. D 22, 521–526 (2003).
[CrossRef]

Fox, N.

J. Zwinkels, E. Ikonen, N. Fox, G. Ulm, and M. L. Rastello, “Photometry, radiometry and the candela: evolution in the classical and quantum world,” Metrologia, to appear.

Furfaro, 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] [PubMed]

Gatti, A.

G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. Ruo-Berchera, “Measurement of sub-shot-noise spatial correlations without background subtraction,” Phys Rev. Lett. 102, 213602 (2009).
[CrossRef] [PubMed]

E. Brambilla, L. Caspani, O. Jedrkiewicz, L. A. Lugiato, and A. Gatti, “High-sensitivity imaging with multi-mode twin beams,” Phys. Rev. A. 77, 053807 (2008).
[CrossRef]

O. Jedrkievicz, Y.-K Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion,” Phys. Rev. Lett. 93, 243601 (2004).
[CrossRef]

E. Brambilla, A. Gatti, M. Bache, and L. A. Lugiato, “Simultaneous near-field and far-field spatial quantum correlations in the high-gain regime of parametric down-conversion,” Phys. Rev. A 69, 023802 (2004).
[CrossRef]

Genovese, M.

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

G. Brida, M. Chekhova, M. Genovese, M. L. Rastello, and I. Ruo Berchera, “Absolute calibration of Analog Detector using Stimulated Parametric Down Conversion,” J. Mod. Opt. 56(2–3), 401–408 (2009).
[CrossRef]

G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. Ruo-Berchera, “Measurement of sub-shot-noise spatial correlations without background subtraction,” Phys Rev. Lett. 102, 213602 (2009).
[CrossRef] [PubMed]

G. Brida, M. Genovese, A. Meda, E. Predazzi, and I. Ruo Berchera, “Tailoring PDC speckle structure,” J. Mod. Opt. 56, 201–208 (2009).
[CrossRef]

G. Brida, M. Genovese, A. Meda, E. Predazzi, and I. Ruo Berchera, “Systematic study of the PDC speckle structure for quantum imaging applications,” Int. Journ. Quantum Inf. 7, 139–147 (2009).
[CrossRef]

G. Brida, M. Chekhova, M. Genovese, and I. Ruo-Berchera, “Analysis of the possibility of analog detectors calibration by exploiting Stimulated Parametric Down Conversion,” Opt. Express 1612550–12558 (2008).
[CrossRef] [PubMed]

G. Brida, M. Genovese, and M. Gramegna, “Twin-Photon techniques for photo-detector calibration,” Laser Phys. Lett. 3, 115–123 (2006)
[CrossRef]

G. Brida, M. Chekhova, M. Genovese, A. Penin, and I. Ruo-Berchera, “The possibility of absolute calibration of analog detectors by using parametric down-conversion: a systematic study,” J. Opt. Soc. Am. B 23, 2185–2193 (2006).
[CrossRef]

G. Brida, M. Chekhova, M. Genovese, M. Gramegna, L. Krivitsky, and M. L. Rastello, “Single-Photon detectors calibration by means of conditional polarization rotation,” J. Opt. Soc. Am. B 22, 488–492 (2005).
[CrossRef]

M. Genovese, “Research on hidden variable theories: A review on recent progresses,” Phys. Rep. 413(6), 319–398 (2005), and references therein.
[CrossRef]

M. Genovese, G. Brida, and C. Novero, “An application of two photons entangled states to quantum metrology,” J. Mod. Opt. 47, 2099-2104 (2000).

G. Brida, S. Castelletto, I. Degiovanni, M. Genovese, C. Novero, and M. L. Rastello, “Toward an accuracy budget in quantum efficiency measurement with parametric fluorescence,” Metrologia 37(5), 629–632 (2000).
[CrossRef]

Ginzburg, V. M.

V. M. Ginzburg, N. G. Keratishvili, E. L. Korzhenevich, G. V. Lunev, A. N. Penin, and V. I. Sapritsky, “Absolute meter of photodetector quantum efficiency based on the parametric down-conversion effect,” Opt. Eng. 32(11), 2911–2916 (1993).
[CrossRef]

Gramegna, M.

Ikonen, E.

