Abstract

When measuring atmospheric turbulence along the propagation path to an extended non-cooperative target, a wavefront sensor normally suffers from severe noise due to speckle. In this work, we quantify the benefits of speckle mitigation via polychromatic illumination for a Shack–Hartmann wavefront sensor. We obtain results over a wide range of conditions by using the spectral-slicing approach to polychromatic wave-optics simulations. To quantify speckle noise, even when turbulence is present, we introduce a metric involving racetrack-mode strength in slope-discrepancy space. The results show that polychromatic illumination greatly reduces speckle noise under realistic conditions. Even with near worst-case conditions, 15 coherence lengths per resolution cell reduce the wavefront-measurement error by 56%.

Full Article  |  PDF Article
OSA Recommended Articles
Polychromatic wave-optics models for image-plane speckle. 2. Unresolved objects

Noah R. Van Zandt, Mark F. Spencer, Michael J. Steinbock, Brian M. Anderson, Milo W. Hyde, and Steven T. Fiorino
Appl. Opt. 57(15) 4103-4110 (2018)

Polychromatic wave-optics models for image-plane speckle. 1. Well-resolved objects

Noah R. Van Zandt, Jack E. McCrae, Mark F. Spencer, Michael J. Steinbock, Milo W. Hyde, and Steven T. Fiorino
Appl. Opt. 57(15) 4090-4102 (2018)

Target-in-the-loop wavefront sensing and control with a Collett-Wolf beacon: speckle-average phase conjugation

Mikhail A. Vorontsov, Valeriy V. Kolosov, and Ernst Polnau
Appl. Opt. 48(1) A13-A29 (2009)

