Abstract

The fluctuations of measured signals are not always artifacts. A variety of active sensing circumstances where the excitation fields interact with random potentials result in measured signals that fluctuate. As inverse problems are notoriously ill posed, only stochastic information is available in these conditions. Here, we demonstrate a stochastic sensing technique where the statistically non-stationary properties of the excitation fields are purposely manipulated such that the fluctuations of the scattered intensity are enhanced and further exploited to recover information about the interaction potentials. The numerical and experimental results establish the efficacy of this new sensing approach and validate its robustness against various sources of perturbations. A range of remote sensing and biomedical applications that rely on recovering the properties of random scattering potentials and are usually limited by noise could benefit from the sturdy performance of this sensing procedure.

© 2016 Optical Society of America

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References

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  1. B. J. Berne and R. Pecora, Dynamic Light Scattering: with Applications to Chemistry, Biology, and Physics (Courier Corporation, 2000).
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    [Crossref]
  4. H. Bayley and P. S. Cremer, “Stochastic sensors inspired by biology,” Nature 413, 226–230 (2001).
    [Crossref]
  5. L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70, 223–287 (1998).
    [Crossref]
  6. A. Dogariu and E. Wolf, “Spectral changes produced by static scattering on a system of particles,” Opt. Lett. 23, 1340–1342 (1998).
    [Crossref]
  7. 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]
  8. J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78, 061802 (2008).
    [Crossref]
  9. J. H. Shapiro and R. W. Boyd, “The physics of ghost imaging,” Quantum Inf. Process. 11, 949–993 (2012).
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  10. J. M. Mendel, “Tutorial on higher-order statistics (spectra) in signal processing and system theory: theoretical results and some applications,” Proc. IEEE 79, 278–305 (1991).
    [Crossref]
  11. D. H. Lenschow, V. Wulfmeyer, and C. Senff, “Measuring second-through fourth-order moments in noisy data,” J. Atmos. Ocean. Technol. 17, 1330–1347 (2000).
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  12. A. Behrendt, V. Wulfmeyer, E. Hammann, S. K. Muppa, and S. Pal, “Profiles of second- to fourth-order moments of turbulent temperature fluctuations in the convective boundary layer: first measurements with rotational Raman lidar,” Atmos. Chem. Phys. 15, 5485–5500 (2015).
    [Crossref]
  13. W. J. Padgett and C. P. Tsokos, “Existence of a solution of a stochastic integral equation in turbulence theory,” J. Math. Phys. 12, 210–212 (1971).
    [Crossref]
  14. U. Fano, “Ionization yield of radiations. II. The fluctuations of the number of ions,” Phys. Rev. 72, 26–29 (1947).
    [Crossref]
  15. A. Bousselham, H. H. Barrett, V. Bora, and K. Shah, “Photoelectron anticorrelations and sub-Poisson statistics in scintillation detectors,” Nucl. Instrum. Methods Phys. Res. A 620, 359–362 (2010).
    [Crossref]
  16. K. Balachandran, K. Sumathy, and H. H. Kuo, “Existence of solutions of general nonlinear stochastic volterra fredholm integral equations,” Stoch. Anal. Appl. 23, 827–851 (2005).
    [Crossref]
  17. E. Jakeman and P. N. Pusey, “Significance of K distributions in scattering experiments,” Phys. Rev. Lett. 40, 546–550 (1978).
    [Crossref]
  18. R. Barakat, “Direct derivation of intensity and phase statistics of speckle produced by a weak scatterer from the random sinusoid model,” J. Opt. Soc. Am. 71, 86–90 (1981).
    [Crossref]
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  20. K. Kanazawa, T. Sagawa, and H. Hayakawa, “Stochastic energetics for non-Gaussian processes,” Phys. Rev. Lett. 108, 210601 (2012).
    [Crossref]
  21. N. Brenner and Y. Shokef, “Nonequilibrium statistical mechanics of dividing cell populations,” Phys. Rev. Lett. 99, 138102 (2007).
    [Crossref]
  22. C. Plathow, C. Fink, S. Ley, M. Puderbach, M. Eichinger, I. Zuna, A. Schmähl, and H. U. Kauczor, “Radiotherapy and oncolog,” Radiotherapy Oncology 73, 349–354 (2004).
    [Crossref]
  23. M. Parrinello and A. Rahman, “Crystal structure and pair potentials: a molecular-dynamics study,” Phys. Rev. Lett. 45, 1196–1199 (1980).
    [Crossref]
  24. A. S. Keys, A. R. Abate, S. C. Glotzer, and D. J. Durian, “Measurement of growing dynamical length scales and prediction of the jamming transition in a granular material,” Nat. Phys. 3, 260–264 (2007).
    [Crossref]
  25. D. H. Lenschow and B. B. Stankov, “Length scales in the convective boundary layer,” J. Atmos. Sci. 43, 1198–1209 (1986).
    [Crossref]
  26. C. Tong, J. C. Wyngaard, S. Khanna, and J. G. Brasseur, “Resolvable-and subgrid-scale measurement in the atmospheric surface layer: Technique and issues,” J. Atmos. Sci. 55, 3114–3126 (1998).
    [Crossref]
  27. S. Alexander, G. E. Koehl, M. Hirschberg, E. K. Geissler, and P. Friedl, “Dynamic imaging of cancer growth and invasion: a modified skin-fold chamber model,” Histochem. Cell Biol. 130, 1147–1154 (2008).
    [Crossref]