J. Zwinkels, E. Ikonen, N. Fox, G. Ulm, and M. L. Rastello, “Photometry, radiometry and the candela: evolution in the classical and quantum world,” Metrologia, to appear.

Ishkakov, T.

T. Ishkakov, M. Chekhova, and G. Leuchs, “Generation and Direct Detection of broadband mesoscopic polarization-squeezed vacuum,” Phys. Rev. Lett. 102, 183602 (2009).
[CrossRef]

Iskhakov, T. S.

T. S. Iskhakov, E. D. Lopaeva, A. N. Penin, G. O. Rytikov, and M. V. Chekhova, “Two methods for detecting nonclassical correlations in parametric scattering of light,” JETP Lett. 88(10), 660-664 (2008).
[CrossRef]

Jedrkievicz, O.

O. Jedrkievicz, Y.-K Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion,” Phys. Rev. Lett. 93, 243601 (2004).
[CrossRef]

Jedrkiewicz, O.

E. Brambilla, L. Caspani, O. Jedrkiewicz, L. A. Lugiato, and A. Gatti, “High-sensitivity imaging with multi-mode twin beams,” Phys. Rev. A. 77, 053807 (2008).
[CrossRef]

O. Jedrkiewicz, P. Di Trapani, Y. Jiang, S. Minardi, A. Mosset, E. Lantz, and F. Devaux, “Retrieval of spatial shot-noise in the full dynamic range of calibrated CCD cameras,” Eur. Phys. J. D 22, 521–526 (2003).
[CrossRef]

Jiang, Y.

O. Jedrkiewicz, P. Di Trapani, Y. Jiang, S. Minardi, A. Mosset, E. Lantz, and F. Devaux, “Retrieval of spatial shot-noise in the full dynamic range of calibrated CCD cameras,” Eur. Phys. J. D 22, 521–526 (2003).
[CrossRef]

Jiang, Y.-K

O. Jedrkievicz, Y.-K Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion,” Phys. Rev. Lett. 93, 243601 (2004).
[CrossRef]

Keratishvili, N. G.

V. M. Ginzburg, N. G. Keratishvili, E. L. Korzhenevich, G. V. Lunev, A. N. Penin, and V. I. Sapritsky, “Absolute meter of photodetector quantum efficiency based on the parametric down-conversion effect,” Opt. Eng. 32(11), 2911–2916 (1993).
[CrossRef]

Klyshko, D. N.

D. N. Klyshko, “Use of two-photon light for absolute calibration of photoelectric detectors,” Sov. J. Quantum Electron. 10, 1112–1116 (1980).
[CrossRef]

Klyshko, D.N.

B. Y. Zel’dovich and D.N. Klyshko, “Statistics of field in parametric luminescence,” Sov. Phys. JETP Lett. 940–44 (1969).

Kofler, J.

M. Lindenthal and J. Kofler, “Measuring of the absolute photodetection efficiency using photon number correlations,” Appl. Opt. 45(24), 6059–6064 (2006).
[CrossRef]

Korzhenevich, E. L.

V. M. Ginzburg, N. G. Keratishvili, E. L. Korzhenevich, G. V. Lunev, A. N. Penin, and V. I. Sapritsky, “Absolute meter of photodetector quantum efficiency based on the parametric down-conversion effect,” Opt. Eng. 32(11), 2911–2916 (1993).
[CrossRef]

Krivitsky, L.

Lantz, E.

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] [PubMed]

O. Jedrkiewicz, P. Di Trapani, Y. Jiang, S. Minardi, A. Mosset, E. Lantz, and F. Devaux, “Retrieval of spatial shot-noise in the full dynamic range of calibrated CCD cameras,” Eur. Phys. J. D 22, 521–526 (2003).
[CrossRef]

Lett, P. D.

V. Boyer, A. M. Marino, and P. D. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett. 100, 143601 (2008).
[CrossRef] [PubMed]

Leuchs, G.

T. Ishkakov, M. Chekhova, and G. Leuchs, “Generation and Direct Detection of broadband mesoscopic polarization-squeezed vacuum,” Phys. Rev. Lett. 102, 183602 (2009).
[CrossRef]

Lindenthal, M.