References

  • View by:
  • |
  • |
  • |

  1. R. K. Tyson, Introduction to Adaptive Optics (SPIE, 2000), Chaps. 1 and 7.
  2. J. M. Geary, Introduction to Wavefront Sensors (SPIE, 1995), Chap. 6.
  3. J. D. Barchers, D. L. Fried, and D. J. Link, “Evaluation of the performance of Hartmann sensors in strong scintillation,” Appl. Opt. 41, 1012–1021 (2002).
    [Crossref]
  4. J. D. Barchers, D. L. Fried, D. J. Link, G. A. Tyler, W. Moretti, T. J. Brennan, and R. Q. Fugate, “The performance of wavefront sensors in strong scintillation,” Proc. SPIE 4839, 217–227 (2003).
    [Crossref]
  5. M. A. Vorontsov, V. V. Kolosov, and A. Kohnle, “Adaptive laser beam projection on an extended target: phase- and field-conjugate precompensation,” J. Opt. Soc. Am. A 24, 1975–1993 (2007).
    [Crossref]
  6. M. F. Spencer, R. A. Raynor, M. T. Banet, and D. K. Marker, “Deep turbulence wavefront sensing using digital holographic detection in the off-axis image recording geometry,” Opt. Eng. 56, 031213 (2017).
    [Crossref]
  7. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).
  8. R. K. Tyson, Principles of Adaptive Optics (CRC Press, 2016).
  9. N. R. Van Zandt, S. J. Cusumano, R. J. Bartell, S. Basu, J. E. McCrae, and S. T. Fiorino, “Comparison of coherent and incoherent laser beam combination for tactical engagements,” Opt. Eng. 51, 104301 (2012).
    [Crossref]
  10. V. P. Lukin and B. V. Fortes, Adaptive Beaming and Imaging in the Turbulent Atmosphere (SPIE, 2002).
  11. M. Belen’kii and K. Hughes, “Beacon anisoplanatism,” Proc. SPIE 5087, 69–82 (2003).
    [Crossref]
  12. M. C. Roggemann, “Fundamental considerations for wave front sensing with extended random beacons,” Proc. SPIE 5552, 189–199 (2004).
    [Crossref]
  13. G. A. Tyler, “Adaptive optics compensation for propagation through deep turbulence: initial investigation of gradient descent tomography,” J. Opt. Soc. Am. A 23, 1914–1923 (2006).
    [Crossref]
  14. A. Sergeyev, P. Piatrou, and M. C. Roggemann, “Bootstrap beacon creation for overcoming the effects of beacon anisoplanatism in a laser beam projection system,” Appl. Opt. 47, 2399–2413 (2008).
    [Crossref]
  15. G. A. Tyler, “Adaptive optics compensation for propagation through deep turbulence: a study of some interesting approaches,” Opt. Eng. 52, 021011 (2012).
    [Crossref]
  16. N. R. Van Zandt, J. E. McCrae, M. F. Spencer, M. J. Steinbock, M. W. Hyde, and S. T. Fiorino, “Polychromatic wave-optics models for image-plane speckle. 1. Well-resolved objects,” Appl. Opt. 57, 4090–4102 (2018).
    [Crossref]
  17. N. R. Van Zandt, M. F. Spencer, M. J. Steinbock, B. M. Anderson, M. W. Hyde, and S. T. Fiorino, “Polychromatic wave-optics models for image-plane speckle. 2. Unresolved objects,” Appl. Opt. 57, 4103–4110 (2018).
    [Crossref]
  18. G. Artzner, “Microlens arrays for Shack-Hartmann wavefront sensors,” Opt. Eng. 31, 1311–1322 (1992).
    [Crossref]
  19. T. S. McKechnie, “Image-plane speckle in partially coherent illumination,” Opt. Quantum Electron. 8, 61–67 (1976).
    [Crossref]
  20. Y.-Q. Hu, “Dependence of polychromatic-speckle-pattern contrast on imaging and illumination directions,” Appl. Opt. 33, 2707–2714 (1994).
    [Crossref]
  21. J. M. Huntley, “Simple model for image-plane polychromatic speckle contrast,” Appl. Opt. 38, 2212–2215 (1999).
    [Crossref]
  22. C. M. P. Rodrigues and J. L. Pinto, “Contrast of polychromatic speckle patterns and its dependence to surface heights distribution,” Opt. Eng. 42, 1699–1703 (2003).
    [Crossref]
  23. L. Tchvialeva, I. Markhvida, and T. K. Lee, “Error analysis for polychromatic speckle contrast measurements,” Opt. Laser. Eng. 49, 1397–1401 (2011).
    [Crossref]
  24. N. R. Van Zandt, J. E. McCrae, and S. T. Fiorino, “Modeled and measured image-plane polychromatic speckle contrast,” Opt. Eng. 55, 024106 (2016).
    [Crossref]
  25. G. A. Tyler, “Reconstruction and assessment of the least-squares and slope discrepancy components of the phase,” J. Opt. Soc. Am. A 17, 1828–1839 (2000).
    [Crossref]
  26. D. L. Fried, “Branch point problem in adaptive optics,” J. Opt. Soc. Am. A 15, 2759–2768 (1998).
    [Crossref]
  27. T. Brennan, Prime Plexus, 1138 East Little Drive, Placentia, CA, 92870, USA (personal communication, 2017).
  28. D. G. Voelz, K. A. Bush, and P. S. Idell, “Illumination coherence effects in laser-speckle imaging: modeling and experimental demonstration,” Appl. Opt. 36, 1781–1788 (1997).
    [Crossref]
  29. N. R. Van Zandt and M. W. Hyde, S. Bose-Pillai, D. G. Voelz, X. Xiao, and S. T. Fiorino, “Synthesizing time-evolving partially-coherent Schell-model sources,” Opt. Commun. 387, 377–384 (2017).
    [Crossref]
  30. P. Polynkin, A. Peleg, L. Klein, T. Rhoadarmer, and J. Moloney, “Optimized multiemitter beams for free-space optical communications through turbulent atmosphere,” Opt. Lett. 32, 885–887 (2007).
    [Crossref]
  31. J. D. Schmidt, Numerical Simulation of Optical Wave Propagation—With Examples in MATLAB (SPIE, 2010).
  32. D. Voelz, Computational Fourier Optics (SPIE, 2011).