2015 (1)

A. Behrendt, V. Wulfmeyer, E. Hammann, S. K. Muppa, and S. Pal, “Profiles of second- to fourth-order moments of turbulent temperature fluctuations in the convective boundary layer: first measurements with rotational Raman lidar,” Atmos. Chem. Phys. 15, 5485–5500 (2015).
[Crossref]

2012 (2)

J. H. Shapiro and R. W. Boyd, “The physics of ghost imaging,” Quantum Inf. Process. 11, 949–993 (2012).
[Crossref]

K. Kanazawa, T. Sagawa, and H. Hayakawa, “Stochastic energetics for non-Gaussian processes,” Phys. Rev. Lett. 108, 210601 (2012).
[Crossref]

2010 (1)

A. Bousselham, H. H. Barrett, V. Bora, and K. Shah, “Photoelectron anticorrelations and sub-Poisson statistics in scintillation detectors,” Nucl. Instrum. Methods Phys. Res. A 620, 359–362 (2010).
[Crossref]

2008 (4)

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78, 061802 (2008).
[Crossref]

S. Alexander, G. E. Koehl, M. Hirschberg, E. K. Geissler, and P. Friedl, “Dynamic imaging of cancer growth and invasion: a modified skin-fold chamber model,” Histochem. Cell Biol. 130, 1147–1154 (2008).
[Crossref]

S. Sukhov, D. Haefner, and A. Dogariu, “Stochastic sensing of relative anisotropic polarizabilities,” Phys. Rev. A 77, 043820 (2008).
[Crossref]

D. Haefner, S. Sukhov, and A. Dogariu, “Stochastic scattering polarimetry,” Phys. Rev. Lett. 100, 043901 (2008).
[Crossref]

2007 (2)

N. Brenner and Y. Shokef, “Nonequilibrium statistical mechanics of dividing cell populations,” Phys. Rev. Lett. 99, 138102 (2007).
[Crossref]

A. S. Keys, A. R. Abate, S. C. Glotzer, and D. J. Durian, “Measurement of growing dynamical length scales and prediction of the jamming transition in a granular material,” Nat. Phys. 3, 260–264 (2007).
[Crossref]

2005 (1)

K. Balachandran, K. Sumathy, and H. H. Kuo, “Existence of solutions of general nonlinear stochastic volterra fredholm integral equations,” Stoch. Anal. Appl. 23, 827–851 (2005).
[Crossref]

2004 (1)

C. Plathow, C. Fink, S. Ley, M. Puderbach, M. Eichinger, I. Zuna, A. Schmähl, and H. U. Kauczor, “Radiotherapy and oncolog,” Radiotherapy Oncology 73, 349–354 (2004).
[Crossref]

2001 (1)