M. Lindenthal and J. Kofler, “Measuring of the absolute photodetection efficiency using photon number correlations,” Appl. Opt. 45(24), 6059–6064 (2006).
[CrossRef]

Lopaeva, E. D.

T. S. Iskhakov, E. D. Lopaeva, A. N. Penin, G. O. Rytikov, and M. V. Chekhova, “Two methods for detecting nonclassical correlations in parametric scattering of light,” JETP Lett. 88(10), 660-664 (2008).
[CrossRef]

Lugiato, L. A.

E. Brambilla, L. Caspani, O. Jedrkiewicz, L. A. Lugiato, and A. Gatti, “High-sensitivity imaging with multi-mode twin beams,” Phys. Rev. A. 77, 053807 (2008).
[CrossRef]

O. Jedrkievicz, Y.-K Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion,” Phys. Rev. Lett. 93, 243601 (2004).
[CrossRef]

E. Brambilla, A. Gatti, M. Bache, and L. A. Lugiato, “Simultaneous near-field and far-field spatial quantum correlations in the high-gain regime of parametric down-conversion,” Phys. Rev. A 69, 023802 (2004).
[CrossRef]

Lunev, G. V.

V. M. Ginzburg, N. G. Keratishvili, E. L. Korzhenevich, G. V. Lunev, A. N. Penin, and V. I. Sapritsky, “Absolute meter of photodetector quantum efficiency based on the parametric down-conversion effect,” Opt. Eng. 32(11), 2911–2916 (1993).
[CrossRef]

Malygin, A. A.

A. A. Malygin, A. N. Penin, and A. V. Sergienko, “Absolute calibration of the sensitivity of photodetectors using a two-photon field,” Sov. Phys. JETP Lett. 33, 477–480 (1981).

Marino, A. M.

V. Boyer, A. M. Marino, and P. D. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett. 100, 143601 (2008).
[CrossRef] [PubMed]

Meda, A.

G. Brida, M. Genovese, A. Meda, E. Predazzi, and I. Ruo Berchera, “Tailoring PDC speckle structure,” J. Mod. Opt. 56, 201–208 (2009).
[CrossRef]

G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. Ruo-Berchera, “Measurement of sub-shot-noise spatial correlations without background subtraction,” Phys Rev. Lett. 102, 213602 (2009).
[CrossRef] [PubMed]

G. Brida, M. Genovese, A. Meda, E. Predazzi, and I. Ruo Berchera, “Systematic study of the PDC speckle structure for quantum imaging applications,” Int. Journ. Quantum Inf. 7, 139–147 (2009).
[CrossRef]

Migdall, A.

Minardi, S.

O. Jedrkiewicz, P. Di Trapani, Y. Jiang, S. Minardi, A. Mosset, E. Lantz, and F. Devaux, “Retrieval of spatial shot-noise in the full dynamic range of calibrated CCD cameras,” Eur. Phys. J. D 22, 521–526 (2003).
[CrossRef]

Mosset, A.

O. Jedrkiewicz, P. Di Trapani, Y. Jiang, S. Minardi, A. Mosset, E. Lantz, and F. Devaux, “Retrieval of spatial shot-noise in the full dynamic range of calibrated CCD cameras,” Eur. Phys. J. D 22, 521–526 (2003).
[CrossRef]

Novero, C.

M. Genovese, G. Brida, and C. Novero, “An application of two photons entangled states to quantum metrology,” J. Mod. Opt. 47, 2099-2104 (2000).

G. Brida, S. Castelletto, I. Degiovanni, M. Genovese, C. Novero, and M. L. Rastello, “Toward an accuracy budget in quantum efficiency measurement with parametric fluorescence,” Metrologia 37(5), 629–632 (2000).
[CrossRef]

Paris, M.

M. Bondani, A. Allevi, G. Zambra, M. Paris, and A. Andreoni, “Sub-shot-noise photon-number correlation in a mesoscopic twin beam of light,” Phy. Rev. A 76, 013833 (2007).
[CrossRef]

Penin, A.

Penin, A. N.