2018 (2)

2017 (2)

M. F. Spencer, R. A. Raynor, M. T. Banet, and D. K. Marker, “Deep turbulence wavefront sensing using digital holographic detection in the off-axis image recording geometry,” Opt. Eng. 56, 031213 (2017).
[Crossref]

N. R. Van Zandt and M. W. Hyde, S. Bose-Pillai, D. G. Voelz, X. Xiao, and S. T. Fiorino, “Synthesizing time-evolving partially-coherent Schell-model sources,” Opt. Commun. 387, 377–384 (2017).
[Crossref]

N. R. Van Zandt and M. W. Hyde, S. Bose-Pillai, D. G. Voelz, X. Xiao, and S. T. Fiorino, “Synthesizing time-evolving partially-coherent Schell-model sources,” Opt. Commun. 387, 377–384 (2017).
[Crossref]

2016 (1)

N. R. Van Zandt, J. E. McCrae, and S. T. Fiorino, “Modeled and measured image-plane polychromatic speckle contrast,” Opt. Eng. 55, 024106 (2016).
[Crossref]

2012 (2)

N. R. Van Zandt, S. J. Cusumano, R. J. Bartell, S. Basu, J. E. McCrae, and S. T. Fiorino, “Comparison of coherent and incoherent laser beam combination for tactical engagements,” Opt. Eng. 51, 104301 (2012).
[Crossref]

G. A. Tyler, “Adaptive optics compensation for propagation through deep turbulence: a study of some interesting approaches,” Opt. Eng. 52, 021011 (2012).
[Crossref]

2011 (1)

L. Tchvialeva, I. Markhvida, and T. K. Lee, “Error analysis for polychromatic speckle contrast measurements,” Opt. Laser. Eng. 49, 1397–1401 (2011).
[Crossref]

2008 (1)

2007 (2)

2006 (1)

2004 (1)

M. C. Roggemann, “Fundamental considerations for wave front sensing with extended random beacons,” Proc. SPIE 5552, 189–199 (2004).
[Crossref]

2003 (3)

J. D. Barchers, D. L. Fried, D. J. Link, G. A. Tyler, W. Moretti, T. J. Brennan, and R. Q. Fugate, “The performance of wavefront sensors in strong scintillation,” Proc. SPIE 4839, 217–227 (2003).
[Crossref]

M. Belen’kii and K. Hughes, “Beacon anisoplanatism,” Proc. SPIE 5087, 69–82 (2003).
[Crossref]

C. M. P. Rodrigues and J. L. Pinto, “Contrast of polychromatic speckle patterns and its dependence to surface heights distribution,” Opt. Eng. 42, 1699–1703 (2003).
[Crossref]

2002 (1)

2000 (1)

1999 (1)

1998 (1)

1997 (1)

1994 (1)

1992 (1)

G. Artzner, “Microlens arrays for Shack-Hartmann wavefront sensors,” Opt. Eng. 31, 1311–1322 (1992).
[Crossref]

1976 (1)

T. S. McKechnie, “Image-plane speckle in partially coherent illumination,” Opt. Quantum Electron. 8, 61–67 (1976).
[Crossref]

Anderson, B. M.

Andrews, L. C.

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

Artzner, G.

G. Artzner, “Microlens arrays for Shack-Hartmann wavefront sensors,” Opt. Eng. 31, 1311–1322 (1992).
[Crossref]

Banet, M. T.

M. F. Spencer, R. A. Raynor, M. T. Banet, and D. K. Marker, “Deep turbulence wavefront sensing using digital holographic detection in the off-axis image recording geometry,” Opt. Eng. 56, 031213 (2017).
[Crossref]

Barchers, J. D.

J. D. Barchers, D. L. Fried, D. J. Link, G. A. Tyler, W. Moretti, T. J. Brennan, and R. Q. Fugate, “The performance of wavefront sensors in strong scintillation,” Proc. SPIE 4839, 217–227 (2003).
[Crossref]

J. D. Barchers, D. L. Fried, and D. J. Link, “Evaluation of the performance of Hartmann sensors in strong scintillation,” Appl. Opt. 41, 1012–1021 (2002).
[Crossref]

Bartell, R. J.

N. R. Van Zandt, S. J. Cusumano, R. J. Bartell, S. Basu, J. E. McCrae, and S. T. Fiorino, “Comparison of coherent and incoherent laser beam combination for tactical engagements,” Opt. Eng. 51, 104301 (2012).
[Crossref]

Basu, S.