H. Bayley and P. S. Cremer, “Stochastic sensors inspired by biology,” Nature 413, 226–230 (2001).
[Crossref]

2000 (1)

D. H. Lenschow, V. Wulfmeyer, and C. Senff, “Measuring second-through fourth-order moments in noisy data,” J. Atmos. Ocean. Technol. 17, 1330–1347 (2000).
[Crossref]

1998 (3)

L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70, 223–287 (1998).
[Crossref]

A. Dogariu and E. Wolf, “Spectral changes produced by static scattering on a system of particles,” Opt. Lett. 23, 1340–1342 (1998).
[Crossref]

C. Tong, J. C. Wyngaard, S. Khanna, and J. G. Brasseur, “Resolvable-and subgrid-scale measurement in the atmospheric surface layer: Technique and issues,” J. Atmos. Sci. 55, 3114–3126 (1998).
[Crossref]

1995 (1)

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]

1991 (1)

J. M. Mendel, “Tutorial on higher-order statistics (spectra) in signal processing and system theory: theoretical results and some applications,” Proc. IEEE 79, 278–305 (1991).
[Crossref]

1988 (1)

E. Jakeman and R. J. A. Tough, “Non-Gaussian models for the statistics of scattered waves,” Adv. Phys. 37, 471–529 (1988).
[Crossref]

1986 (1)

D. H. Lenschow and B. B. Stankov, “Length scales in the convective boundary layer,” J. Atmos. Sci. 43, 1198–1209 (1986).
[Crossref]

1981 (1)

1980 (1)

M. Parrinello and A. Rahman, “Crystal structure and pair potentials: a molecular-dynamics study,” Phys. Rev. Lett. 45, 1196–1199 (1980).
[Crossref]

1978 (1)

E. Jakeman and P. N. Pusey, “Significance of K distributions in scattering experiments,” Phys. Rev. Lett. 40, 546–550 (1978).
[Crossref]

1971 (1)

W. J. Padgett and C. P. Tsokos, “Existence of a solution of a stochastic integral equation in turbulence theory,” J. Math. Phys. 12, 210–212 (1971).
[Crossref]

1947 (1)

U. Fano, “Ionization yield of radiations. II. The fluctuations of the number of ions,” Phys. Rev. 72, 26–29 (1947).
[Crossref]

Abate, A. R.

A. S. Keys, A. R. Abate, S. C. Glotzer, and D. J. Durian, “Measurement of growing dynamical length scales and prediction of the jamming transition in a granular material,” Nat. Phys. 3, 260–264 (2007).
[Crossref]

Alexander, S.

S. Alexander, G. E. Koehl, M. Hirschberg, E. K. Geissler, and P. Friedl, “Dynamic imaging of cancer growth and invasion: a modified skin-fold chamber model,” Histochem. Cell Biol. 130, 1147–1154 (2008).
[Crossref]

Balachandran, K.

K. Balachandran, K. Sumathy, and H. H. Kuo, “Existence of solutions of general nonlinear stochastic volterra fredholm integral equations,” Stoch. Anal. Appl. 23, 827–851 (2005).
[Crossref]

Barakat, R.

Barrett, H. H.

A. Bousselham, H. H. Barrett, V. Bora, and K. Shah, “Photoelectron anticorrelations and sub-Poisson statistics in scintillation detectors,” Nucl. Instrum. Methods Phys. Res. A 620, 359–362 (2010).
[Crossref]

Bayley, H.

H. Bayley and P. S. Cremer, “Stochastic sensors inspired by biology,” Nature 413, 226–230 (2001).
[Crossref]

Behrendt, A.

A. Behrendt, V. Wulfmeyer, E. Hammann, S. K. Muppa, and S. Pal, “Profiles of second- to fourth-order moments of turbulent temperature fluctuations in the convective boundary layer: first measurements with rotational Raman lidar,” Atmos. Chem. Phys. 15, 5485–5500 (2015).
[Crossref]

Berne, B. J.

B. J. Berne and R. Pecora, Dynamic Light Scattering: with Applications to Chemistry, Biology, and Physics (Courier Corporation, 2000).

Bora, V.