T. S. Iskhakov, E. D. Lopaeva, A. N. Penin, G. O. Rytikov, and M. V. Chekhova, “Two methods for detecting nonclassical correlations in parametric scattering of light,” JETP Lett. 88(10), 660-664 (2008).
[CrossRef]

V. M. Ginzburg, N. G. Keratishvili, E. L. Korzhenevich, G. V. Lunev, A. N. Penin, and V. I. Sapritsky, “Absolute meter of photodetector quantum efficiency based on the parametric down-conversion effect,” Opt. Eng. 32(11), 2911–2916 (1993).
[CrossRef]

A. V. Sergienko and A. N. Penin, “Absolute calibration of analog photodetectors using biphotonic fields,” Sov. Tech. Phys. Lett. 12, 328–329 (1986).

A. A. Malygin, A. N. Penin, and A. V. Sergienko, “Absolute calibration of the sensitivity of photodetectors using a two-photon field,” Sov. Phys. JETP Lett. 33, 477–480 (1981).

Polyakov, S.

Predazzi, E.

G. Brida, M. Genovese, A. Meda, E. Predazzi, and I. Ruo Berchera, “Tailoring PDC speckle structure,” J. Mod. Opt. 56, 201–208 (2009).
[CrossRef]

G. Brida, M. Genovese, A. Meda, E. Predazzi, and I. Ruo Berchera, “Systematic study of the PDC speckle structure for quantum imaging applications,” Int. Journ. Quantum Inf. 7, 139–147 (2009).
[CrossRef]

Rastello, M. L.

G. Brida, M. Chekhova, M. Genovese, M. L. Rastello, and I. Ruo Berchera, “Absolute calibration of Analog Detector using Stimulated Parametric Down Conversion,” J. Mod. Opt. 56(2–3), 401–408 (2009).
[CrossRef]

G. Brida, M. Chekhova, M. Genovese, M. Gramegna, L. Krivitsky, and M. L. Rastello, “Single-Photon detectors calibration by means of conditional polarization rotation,” J. Opt. Soc. Am. B 22, 488–492 (2005).
[CrossRef]

G. Brida, S. Castelletto, I. Degiovanni, M. Genovese, C. Novero, and M. L. Rastello, “Toward an accuracy budget in quantum efficiency measurement with parametric fluorescence,” Metrologia 37(5), 629–632 (2000).
[CrossRef]

J. Zwinkels, E. Ikonen, N. Fox, G. Ulm, and M. L. Rastello, “Photometry, radiometry and the candela: evolution in the classical and quantum world,” Metrologia, to appear.

Ruo Berchera, I.

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

G. Brida, M. Chekhova, M. Genovese, M. L. Rastello, and I. Ruo Berchera, “Absolute calibration of Analog Detector using Stimulated Parametric Down Conversion,” J. Mod. Opt. 56(2–3), 401–408 (2009).
[CrossRef]

G. Brida, M. Genovese, A. Meda, E. Predazzi, and I. Ruo Berchera, “Tailoring PDC speckle structure,” J. Mod. Opt. 56, 201–208 (2009).
[CrossRef]

G. Brida, M. Genovese, A. Meda, E. Predazzi, and I. Ruo Berchera, “Systematic study of the PDC speckle structure for quantum imaging applications,” Int. Journ. Quantum Inf. 7, 139–147 (2009).
[CrossRef]

I. Ruo Berchera, “Theory of PDC in a continuous variables framework and its applications to the absolute calibration of photo-detectors,” Adv. Sci. Lett. 2, 407–429 (2009).
[CrossRef]

Ruo-Berchera, I.

Rytikov, G. O.

T. S. Iskhakov, E. D. Lopaeva, A. N. Penin, G. O. Rytikov, and M. V. Chekhova, “Two methods for detecting nonclassical correlations in parametric scattering of light,” JETP Lett. 88(10), 660-664 (2008).
[CrossRef]

Sapritsky, V. I.

V. M. Ginzburg, N. G. Keratishvili, E. L. Korzhenevich, G. V. Lunev, A. N. Penin, and V. I. Sapritsky, “Absolute meter of photodetector quantum efficiency based on the parametric down-conversion effect,” Opt. Eng. 32(11), 2911–2916 (1993).
[CrossRef]

Sergienko, A. V.

A. V. Sergienko and A. N. Penin, “Absolute calibration of analog photodetectors using biphotonic fields,” Sov. Tech. Phys. Lett. 12, 328–329 (1986).