N. R. Van Zandt, S. J. Cusumano, R. J. Bartell, S. Basu, J. E. McCrae, and S. T. Fiorino, “Comparison of coherent and incoherent laser beam combination for tactical engagements,” Opt. Eng. 51, 104301 (2012).
[Crossref]

Belen’kii, M.

M. Belen’kii and K. Hughes, “Beacon anisoplanatism,” Proc. SPIE 5087, 69–82 (2003).
[Crossref]

Bose-Pillai, S.

N. R. Van Zandt and M. W. Hyde, S. Bose-Pillai, D. G. Voelz, X. Xiao, and S. T. Fiorino, “Synthesizing time-evolving partially-coherent Schell-model sources,” Opt. Commun. 387, 377–384 (2017).
[Crossref]

Brennan, T.

T. Brennan, Prime Plexus, 1138 East Little Drive, Placentia, CA, 92870, USA (personal communication, 2017).

Brennan, T. J.

J. D. Barchers, D. L. Fried, D. J. Link, G. A. Tyler, W. Moretti, T. J. Brennan, and R. Q. Fugate, “The performance of wavefront sensors in strong scintillation,” Proc. SPIE 4839, 217–227 (2003).
[Crossref]

Bush, K. A.

Cusumano, S. J.

N. R. Van Zandt, S. J. Cusumano, R. J. Bartell, S. Basu, J. E. McCrae, and S. T. Fiorino, “Comparison of coherent and incoherent laser beam combination for tactical engagements,” Opt. Eng. 51, 104301 (2012).
[Crossref]

Fiorino, S. T.

N. R. Van Zandt, J. E. McCrae, M. F. Spencer, M. J. Steinbock, M. W. Hyde, and S. T. Fiorino, “Polychromatic wave-optics models for image-plane speckle. 1. Well-resolved objects,” Appl. Opt. 57, 4090–4102 (2018).
[Crossref]

N. R. Van Zandt, M. F. Spencer, M. J. Steinbock, B. M. Anderson, M. W. Hyde, and S. T. Fiorino, “Polychromatic wave-optics models for image-plane speckle. 2. Unresolved objects,” Appl. Opt. 57, 4103–4110 (2018).
[Crossref]

N. R. Van Zandt and M. W. Hyde, S. Bose-Pillai, D. G. Voelz, X. Xiao, and S. T. Fiorino, “Synthesizing time-evolving partially-coherent Schell-model sources,” Opt. Commun. 387, 377–384 (2017).
[Crossref]

N. R. Van Zandt, J. E. McCrae, and S. T. Fiorino, “Modeled and measured image-plane polychromatic speckle contrast,” Opt. Eng. 55, 024106 (2016).
[Crossref]

N. R. Van Zandt, S. J. Cusumano, R. J. Bartell, S. Basu, J. E. McCrae, and S. T. Fiorino, “Comparison of coherent and incoherent laser beam combination for tactical engagements,” Opt. Eng. 51, 104301 (2012).
[Crossref]

Fortes, B. V.

V. P. Lukin and B. V. Fortes, Adaptive Beaming and Imaging in the Turbulent Atmosphere (SPIE, 2002).

Fried, D. L.

J. D. Barchers, D. L. Fried, D. J. Link, G. A. Tyler, W. Moretti, T. J. Brennan, and R. Q. Fugate, “The performance of wavefront sensors in strong scintillation,” Proc. SPIE 4839, 217–227 (2003).
[Crossref]

J. D. Barchers, D. L. Fried, and D. J. Link, “Evaluation of the performance of Hartmann sensors in strong scintillation,” Appl. Opt. 41, 1012–1021 (2002).
[Crossref]

D. L. Fried, “Branch point problem in adaptive optics,” J. Opt. Soc. Am. A 15, 2759–2768 (1998).
[Crossref]

Fugate, R. Q.

J. D. Barchers, D. L. Fried, D. J. Link, G. A. Tyler, W. Moretti, T. J. Brennan, and R. Q. Fugate, “The performance of wavefront sensors in strong scintillation,” Proc. SPIE 4839, 217–227 (2003).
[Crossref]

Geary, J. M.

J. M. Geary, Introduction to Wavefront Sensors (SPIE, 1995), Chap. 6.

Hu, Y.-Q.