A. Bousselham, H. H. Barrett, V. Bora, and K. Shah, “Photoelectron anticorrelations and sub-Poisson statistics in scintillation detectors,” Nucl. Instrum. Methods Phys. Res. A 620, 359–362 (2010).
[Crossref]

Bousselham, A.

A. Bousselham, H. H. Barrett, V. Bora, and K. Shah, “Photoelectron anticorrelations and sub-Poisson statistics in scintillation detectors,” Nucl. Instrum. Methods Phys. Res. A 620, 359–362 (2010).
[Crossref]

Boyd, R. W.

J. H. Shapiro and R. W. Boyd, “The physics of ghost imaging,” Quantum Inf. Process. 11, 949–993 (2012).
[Crossref]

Brasseur, J. G.

C. Tong, J. C. Wyngaard, S. Khanna, and J. G. Brasseur, “Resolvable-and subgrid-scale measurement in the atmospheric surface layer: Technique and issues,” J. Atmos. Sci. 55, 3114–3126 (1998).
[Crossref]

Brenner, N.

N. Brenner and Y. Shokef, “Nonequilibrium statistical mechanics of dividing cell populations,” Phys. Rev. Lett. 99, 138102 (2007).
[Crossref]

Cremer, P. S.

H. Bayley and P. S. Cremer, “Stochastic sensors inspired by biology,” Nature 413, 226–230 (2001).
[Crossref]

Dogariu, A.

D. Haefner, S. Sukhov, and A. Dogariu, “Stochastic scattering polarimetry,” Phys. Rev. Lett. 100, 043901 (2008).
[Crossref]

S. Sukhov, D. Haefner, and A. Dogariu, “Stochastic sensing of relative anisotropic polarizabilities,” Phys. Rev. A 77, 043820 (2008).
[Crossref]

A. Dogariu and E. Wolf, “Spectral changes produced by static scattering on a system of particles,” Opt. Lett. 23, 1340–1342 (1998).
[Crossref]

Durian, D. J.

A. S. Keys, A. R. Abate, S. C. Glotzer, and D. J. Durian, “Measurement of growing dynamical length scales and prediction of the jamming transition in a granular material,” Nat. Phys. 3, 260–264 (2007).
[Crossref]

Eichinger, M.

C. Plathow, C. Fink, S. Ley, M. Puderbach, M. Eichinger, I. Zuna, A. Schmähl, and H. U. Kauczor, “Radiotherapy and oncolog,” Radiotherapy Oncology 73, 349–354 (2004).
[Crossref]

Fano, U.

U. Fano, “Ionization yield of radiations. II. The fluctuations of the number of ions,” Phys. Rev. 72, 26–29 (1947).
[Crossref]

Fink, C.

C. Plathow, C. Fink, S. Ley, M. Puderbach, M. Eichinger, I. Zuna, A. Schmähl, and H. U. Kauczor, “Radiotherapy and oncolog,” Radiotherapy Oncology 73, 349–354 (2004).
[Crossref]

Friedl, P.

S. Alexander, G. E. Koehl, M. Hirschberg, E. K. Geissler, and P. Friedl, “Dynamic imaging of cancer growth and invasion: a modified skin-fold chamber model,” Histochem. Cell Biol. 130, 1147–1154 (2008).
[Crossref]

Gammaitoni, L.

L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70, 223–287 (1998).
[Crossref]

Geissler, E. K.

S. Alexander, G. E. Koehl, M. Hirschberg, E. K. Geissler, and P. Friedl, “Dynamic imaging of cancer growth and invasion: a modified skin-fold chamber model,” Histochem. Cell Biol. 130, 1147–1154 (2008).
[Crossref]

Glotzer, S. C.

A. S. Keys, A. R. Abate, S. C. Glotzer, and D. J. Durian, “Measurement of growing dynamical length scales and prediction of the jamming transition in a granular material,” Nat. Phys. 3, 260–264 (2007).
[Crossref]

Haefner, D.

D. Haefner, S. Sukhov, and A. Dogariu, “Stochastic scattering polarimetry,” Phys. Rev. Lett. 100, 043901 (2008).
[Crossref]

S. Sukhov, D. Haefner, and A. Dogariu, “Stochastic sensing of relative anisotropic polarizabilities,” Phys. Rev. A 77, 043820 (2008).
[Crossref]

Hammann, E.