A. A. Malygin, A. N. Penin, and A. V. Sergienko, “Absolute calibration of the sensitivity of photodetectors using a two-photon field,” Sov. Phys. JETP Lett. 33, 477–480 (1981).

Ulm, G.

J. Zwinkels, E. Ikonen, N. Fox, G. Ulm, and M. L. Rastello, “Photometry, radiometry and the candela: evolution in the classical and quantum world,” Metrologia, to appear.

Weinberg, D. L.

D. C. Burnham and D. L. Weinberg, “Observation of simultaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).
[CrossRef]

Zambra, G.

M. Bondani, A. Allevi, G. Zambra, M. Paris, and A. Andreoni, “Sub-shot-noise photon-number correlation in a mesoscopic twin beam of light,” Phy. Rev. A 76, 013833 (2007).
[CrossRef]

Zel’dovich, B. Y.

B. Y. Zel’dovich and D.N. Klyshko, “Statistics of field in parametric luminescence,” Sov. Phys. JETP Lett. 940–44 (1969).

Zwinkels, J.

J. Zwinkels, E. Ikonen, N. Fox, G. Ulm, and M. L. Rastello, “Photometry, radiometry and the candela: evolution in the classical and quantum world,” Metrologia, to appear.

Adv. Sci. Lett. (1)

I. Ruo Berchera, “Theory of PDC in a continuous variables framework and its applications to the absolute calibration of photo-detectors,” Adv. Sci. Lett. 2, 407–429 (2009).
[CrossRef]

App. Opt. (1)

M. Lindenthal and J. Kofler, “Measuring of the absolute photodetection efficiency using photon number correlations,” Appl. Opt. 45(24), 6059–6064 (2006).
[CrossRef]

Eur. Phys. J. D (1)

O. Jedrkiewicz, P. Di Trapani, Y. Jiang, S. Minardi, A. Mosset, E. Lantz, and F. Devaux, “Retrieval of spatial shot-noise in the full dynamic range of calibrated CCD cameras,” Eur. Phys. J. D 22, 521–526 (2003).
[CrossRef]

Int. Journ. Quantum Inf. (1)

G. Brida, M. Genovese, A. Meda, E. Predazzi, and I. Ruo Berchera, “Systematic study of the PDC speckle structure for quantum imaging applications,” Int. Journ. Quantum Inf. 7, 139–147 (2009).
[CrossRef]

J. Mod. Opt. (3)

G. Brida, M. Genovese, A. Meda, E. Predazzi, and I. Ruo Berchera, “Tailoring PDC speckle structure,” J. Mod. Opt. 56, 201–208 (2009).
[CrossRef]

G. Brida, M. Chekhova, M. Genovese, M. L. Rastello, and I. Ruo Berchera, “Absolute calibration of Analog Detector using Stimulated Parametric Down Conversion,” J. Mod. Opt. 56(2–3), 401–408 (2009).
[CrossRef]

M. Genovese, G. Brida, and C. Novero, “An application of two photons entangled states to quantum metrology,” J. Mod. Opt. 47, 2099-2104 (2000).

J. Opt. Soc. Am. B (2)

JETP Lett. (1)

T. S. Iskhakov, E. D. Lopaeva, A. N. Penin, G. O. Rytikov, and M. V. Chekhova, “Two methods for detecting nonclassical correlations in parametric scattering of light,” JETP Lett. 88(10), 660-664 (2008).
[CrossRef]

Laser Phys. Lett. (1)

G. Brida, M. Genovese, and M. Gramegna, “Twin-Photon techniques for photo-detector calibration,” Laser Phys. Lett. 3, 115–123 (2006)
[CrossRef]

Metrologia (2)

J. Zwinkels, E. Ikonen, N. Fox, G. Ulm, and M. L. Rastello, “Photometry, radiometry and the candela: evolution in the classical and quantum world,” Metrologia, to appear.