Hughes, K.

M. Belen’kii and K. Hughes, “Beacon anisoplanatism,” Proc. SPIE 5087, 69–82 (2003).
[Crossref]

Huntley, J. M.

Hyde, M. W.

Idell, P. S.

Klein, L.

Kohnle, A.

Kolosov, V. V.

Lee, T. K.

L. Tchvialeva, I. Markhvida, and T. K. Lee, “Error analysis for polychromatic speckle contrast measurements,” Opt. Laser. Eng. 49, 1397–1401 (2011).
[Crossref]

Link, D. J.

J. D. Barchers, D. L. Fried, D. J. Link, G. A. Tyler, W. Moretti, T. J. Brennan, and R. Q. Fugate, “The performance of wavefront sensors in strong scintillation,” Proc. SPIE 4839, 217–227 (2003).
[Crossref]

J. D. Barchers, D. L. Fried, and D. J. Link, “Evaluation of the performance of Hartmann sensors in strong scintillation,” Appl. Opt. 41, 1012–1021 (2002).
[Crossref]

Lukin, V. P.

V. P. Lukin and B. V. Fortes, Adaptive Beaming and Imaging in the Turbulent Atmosphere (SPIE, 2002).

Marker, D. K.

M. F. Spencer, R. A. Raynor, M. T. Banet, and D. K. Marker, “Deep turbulence wavefront sensing using digital holographic detection in the off-axis image recording geometry,” Opt. Eng. 56, 031213 (2017).
[Crossref]

Markhvida, I.

L. Tchvialeva, I. Markhvida, and T. K. Lee, “Error analysis for polychromatic speckle contrast measurements,” Opt. Laser. Eng. 49, 1397–1401 (2011).
[Crossref]

McCrae, J. E.

N. R. Van Zandt, J. E. McCrae, M. F. Spencer, M. J. Steinbock, M. W. Hyde, and S. T. Fiorino, “Polychromatic wave-optics models for image-plane speckle. 1. Well-resolved objects,” Appl. Opt. 57, 4090–4102 (2018).
[Crossref]

N. R. Van Zandt, J. E. McCrae, and S. T. Fiorino, “Modeled and measured image-plane polychromatic speckle contrast,” Opt. Eng. 55, 024106 (2016).
[Crossref]

N. R. Van Zandt, S. J. Cusumano, R. J. Bartell, S. Basu, J. E. McCrae, and S. T. Fiorino, “Comparison of coherent and incoherent laser beam combination for tactical engagements,” Opt. Eng. 51, 104301 (2012).
[Crossref]

McKechnie, T. S.

T. S. McKechnie, “Image-plane speckle in partially coherent illumination,” Opt. Quantum Electron. 8, 61–67 (1976).
[Crossref]

Moloney, J.

Moretti, W.

J. D. Barchers, D. L. Fried, D. J. Link, G. A. Tyler, W. Moretti, T. J. Brennan, and R. Q. Fugate, “The performance of wavefront sensors in strong scintillation,” Proc. SPIE 4839, 217–227 (2003).
[Crossref]

Peleg, A.

Phillips, R. L.

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

Piatrou, P.

Pinto, J. L.

C. M. P. Rodrigues and J. L. Pinto, “Contrast of polychromatic speckle patterns and its dependence to surface heights distribution,” Opt. Eng. 42, 1699–1703 (2003).
[Crossref]

Polynkin, P.

Raynor, R. A.

M. F. Spencer, R. A. Raynor, M. T. Banet, and D. K. Marker, “Deep turbulence wavefront sensing using digital holographic detection in the off-axis image recording geometry,” Opt. Eng. 56, 031213 (2017).
[Crossref]

Rhoadarmer, T.

Rodrigues, C. M. P.

C. M. P. Rodrigues and J. L. Pinto, “Contrast of polychromatic speckle patterns and its dependence to surface heights distribution,” Opt. Eng. 42, 1699–1703 (2003).
[Crossref]

Roggemann, M. C.

Schmidt, J. D.

J. D. Schmidt, Numerical Simulation of Optical Wave Propagation—With Examples in MATLAB (SPIE, 2010).

Sergeyev, A.