A. Behrendt, V. Wulfmeyer, E. Hammann, S. K. Muppa, and S. Pal, “Profiles of second- to fourth-order moments of turbulent temperature fluctuations in the convective boundary layer: first measurements with rotational Raman lidar,” Atmos. Chem. Phys. 15, 5485–5500 (2015).
[Crossref]

Hänggi, P.

L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70, 223–287 (1998).
[Crossref]

Hayakawa, H.

K. Kanazawa, T. Sagawa, and H. Hayakawa, “Stochastic energetics for non-Gaussian processes,” Phys. Rev. Lett. 108, 210601 (2012).
[Crossref]

Hirschberg, M.

S. Alexander, G. E. Koehl, M. Hirschberg, E. K. Geissler, and P. Friedl, “Dynamic imaging of cancer growth and invasion: a modified skin-fold chamber model,” Histochem. Cell Biol. 130, 1147–1154 (2008).
[Crossref]

Jakeman, E.

E. Jakeman and R. J. A. Tough, “Non-Gaussian models for the statistics of scattered waves,” Adv. Phys. 37, 471–529 (1988).
[Crossref]

E. Jakeman and P. N. Pusey, “Significance of K distributions in scattering experiments,” Phys. Rev. Lett. 40, 546–550 (1978).
[Crossref]

Jung, P.

L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70, 223–287 (1998).
[Crossref]

Kanazawa, K.

K. Kanazawa, T. Sagawa, and H. Hayakawa, “Stochastic energetics for non-Gaussian processes,” Phys. Rev. Lett. 108, 210601 (2012).
[Crossref]

Kauczor, H. U.

C. Plathow, C. Fink, S. Ley, M. Puderbach, M. Eichinger, I. Zuna, A. Schmähl, and H. U. Kauczor, “Radiotherapy and oncolog,” Radiotherapy Oncology 73, 349–354 (2004).
[Crossref]

Keys, A. S.

A. S. Keys, A. R. Abate, S. C. Glotzer, and D. J. Durian, “Measurement of growing dynamical length scales and prediction of the jamming transition in a granular material,” Nat. Phys. 3, 260–264 (2007).
[Crossref]

Khanna, S.

C. Tong, J. C. Wyngaard, S. Khanna, and J. G. Brasseur, “Resolvable-and subgrid-scale measurement in the atmospheric surface layer: Technique and issues,” J. Atmos. Sci. 55, 3114–3126 (1998).
[Crossref]

Koehl, G. E.

S. Alexander, G. E. Koehl, M. Hirschberg, E. K. Geissler, and P. Friedl, “Dynamic imaging of cancer growth and invasion: a modified skin-fold chamber model,” Histochem. Cell Biol. 130, 1147–1154 (2008).
[Crossref]

Kuo, H. H.

K. Balachandran, K. Sumathy, and H. H. Kuo, “Existence of solutions of general nonlinear stochastic volterra fredholm integral equations,” Stoch. Anal. Appl. 23, 827–851 (2005).
[Crossref]

Lenschow, D. H.

D. H. Lenschow, V. Wulfmeyer, and C. Senff, “Measuring second-through fourth-order moments in noisy data,” J. Atmos. Ocean. Technol. 17, 1330–1347 (2000).
[Crossref]

D. H. Lenschow and B. B. Stankov, “Length scales in the convective boundary layer,” J. Atmos. Sci. 43, 1198–1209 (1986).
[Crossref]

Ley, S.

C. Plathow, C. Fink, S. Ley, M. Puderbach, M. Eichinger, I. Zuna, A. Schmähl, and H. U. Kauczor, “Radiotherapy and oncolog,” Radiotherapy Oncology 73, 349–354 (2004).
[Crossref]

Marchesoni, F.

L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70, 223–287 (1998).
[Crossref]

Mendel, J. M.

J. M. Mendel, “Tutorial on higher-order statistics (spectra) in signal processing and system theory: theoretical results and some applications,” Proc. IEEE 79, 278–305 (1991).
[Crossref]

Muppa, S. K.

