Abstract

Tsang and Nair [Optica 6, 400 (2019) [CrossRef]  ] suggest that there are fundamental problems with the results reported in [Optica 5, 1382 (2018) [CrossRef]  ] regarding the ultimate sensitivity of estimates of the separation between two emitters under conditions of partial coherence. We show here that their conclusions are based on an inconsistent model.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. W. Larson and B. E. A. Saleh, “Resurgence of Rayleigh’s curse in the presence of partial coherence,” Optica 5, 1382–1389 (2018).
    [Crossref]
  2. M. Tsang and R. Nair, “Resurgence of Rayleigh’s curse in the presence of partial coherence: comment,” Optica 6, 400–401 (2019).
    [Crossref]
  3. M. Tsang, R. Nair, and X.-M. Lu, “Semiclassical theory of superresolution for two incoherent optical point sources,” Phys. Rev. X 6, 031033 (2016).
  4. J. Rehacek, Z. Hradil, B. Stoklasa, M. Paur, J. Grover, A. Krzic, and L. L. Sanchez-Soto, “Multiparameter quantum metrology of incoherent point sources: towards realistic superresolution,” Phys. Rev. A 96, 062107 (2017).
    [Crossref]
  5. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999), Chap. 10.
  6. J. W. Goodman, Statistical Optics, 2nd ed. (Wiley, 2015), Chap. 7.

2019 (1)

2018 (1)

2017 (1)

J. Rehacek, Z. Hradil, B. Stoklasa, M. Paur, J. Grover, A. Krzic, and L. L. Sanchez-Soto, “Multiparameter quantum metrology of incoherent point sources: towards realistic superresolution,” Phys. Rev. A 96, 062107 (2017).
[Crossref]

2016 (1)

M. Tsang, R. Nair, and X.-M. Lu, “Semiclassical theory of superresolution for two incoherent optical point sources,” Phys. Rev. X 6, 031033 (2016).

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999), Chap. 10.

Goodman, J. W.

J. W. Goodman, Statistical Optics, 2nd ed. (Wiley, 2015), Chap. 7.

Grover, J.

J. Rehacek, Z. Hradil, B. Stoklasa, M. Paur, J. Grover, A. Krzic, and L. L. Sanchez-Soto, “Multiparameter quantum metrology of incoherent point sources: towards realistic superresolution,” Phys. Rev. A 96, 062107 (2017).
[Crossref]

Hradil, Z.

J. Rehacek, Z. Hradil, B. Stoklasa, M. Paur, J. Grover, A. Krzic, and L. L. Sanchez-Soto, “Multiparameter quantum metrology of incoherent point sources: towards realistic superresolution,” Phys. Rev. A 96, 062107 (2017).
[Crossref]

Krzic, A.

J. Rehacek, Z. Hradil, B. Stoklasa, M. Paur, J. Grover, A. Krzic, and L. L. Sanchez-Soto, “Multiparameter quantum metrology of incoherent point sources: towards realistic superresolution,” Phys. Rev. A 96, 062107 (2017).
[Crossref]

Larson, W.

Lu, X.-M.

M. Tsang, R. Nair, and X.-M. Lu, “Semiclassical theory of superresolution for two incoherent optical point sources,” Phys. Rev. X 6, 031033 (2016).

Nair, R.

M. Tsang and R. Nair, “Resurgence of Rayleigh’s curse in the presence of partial coherence: comment,” Optica 6, 400–401 (2019).
[Crossref]

M. Tsang, R. Nair, and X.-M. Lu, “Semiclassical theory of superresolution for two incoherent optical point sources,” Phys. Rev. X 6, 031033 (2016).

Paur, M.

J. Rehacek, Z. Hradil, B. Stoklasa, M. Paur, J. Grover, A. Krzic, and L. L. Sanchez-Soto, “Multiparameter quantum metrology of incoherent point sources: towards realistic superresolution,” Phys. Rev. A 96, 062107 (2017).
[Crossref]

Rehacek, J.

J. Rehacek, Z. Hradil, B. Stoklasa, M. Paur, J. Grover, A. Krzic, and L. L. Sanchez-Soto, “Multiparameter quantum metrology of incoherent point sources: towards realistic superresolution,” Phys. Rev. A 96, 062107 (2017).
[Crossref]

Saleh, B. E. A.

Sanchez-Soto, L. L.

J. Rehacek, Z. Hradil, B. Stoklasa, M. Paur, J. Grover, A. Krzic, and L. L. Sanchez-Soto, “Multiparameter quantum metrology of incoherent point sources: towards realistic superresolution,” Phys. Rev. A 96, 062107 (2017).
[Crossref]

Stoklasa, B.

J. Rehacek, Z. Hradil, B. Stoklasa, M. Paur, J. Grover, A. Krzic, and L. L. Sanchez-Soto, “Multiparameter quantum metrology of incoherent point sources: towards realistic superresolution,” Phys. Rev. A 96, 062107 (2017).
[Crossref]

Tsang, M.

M. Tsang and R. Nair, “Resurgence of Rayleigh’s curse in the presence of partial coherence: comment,” Optica 6, 400–401 (2019).
[Crossref]

M. Tsang, R. Nair, and X.-M. Lu, “Semiclassical theory of superresolution for two incoherent optical point sources,” Phys. Rev. X 6, 031033 (2016).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999), Chap. 10.

Optica (2)

Phys. Rev. A (1)

J. Rehacek, Z. Hradil, B. Stoklasa, M. Paur, J. Grover, A. Krzic, and L. L. Sanchez-Soto, “Multiparameter quantum metrology of incoherent point sources: towards realistic superresolution,” Phys. Rev. A 96, 062107 (2017).
[Crossref]

Phys. Rev. X (1)

M. Tsang, R. Nair, and X.-M. Lu, “Semiclassical theory of superresolution for two incoherent optical point sources,” Phys. Rev. X 6, 031033 (2016).

Other (2)

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999), Chap. 10.

J. W. Goodman, Statistical Optics, 2nd ed. (Wiley, 2015), Chap. 7.

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Figures (2)

Fig. 1.
Fig. 1. Precision of estimates of the separation s based on calculation of the quantum Fisher information assuming an exactly known degree of coherence γ . Results are plotted for negative γ (solid) and positive γ (dashed).
Fig. 2.
Fig. 2. Precision of estimates of the separation s based on the QFIM, assuming concurrent estimation of an unknown degree of coherence γ for γ = 1 , 2 / 3 , 1 / 3 , 0 , 1 / 3 , 2 / 3 , and 1. In all cases, the sensitivity approaches zero as the separation s approaches zero (Rayleigh’s curse).