Abstract

A laser beam propagating to a remote target through atmospheric turbulence acquires intensity fluctuations. If the target is cooperative and provides a coherent return beam, the phase measured near the beam transmitter and adaptive optics, in principle, can correct these fluctuations. Generally, however, the target is uncooperative. In this case, we show that an incoherent return from the target can be used instead. Using the principle of reciprocity, we derive a novel relation between the field at the target and the returned field at a detector. We simulate an adaptive optics system that utilizes this relation to focus a beam through atmospheric turbulence onto a rough surface.

© 2016 Optical Society of America

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References

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  1. P. W. Milonni and J. H. Eberly, Laser Physics (Wiley, 2010).
  2. R. L. Fante, Proc. IEEE 63, 1669 (1975).
    [Crossref]
  3. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).
  4. V. A. Banakh and V. L. Mironov, LIDAR in a Turbulent Atmosphere (Artech House, 1987).
  5. V. P. Lukin, Atmospheric Adaptive Optics (SPIE, 1995).
  6. J. H. Shapiro and A. L. Puryear, J. Opt. Commun. Netw. 4, 947 (2012).
    [Crossref]
  7. V. P. Lukin and M. I. Charnotskii, Sov. J. Quantum Electron. 12, 602 (1982).
    [Crossref]
  8. A. L. Puryear, J. H. Shapiro, and R. R. Parenti, J. Opt. Commun. Netw. 5, 888 (2013).
    [Crossref]
  9. J. H. Shapiro, J. Opt. Soc. Am. 61, 492 (1971).
    [Crossref]
  10. W. Nelson, J. P. Palastro, C. Wu, and C. C. Davis, J. Opt. Soc. Am. A 32, 1371 (2015).
    [Crossref]
  11. J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts & Company, 2007).
  12. D. L. Fried, J. Opt. Soc. Am. 56, 1372 (1966).
    [Crossref]
  13. H. Kadono, T. Asakura, and N. Takai, Appl. Phys. B 44, 167 (1987).
    [Crossref]
  14. W. Nelson, J. P. Palastro, C. C. Davis, and P. Sprangle, J. Opt. Soc. Am. A 31, 603 (2014).
    [Crossref]
  15. J. A. Fleck, J. R. Morris, and M. D. Feit, Appl. Phys. 10, 129 (1976).
    [Crossref]
  16. M. A. Vorontsov, G. W. Carhart, and J. C. Ricklin, Opt. Lett. 22, 907 (1997).
    [Crossref]
  17. V. P. Lukin, F. Y. Kanev, V. A. Sennlkov, N. A. Makenova, V. A. Tartakovskli, and P. A. Konyaev, Quantum Electron. 34, 825 (2004).
    [Crossref]
  18. C. A. Primmerman, T. R. Price, R. A. Humphreys, B. G. Zollars, H. T. Barclay, and J. Herrmann, Appl. Opt. 34, 2081 (1995).
    [Crossref]
  19. M. C. Roggemann and D. J. Lee, Appl. Opt. 37, 4577 (1998).
    [Crossref]

2015 (1)

2014 (1)

2013 (1)

2012 (1)

2004 (1)

V. P. Lukin, F. Y. Kanev, V. A. Sennlkov, N. A. Makenova, V. A. Tartakovskli, and P. A. Konyaev, Quantum Electron. 34, 825 (2004).
[Crossref]

1998 (1)

1997 (1)

1995 (1)

1987 (1)

H. Kadono, T. Asakura, and N. Takai, Appl. Phys. B 44, 167 (1987).
[Crossref]

1982 (1)

V. P. Lukin and M. I. Charnotskii, Sov. J. Quantum Electron. 12, 602 (1982).
[Crossref]

1976 (1)

J. A. Fleck, J. R. Morris, and M. D. Feit, Appl. Phys. 10, 129 (1976).
[Crossref]

1975 (1)

R. L. Fante, Proc. IEEE 63, 1669 (1975).
[Crossref]

1971 (1)

1966 (1)

Andrews, L. C.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).

Asakura, T.

H. Kadono, T. Asakura, and N. Takai, Appl. Phys. B 44, 167 (1987).
[Crossref]

Banakh, V. A.

V. A. Banakh and V. L. Mironov, LIDAR in a Turbulent Atmosphere (Artech House, 1987).

Barclay, H. T.

Carhart, G. W.

Charnotskii, M. I.

V. P. Lukin and M. I. Charnotskii, Sov. J. Quantum Electron. 12, 602 (1982).
[Crossref]

Davis, C. C.

Eberly, J. H.

P. W. Milonni and J. H. Eberly, Laser Physics (Wiley, 2010).

Fante, R. L.

R. L. Fante, Proc. IEEE 63, 1669 (1975).
[Crossref]

Feit, M. D.

J. A. Fleck, J. R. Morris, and M. D. Feit, Appl. Phys. 10, 129 (1976).
[Crossref]

Fleck, J. A.

J. A. Fleck, J. R. Morris, and M. D. Feit, Appl. Phys. 10, 129 (1976).
[Crossref]

Fried, D. L.

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts & Company, 2007).

Herrmann, J.

Humphreys, R. A.

Kadono, H.

H. Kadono, T. Asakura, and N. Takai, Appl. Phys. B 44, 167 (1987).
[Crossref]

Kanev, F. Y.

V. P. Lukin, F. Y. Kanev, V. A. Sennlkov, N. A. Makenova, V. A. Tartakovskli, and P. A. Konyaev, Quantum Electron. 34, 825 (2004).
[Crossref]

Konyaev, P. A.