A. Behrendt, V. Wulfmeyer, E. Hammann, S. K. Muppa, and S. Pal, “Profiles of second- to fourth-order moments of turbulent temperature fluctuations in the convective boundary layer: first measurements with rotational Raman lidar,” Atmos. Chem. Phys. 15, 5485–5500 (2015).
[Crossref]

Padgett, W. J.

W. J. Padgett and C. P. Tsokos, “Existence of a solution of a stochastic integral equation in turbulence theory,” J. Math. Phys. 12, 210–212 (1971).
[Crossref]

Pal, S.

A. Behrendt, V. Wulfmeyer, E. Hammann, S. K. Muppa, and S. Pal, “Profiles of second- to fourth-order moments of turbulent temperature fluctuations in the convective boundary layer: first measurements with rotational Raman lidar,” Atmos. Chem. Phys. 15, 5485–5500 (2015).
[Crossref]

Parrinello, M.

M. Parrinello and A. Rahman, “Crystal structure and pair potentials: a molecular-dynamics study,” Phys. Rev. Lett. 45, 1196–1199 (1980).
[Crossref]

Pecora, R.

B. J. Berne and R. Pecora, Dynamic Light Scattering: with Applications to Chemistry, Biology, and Physics (Courier Corporation, 2000).

Pittman, T. B.

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]

Plathow, C.

C. Plathow, C. Fink, S. Ley, M. Puderbach, M. Eichinger, I. Zuna, A. Schmähl, and H. U. Kauczor, “Radiotherapy and oncolog,” Radiotherapy Oncology 73, 349–354 (2004).
[Crossref]

Puderbach, M.

C. Plathow, C. Fink, S. Ley, M. Puderbach, M. Eichinger, I. Zuna, A. Schmähl, and H. U. Kauczor, “Radiotherapy and oncolog,” Radiotherapy Oncology 73, 349–354 (2004).
[Crossref]

Pusey, P. N.

E. Jakeman and P. N. Pusey, “Significance of K distributions in scattering experiments,” Phys. Rev. Lett. 40, 546–550 (1978).
[Crossref]

Rahman, A.

M. Parrinello and A. Rahman, “Crystal structure and pair potentials: a molecular-dynamics study,” Phys. Rev. Lett. 45, 1196–1199 (1980).
[Crossref]

Sagawa, T.

K. Kanazawa, T. Sagawa, and H. Hayakawa, “Stochastic energetics for non-Gaussian processes,” Phys. Rev. Lett. 108, 210601 (2012).
[Crossref]

Schmähl, A.

C. Plathow, C. Fink, S. Ley, M. Puderbach, M. Eichinger, I. Zuna, A. Schmähl, and H. U. Kauczor, “Radiotherapy and oncolog,” Radiotherapy Oncology 73, 349–354 (2004).
[Crossref]

Senff, C.

D. H. Lenschow, V. Wulfmeyer, and C. Senff, “Measuring second-through fourth-order moments in noisy data,” J. Atmos. Ocean. Technol. 17, 1330–1347 (2000).
[Crossref]

Sergienko, A. V.

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]

Shah, K.

A. Bousselham, H. H. Barrett, V. Bora, and K. Shah, “Photoelectron anticorrelations and sub-Poisson statistics in scintillation detectors,” Nucl. Instrum. Methods Phys. Res. A 620, 359–362 (2010).
[Crossref]

Shapiro, J. H.

J. H. Shapiro and R. W. Boyd, “The physics of ghost imaging,” Quantum Inf. Process. 11, 949–993 (2012).
[Crossref]

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78, 061802 (2008).
[Crossref]

Shih, Y. H.

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]

Shokef, Y.

N. Brenner and Y. Shokef, “Nonequilibrium statistical mechanics of dividing cell populations,” Phys. Rev. Lett. 99, 138102 (2007).
[Crossref]

Stankov, B. B.

D. H. Lenschow and B. B. Stankov, “Length scales in the convective boundary layer,” J. Atmos. Sci. 43, 1198–1209 (1986).
[Crossref]

Strekalov, D. V.