Spencer, M. F.

Steinbock, M. J.

Tchvialeva, L.

L. Tchvialeva, I. Markhvida, and T. K. Lee, “Error analysis for polychromatic speckle contrast measurements,” Opt. Laser. Eng. 49, 1397–1401 (2011).
[Crossref]

Tyler, G. A.

G. A. Tyler, “Adaptive optics compensation for propagation through deep turbulence: a study of some interesting approaches,” Opt. Eng. 52, 021011 (2012).
[Crossref]

G. A. Tyler, “Adaptive optics compensation for propagation through deep turbulence: initial investigation of gradient descent tomography,” J. Opt. Soc. Am. A 23, 1914–1923 (2006).
[Crossref]

J. D. Barchers, D. L. Fried, D. J. Link, G. A. Tyler, W. Moretti, T. J. Brennan, and R. Q. Fugate, “The performance of wavefront sensors in strong scintillation,” Proc. SPIE 4839, 217–227 (2003).
[Crossref]

G. A. Tyler, “Reconstruction and assessment of the least-squares and slope discrepancy components of the phase,” J. Opt. Soc. Am. A 17, 1828–1839 (2000).
[Crossref]

Tyson, R. K.

R. K. Tyson, Introduction to Adaptive Optics (SPIE, 2000), Chaps. 1 and 7.

R. K. Tyson, Principles of Adaptive Optics (CRC Press, 2016).

Van Zandt, N. R.

N. R. Van Zandt, J. E. McCrae, M. F. Spencer, M. J. Steinbock, M. W. Hyde, and S. T. Fiorino, “Polychromatic wave-optics models for image-plane speckle. 1. Well-resolved objects,” Appl. Opt. 57, 4090–4102 (2018).
[Crossref]

N. R. Van Zandt, M. F. Spencer, M. J. Steinbock, B. M. Anderson, M. W. Hyde, and S. T. Fiorino, “Polychromatic wave-optics models for image-plane speckle. 2. Unresolved objects,” Appl. Opt. 57, 4103–4110 (2018).
[Crossref]

N. R. Van Zandt and M. W. Hyde, S. Bose-Pillai, D. G. Voelz, X. Xiao, and S. T. Fiorino, “Synthesizing time-evolving partially-coherent Schell-model sources,” Opt. Commun. 387, 377–384 (2017).
[Crossref]

N. R. Van Zandt, J. E. McCrae, and S. T. Fiorino, “Modeled and measured image-plane polychromatic speckle contrast,” Opt. Eng. 55, 024106 (2016).
[Crossref]

N. R. Van Zandt, S. J. Cusumano, R. J. Bartell, S. Basu, J. E. McCrae, and S. T. Fiorino, “Comparison of coherent and incoherent laser beam combination for tactical engagements,” Opt. Eng. 51, 104301 (2012).
[Crossref]

Voelz, D.

D. Voelz, Computational Fourier Optics (SPIE, 2011).

Voelz, D. G.

N. R. Van Zandt and M. W. Hyde, S. Bose-Pillai, D. G. Voelz, X. Xiao, and S. T. Fiorino, “Synthesizing time-evolving partially-coherent Schell-model sources,” Opt. Commun. 387, 377–384 (2017).
[Crossref]

D. G. Voelz, K. A. Bush, and P. S. Idell, “Illumination coherence effects in laser-speckle imaging: modeling and experimental demonstration,” Appl. Opt. 36, 1781–1788 (1997).
[Crossref]

Vorontsov, M. A.

Xiao, X.

N. R. Van Zandt and M. W. Hyde, S. Bose-Pillai, D. G. Voelz, X. Xiao, and S. T. Fiorino, “Synthesizing time-evolving partially-coherent Schell-model sources,” Opt. Commun. 387, 377–384 (2017).
[Crossref]

Appl. Opt. (7)

J. Opt. Soc. Am. A (4)

Opt. Commun. (1)

N. R. Van Zandt and M. W. Hyde, S. Bose-Pillai, D. G. Voelz, X. Xiao, and S. T. Fiorino, “Synthesizing time-evolving partially-coherent Schell-model sources,” Opt. Commun. 387, 377–384 (2017).
[Crossref]