G. Brida, S. Castelletto, I. Degiovanni, M. Genovese, C. Novero, and M. L. Rastello, “Toward an accuracy budget in quantum efficiency measurement with parametric fluorescence,” Metrologia 37(5), 629–632 (2000).
[CrossRef]

Nat. Photon. (1)

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

Opt. Eng. (1)

V. M. Ginzburg, N. G. Keratishvili, E. L. Korzhenevich, G. V. Lunev, A. N. Penin, and V. I. Sapritsky, “Absolute meter of photodetector quantum efficiency based on the parametric down-conversion effect,” Opt. Eng. 32(11), 2911–2916 (1993).
[CrossRef]

Opt. Express (2)

Phy. Rev. A (1)

M. Bondani, A. Allevi, G. Zambra, M. Paris, and A. Andreoni, “Sub-shot-noise photon-number correlation in a mesoscopic twin beam of light,” Phy. Rev. A 76, 013833 (2007).
[CrossRef]

Phys Rev. Lett. (1)

G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. Ruo-Berchera, “Measurement of sub-shot-noise spatial correlations without background subtraction,” Phys Rev. Lett. 102, 213602 (2009).
[CrossRef] [PubMed]

Phys. Rep. (1)

M. Genovese, “Research on hidden variable theories: A review on recent progresses,” Phys. Rep. 413(6), 319–398 (2005), and references therein.
[CrossRef]

Phys. Rev. A (1)

E. Brambilla, A. Gatti, M. Bache, and L. A. Lugiato, “Simultaneous near-field and far-field spatial quantum correlations in the high-gain regime of parametric down-conversion,” Phys. Rev. A 69, 023802 (2004).
[CrossRef]

Phys. Rev. A. (1)

E. Brambilla, L. Caspani, O. Jedrkiewicz, L. A. Lugiato, and A. Gatti, “High-sensitivity imaging with multi-mode twin beams,” Phys. Rev. A. 77, 053807 (2008).
[CrossRef]

Phys. Rev. Lett. (5)

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] [PubMed]

O. Jedrkievicz, Y.-K Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion,” Phys. Rev. Lett. 93, 243601 (2004).
[CrossRef]

T. Ishkakov, M. Chekhova, and G. Leuchs, “Generation and Direct Detection of broadband mesoscopic polarization-squeezed vacuum,” Phys. Rev. Lett. 102, 183602 (2009).
[CrossRef]

V. Boyer, A. M. Marino, and P. D. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett. 100, 143601 (2008).
[CrossRef] [PubMed]

D. C. Burnham and D. L. Weinberg, “Observation of simultaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).
[CrossRef]

Phys. Today (1)

A. Migdall, “Correlated-photon metrology without absolute standards,” Phys. Today 1, 41–46 (1999).
[CrossRef]

Sov. J. Quantum Electron. (1)

D. N. Klyshko, “Use of two-photon light for absolute calibration of photoelectric detectors,” Sov. J. Quantum Electron. 10, 1112–1116 (1980).
[CrossRef]

Sov. Phys. JETP Lett. (2)

A. A. Malygin, A. N. Penin, and A. V. Sergienko, “Absolute calibration of the sensitivity of photodetectors using a two-photon field,” Sov. Phys. JETP Lett. 33, 477–480 (1981).

B. Y. Zel’dovich and D.N. Klyshko, “Statistics of field in parametric luminescence,” Sov. Phys. JETP Lett. 940–44 (1969).

Sov. Tech. Phys. Lett. (1)

A. V. Sergienko and A. N. Penin, “Absolute calibration of analog photodetectors using biphotonic fields,” Sov. Tech. Phys. Lett. 12, 328–329 (1986).

Other (5)

I. N. Agafonov, M. V. Chekhova, and G. Leuchs, “Two-Color Bright Squeezed Vacuum,” arXiv:0910.4831.

The order of magnitude in our experiment is estimable as large as 2η+MtotV (μ)/μ =V (<Ns +Ni>)/<Ns +Ni>∼ 5·103 (see Tab. 1, first two columns). It is four order of magnitude larger than the excess noise due to the thermal fluctuations.

“Guide to the expression of uncertainty in measurement (GUM),” ISO/IEC Guide 98:1995.

G. Brida, M. Genovese, A. Meda, and I. Ruo Berchera, “Experimental quantum imaging exploiting multi-mode spatial correlation of twin beams,” arXiv:1005.3665v2 [quant-ph].