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]

Sukhov, S.

D. Haefner, S. Sukhov, and A. Dogariu, “Stochastic scattering polarimetry,” Phys. Rev. Lett. 100, 043901 (2008).
[Crossref]

S. Sukhov, D. Haefner, and A. Dogariu, “Stochastic sensing of relative anisotropic polarizabilities,” Phys. Rev. A 77, 043820 (2008).
[Crossref]

Sumathy, K.

K. Balachandran, K. Sumathy, and H. H. Kuo, “Existence of solutions of general nonlinear stochastic volterra fredholm integral equations,” Stoch. Anal. Appl. 23, 827–851 (2005).
[Crossref]

Tong, C.

C. Tong, J. C. Wyngaard, S. Khanna, and J. G. Brasseur, “Resolvable-and subgrid-scale measurement in the atmospheric surface layer: Technique and issues,” J. Atmos. Sci. 55, 3114–3126 (1998).
[Crossref]

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Supplementary Material (1)

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Figures (6)

Fig. 1.
Fig. 1.

Schematic procedure of sensing statistical properties of a random scattering potential V(ρ;lV) interrogated with a controlled stochastic illumination S(ρ,ξ), which is affected by the inherent source noise n(ρ;ξ), and perturbations Ui(ρ,ξ) and Uo(ρ,ξ) in the illumination and recording paths, respectively. The measured signal is the integrated intensity I(ξ).

Fig. 2.
Fig. 2.

Numerical calculation of the Fano spectrum corresponding to (a) random targeted potential consisting of circular disks with lV=Δ, and (b) the corresponding Fano spectrum. The maximum of the Fano spectrum is normalized to unity.

Fig. 3.
Fig. 3.

(a) Simulated reflective target perturbed by illumination noise and (b) the corresponding normalized Fano spectrum. The measurement conditions are similar to those in Fig. 2. (c) Targeted standard microscopy chart under noisy illumination and (d) the corresponding normalized Fano spectrum.

Fig. 4.
Fig. 4.

(a) Normalized Fano spectrum for an unperturbed condition (-) and for the case of lS distributed Gaussianly with a variance of Δ/3 (-.-). (b) Correlation length lσ of the effective illumination (red shadow) as a function of the correlation length lS of the unperturbed illumination (black solid line).

Fig. 5.
Fig. 5.

Simulated reflective targets consisting of randomly shaped objects having, on average, symmetric (a) and asymmetric (b) correlation functions. (c) Normalized Fano spectra corresponding to the symmetric (continuous line) and asymmetric (dashed line) targets, respectively. The inset shows the ratio of the two spectra as a function of the correlation length lS of the illumination pattern.

Fig. 6.
Fig. 6.

Average over 100 Fano spectra corresponding to (a) element five of group 5 of USAF 1951 positive resolution chart, and (b) a live H2c9 cell placed in an aqueous medium.

Equations (6)

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I(ξ)=A1A[(S(x;ξ)+n(x;ξ))P(x;ξ)V(x)+R(x;ξ)]dx,
MV(k)=m˜I(k)m˜σ(k)n=0k22k!m˜R(k2n)(k2n)!(2n)!m˜σ(2n)m˜σ(k)MV(2n).
FV=FImσ(1)mI(1)m˜σ(2)(mI(1)mR(1))m˜R(2)mσ(1)m˜σ(2)(mI(1)mR(1)).
m˜I(2)(lS)=ψ(ρ;ξ,lS,lV)ψ(ρ;ξ,lS,lV)ξdρdρ+m˜R(2),
I˜(ξ;lS)=S˜(ρ;ξ,lS)P(ρ;ξ)V(ρ;lV)dρ+mS(1)P˜(ρ;ξ)V(ρ;lV)dρ+n(ρ;ξ)P(ρ;ξ)V(ρ;lV)dρ+R˜(ρ;ξ)dρ
S˜(ρ;ξ,lS)P(ρ;ξ)V(ρ;lV)dρ=C(ρ;ξ)(e˜(ρ;lS)*P(ρ;ξ)V(ρ;lV))dρ.

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