Opt. Eng. (6)

N. R. Van Zandt, J. E. McCrae, and S. T. Fiorino, “Modeled and measured image-plane polychromatic speckle contrast,” Opt. Eng. 55, 024106 (2016).
[Crossref]

G. A. Tyler, “Adaptive optics compensation for propagation through deep turbulence: a study of some interesting approaches,” Opt. Eng. 52, 021011 (2012).
[Crossref]

C. M. P. Rodrigues and J. L. Pinto, “Contrast of polychromatic speckle patterns and its dependence to surface heights distribution,” Opt. Eng. 42, 1699–1703 (2003).
[Crossref]

M. F. Spencer, R. A. Raynor, M. T. Banet, and D. K. Marker, “Deep turbulence wavefront sensing using digital holographic detection in the off-axis image recording geometry,” Opt. Eng. 56, 031213 (2017).
[Crossref]

G. Artzner, “Microlens arrays for Shack-Hartmann wavefront sensors,” Opt. Eng. 31, 1311–1322 (1992).
[Crossref]

N. R. Van Zandt, S. J. Cusumano, R. J. Bartell, S. Basu, J. E. McCrae, and S. T. Fiorino, “Comparison of coherent and incoherent laser beam combination for tactical engagements,” Opt. Eng. 51, 104301 (2012).
[Crossref]

Opt. Laser. Eng. (1)

L. Tchvialeva, I. Markhvida, and T. K. Lee, “Error analysis for polychromatic speckle contrast measurements,” Opt. Laser. Eng. 49, 1397–1401 (2011).
[Crossref]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

T. S. McKechnie, “Image-plane speckle in partially coherent illumination,” Opt. Quantum Electron. 8, 61–67 (1976).
[Crossref]

Proc. SPIE (3)

M. Belen’kii and K. Hughes, “Beacon anisoplanatism,” Proc. SPIE 5087, 69–82 (2003).
[Crossref]

M. C. Roggemann, “Fundamental considerations for wave front sensing with extended random beacons,” Proc. SPIE 5552, 189–199 (2004).
[Crossref]

J. D. Barchers, D. L. Fried, D. J. Link, G. A. Tyler, W. Moretti, T. J. Brennan, and R. Q. Fugate, “The performance of wavefront sensors in strong scintillation,” Proc. SPIE 4839, 217–227 (2003).
[Crossref]

Other (8)

R. K. Tyson, Introduction to Adaptive Optics (SPIE, 2000), Chaps. 1 and 7.

J. M. Geary, Introduction to Wavefront Sensors (SPIE, 1995), Chap. 6.

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

R. K. Tyson, Principles of Adaptive Optics (CRC Press, 2016).

V. P. Lukin and B. V. Fortes, Adaptive Beaming and Imaging in the Turbulent Atmosphere (SPIE, 2002).

J. D. Schmidt, Numerical Simulation of Optical Wave Propagation—With Examples in MATLAB (SPIE, 2010).

D. Voelz, Computational Fourier Optics (SPIE, 2011).

T. Brennan, Prime Plexus, 1138 East Little Drive, Placentia, CA, 92870, USA (personal communication, 2017).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (13)