V. P. Lukin, F. Y. Kanev, V. A. Sennlkov, N. A. Makenova, V. A. Tartakovskli, and P. A. Konyaev, Quantum Electron. 34, 825 (2004).
[Crossref]

Lee, D. J.

Lukin, V. P.

V. P. Lukin, F. Y. Kanev, V. A. Sennlkov, N. A. Makenova, V. A. Tartakovskli, and P. A. Konyaev, Quantum Electron. 34, 825 (2004).
[Crossref]

V. P. Lukin and M. I. Charnotskii, Sov. J. Quantum Electron. 12, 602 (1982).
[Crossref]

V. P. Lukin, Atmospheric Adaptive Optics (SPIE, 1995).

Makenova, N. A.

V. P. Lukin, F. Y. Kanev, V. A. Sennlkov, N. A. Makenova, V. A. Tartakovskli, and P. A. Konyaev, Quantum Electron. 34, 825 (2004).
[Crossref]

Milonni, P. W.

P. W. Milonni and J. H. Eberly, Laser Physics (Wiley, 2010).

Mironov, V. L.

V. A. Banakh and V. L. Mironov, LIDAR in a Turbulent Atmosphere (Artech House, 1987).

Morris, J. R.

J. A. Fleck, J. R. Morris, and M. D. Feit, Appl. Phys. 10, 129 (1976).
[Crossref]

Nelson, W.

Palastro, J. P.

Parenti, R. R.

Phillips, R. L.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).

Price, T. R.

Primmerman, C. A.

Puryear, A. L.

Ricklin, J. C.

Roggemann, M. C.

Sennlkov, V. A.

V. P. Lukin, F. Y. Kanev, V. A. Sennlkov, N. A. Makenova, V. A. Tartakovskli, and P. A. Konyaev, Quantum Electron. 34, 825 (2004).
[Crossref]

Shapiro, J. H.

Sprangle, P.

Takai, N.

H. Kadono, T. Asakura, and N. Takai, Appl. Phys. B 44, 167 (1987).
[Crossref]

Tartakovskli, V. A.

V. P. Lukin, F. Y. Kanev, V. A. Sennlkov, N. A. Makenova, V. A. Tartakovskli, and P. A. Konyaev, Quantum Electron. 34, 825 (2004).
[Crossref]

Vorontsov, M. A.

Wu, C.

Zollars, B. G.

Appl. Opt. (2)

Appl. Phys. (1)

J. A. Fleck, J. R. Morris, and M. D. Feit, Appl. Phys. 10, 129 (1976).
[Crossref]

Appl. Phys. B (1)

H. Kadono, T. Asakura, and N. Takai, Appl. Phys. B 44, 167 (1987).
[Crossref]

J. Opt. Commun. Netw. (2)

J. Opt. Soc. Am. (2)

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

Opt. Lett. (1)

Proc. IEEE (1)

R. L. Fante, Proc. IEEE 63, 1669 (1975).
[Crossref]

Quantum Electron. (1)

V. P. Lukin, F. Y. Kanev, V. A. Sennlkov, N. A. Makenova, V. A. Tartakovskli, and P. A. Konyaev, Quantum Electron. 34, 825 (2004).
[Crossref]

Sov. J. Quantum Electron. (1)

V. P. Lukin and M. I. Charnotskii, Sov. J. Quantum Electron. 12, 602 (1982).
[Crossref]

Other (5)

P. W. Milonni and J. H. Eberly, Laser Physics (Wiley, 2010).

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).

V. A. Banakh and V. L. Mironov, LIDAR in a Turbulent Atmosphere (Artech House, 1987).

V. P. Lukin, Atmospheric Adaptive Optics (SPIE, 1995).

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts & Company, 2007).

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Figures (4)

Fig. 1.
Fig. 1. Schematic of (a) the propagation geometry and (b) the phase modulator.
Fig. 2.
Fig. 2. Scatter plot of (a) the magnitude and (b) the phase depicting the numerical equivalent of the relation described by Eq. (7).
Fig. 3.
Fig. 3. Top row: (a) initial and (b) final intensity when SPGD was most effective. Bottom row: (c) initial and (d) final intensity profiles when SPGD was least effective.
Fig. 4.
Fig. 4. Histogram of (a) maximum intensities and (b) PIB. Iteration 1 and iteration 100 are denoted by red and blue, respectively.

Equations (10)

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

E O ( r ) = i Θ ( r ) exp ( 2 π i r ^ 0 · r ) .
E T ( r ) = G T O ( r ; r ) E O ( r ) d r
E T ( r ) = i G T O ( r ; r ) Θ ( r ) exp ( 2 π i r ^ 0 · r ) d r .
E R ( r ) = G R T ( r ; r ) E T ( r ) F ( r ) e i ϕ ( r ) d r .
E D ( r ^ ) = i Θ ( r ) exp ( 2 π i r ^ · r ) E R ( r ) d r .
E D ( r ^ ) = i E T ( r ) F ( r ) e i ϕ ( r ) × [ G R T ( r ; r ) Θ ( r ) exp ( i 2 π r ^ · r ) d r ] d r .
E D ( r ^ 0 ) = E T 2 ( r ) F ( r ) e i ϕ ( r ) d r .
E D ( r ^ 0 ) = n = 1 N α n e i φ n ,
u l , m ( n + 1 ) = u l , m ( n ) + γ S l , m ( J + ( n ) J ( n ) ) ,
Θ ( n ) ( r ) = [ 1 H ( r b / 2 ) ] exp [ r 2 / w 0 2 + i u ( n ) ( r ) ] ,

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