Quantum Imaging, M. I.  Kolobov, ed., (Springer, New York, 2007), and references therein.
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Scheme for spatial correlations detection in PDC. The PDC emission from the nonlinear crystal is detected in the far field, reached by a optical ff configuration. The pump transverse size determines an uncertainty in the photon propagation direction. The speckled image showed, has been obtained experimentally in very high gain regime. For this reason, the spatial fluctuations are very strong, and the coherence area is roughly represented by the typical size of the speckles.

Fig. 2
Fig. 2

Determination of center of symmetry. The right hand side presents a typical image obtained by the CCD in the working condition. The images is separated in two portions, one collecting the light from the signal beam (H-polarized) and the other the light of the idler beam (V-polarized). Two regions Rs and Ri (squares) are selected, and subtracted pixel by pixel. The spatial noise of the difference σ is reported in the inserts (right-bottom) in function of the position ξ = (ξ 1, ξ 2) of the idler region in the discrete pixel grid, both in a 1-dimensional graphic in function of ξ 1 having fixed ξ 2 = 0 and in a contour plot.

Fig. 3
Fig. 3

Noise reduction factor in function of the detection area. Abscissa reports the linear size of the detection areas in μm. The two experimental curves refer to the noise reduction factor σα with (red), and without (black) background correction.

Fig. 4
Fig. 4

Standard deviation of σα,B on a number Z of independent measurements. In each measurement a value of σα,B is obtained by formula (10) with the substitutions (12), using a set of N images. Although the standard deviation of the population decreases for larger N , the uncertainty on the mean value, only depends on the total number of images Z · N [See text for further discussion].

Tables (1)

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Table 1 Experimental estimates (row 2) and their statistical uncertainties (row 3). Column 1-2 show the mean counts in the detection area A det,s of the single images and the mean square of fluctuation δ 2 N s ( k ) = ( N s ( k ) E [ N s ] ) 2 . Column 3-4 report the same values related to the background images. Column 5-6 present the experimental values of the compensation factor α and the value corrected for background counts. In column 7-9 are reported the raw noise reduction factor, the one after compensation of the losses, and finally the one after compensation and background correction respectively

Equations (20)

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| ψ ( q ) = n C q ( n ) | n i , q | n s , q ,
δ 2 N j N j ( 1 + E ) = N j ( 1 + N j M tot ) = M tot η j μ ( 1 + η j μ ) ,
δ N i δ N s = M tot η s η i μ ( 1 + μ ) .
σ δ 2 N N i + N s = 1 η + + η 2 2 η + ( 1 2 + μ ) = 1 η + + η 2 4 η + 2 ( η + + N s + N i M tot ) ,
σ α δ 2 ( N s α N i ) 2 N s = 1 2 ( 1 + α ) η s ,
α = E [ N s ( k ) ] E [ N i ( k ) ] ,
σ α = E [ ( N s ( k ) α N i ( k ) ) 2 ] E [ N s ( k ) α N i ( k ) ] 2 E [ N s ( k ) ] + α E [ N i ( k ) ] ,
η true , j = η j τ j ,
σ δ 2 N N s + N i = 1 η + + η 2 2 η + [ μ ¯ + 1 2 + V ( μ ) μ ¯ ( 1 + M tot ) ] .
σ α , B δ 2 ( N s α B N i ) δ 2 ( M s α B M i ) 2 ( N s M s ) = 1 2 ( 1 + α B ) η s ,
α B = E [ N s ( k ) ] E [ M s ( p ) ] E [ N i ( k ) ] E [ M i ( p ) ] ,
δ 2 ( N s α B N i ) E [ ( N s ( k ) α B N i ( k ) ) 2 ] E [ N s ( k ) α B N i ( k ) ] 2 δ 2 ( M s α B M i ) E [ ( M s ( p ) α B M i ( p ) ) 2 ] E [ M s ( p ) α B M i ( p ) ] 2
α | estim = Z 1 l = 1 Z α ( l ) σ α | estim = Z 1 l = 1 Z σ α ( l )
Δ α | estim = [ Z ( Z 1 ) ] 1 l = 1 Z [ α ( l ) α | estim ] 2 Δ σ α | estim = [ Z ( Z 1 ) ] 1 l = 1 Z [ σ α ( l ) σ α | estim ] .
E [ N s ]
E [ δ 2 N s ]
E [ δ 2 M s ]
α B estim
σ α estim
σ α , B estim

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