Fig. 1.
Fig. 1. Wavefront sensing geometry. The Shack–Hartmann wavefront sensor consists of N s subapertures (a.k.a. lenslets) of width d across the total aperture of diameter D . In this work, we set the target width T to N b times the diffraction width of the total aperture. Further, the target possesses a slope angle θ relative to the imaging and illumination line of sight, thus introducing target depth and speckle mitigation when the illumination is polychromatic. Under these conditions, the target Fresnel number N F is simply N b / N s . Additionally, the figure shows Z cell , the effective depth of the target assuming diffraction-limited conditions and a well-resolved target. In this work, the target is not well resolved. However, we will use Z cell as a normalization factor.
Fig. 2.
Fig. 2. Racetrack mode in slope-discrepancy space. Each arrow represents the slope discrepancy in the measurement of a single subaperture of a Shack–Hartmann WFS. Arrow size and direction indicate the magnitude and direction of the discrepancy, respectively. The racetrack mode shown here has strength equal to the root-mean-square (RMS) value of racetrack mode for a target Fresnel number of 0.3 and a vacuum path. The WFS has 15 subapertures across the total aperture and no obscuration. Racetrack mode forms a continuous circulation around the aperture. The arrow to the right of the racetrack-mode plot shows the relative size of the RMS slope measurement for comparison.
Fig. 3.
Fig. 3. Speckle-induced slope-measurement error versus target Fresnel number. In this work, we compute the speckle-induced slope-measurement error by taking the root-mean-square (RMS) of the error in each subaperture’s measurement in both x and y . In this figure, the illuminator is fully coherent. As N F approaches zero, so does the error. For large N F , the error is quite large at greater than 0.2 waves RMS.
Fig. 4.
Fig. 4. Gaussian spectrum broken up into discrete wavelengths for the spectral-slicing method. Here, the center wavelength is 1.064 μm, while the bandwidth yields a coherence length of 1 cm.
Fig. 5.
Fig. 5. Wavefront-sensor geometry with square subapertures within a centrally obscured aperture.
Fig. 6.
Fig. 6. Speckle-induced RMS slope-measurement error versus coherence. In (b), each curve is normalized by its maximum value. The target slope angle is only 5.27°, but error still falls rapidly as the number of coherence lengths per resolution cell ( Z cell / l c ) increases above 4. Over the range of N F shown here, the impact of N F on the percentile reduction in error is rather weak. In fact, error reduction improves as N F drops from 1.05 to 0.35.
Fig. 7.
Fig. 7. Three strongest speckle modes (left to right) in slope-discrepancy space. Here, the illumination is fully coherent, while N F = 0.35 . The strongest mode is racetrack mode, and the next two also involve large rotations.
Fig. 8.
Fig. 8. Strongest speckle mode for each of the four target Fresnel numbers (increasing from left to right) with full coherence. By N F = 2 in (d), the strongest mode is no longer racetrack.
Fig. 9.
Fig. 9. This figure matches Fig. 8, except that the coherence length is now only 1.3 mm (30 coherence lengths per resolution cell). The strongest modes are still racetrack mode or similar, but they are squished vertically due to the shifting of the speckles in x caused by the combination of target slope and polychromatic illumination.
Fig. 10.
Fig. 10. Slope-measurement error due to speckle versus the number of coherence lengths within each resolution cell’s depth. Both vacuum and turbulence-removed cases are shown. The two agree very well, indicating that turbulence does not significantly change the benefits of polychromatic illumination. However, for the two smallest target Fresnel numbers, some differences are visible at short coherence. In fact, the three smallest data points all exhibit differences that exceed the 95% confidence intervals (omitted for clarity). Thus, these results indicate a bit of interaction between speckle and turbulence.
Fig. 11.
Fig. 11. RMS slope-measurement error in discrepancy space divided by the total RMS error versus coherence. These results show little change in this fraction. Thus, any metric that measures only slope consistency or discrepancy (such as racetrack mode) will still provide a good estimate of the overall trends.
Fig. 12.
Fig. 12. Racetrack mode strength versus coherence. The plot shows results both with and without turbulence for all N F 's. The vertical bars about the turbulence data are 95% confidence intervals. Mode strength decreases quite significantly as we increase the number of coherence lengths per resolution cell. The trends appear identical whether or not turbulence is included, providing more evidence that turbulence does not change the benefits of polychromatic speckle mitigation.
Fig. 13.
Fig. 13. Mode strengths in slope-discrepancy space for three coherence states. Here, N F = 0.35 . In vacuum, most of the energy is contained in the strongest modes. These strongest modes change little when turbulence is added, because most of the turbulence energy goes into the weaker modes.

Tables (1)

Tables Icon

Table 1. Sampling Requirements for Shack–Hartmann Wavefront Sensing of Non-Cooperative Targets

Equations (9)

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

Z cell = 3.5 λ R d tan ( θ ) ,
δ = s Γ G s ,
S D = I Γ G ,
N F = D T λ R ,
T = N b λ R / D .
d = D / N s .
N F = N b N s .
E T = E T + S , coh 2 E S , coh 2 .
E T R = E T + S 2 E T 2 .