Abstract

In this paper, we study the use of digital holography in the on-axis phase-shifting recording geometry for the purposes of deep-turbulence wavefront sensing. In particular, we develop closed-form expressions for the field-estimated Strehl ratio and signal-to-noise ratio for three separate phase-shifting strategies—the four-, three-, and two-step methods. These closed-form expressions compare favorably with our detailed wave-optics simulations, which propagate a point-source beacon through deep-turbulence conditions, model digital holography with noise, and calculate the Monte Carlo averages associated with increasing turbulence strengths and decreasing focal-plane array sampling. Overall, the results show the four-step method is the most efficient phase-shifting strategy and deep-turbulence conditions only degrade performance with respect to insufficient focal-plane array sampling and low signal-to-noise ratios. The results also show the strong reference beam from the local oscillator provided by digital holography greatly improves performance by tens of decibels when compared with the self-referencing interferometer.

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

Full Article  |  PDF Article
OSA Recommended Articles
Digital-holographic detection in the off-axis pupil plane recording geometry for deep-turbulence wavefront sensing

Matthias T. Banet, Mark F. Spencer, and Robert A. Raynor
Appl. Opt. 57(3) 465-475 (2018)

LSPV+7, a branch-point-tolerant reconstructor for strong turbulence adaptive optics

Michael J. Steinbock, Milo W. Hyde, and Jason D. Schmidt
Appl. Opt. 53(18) 3821-3831 (2014)

References

  • View by:
  • |
  • |
  • |

  1. J. W. Goodman, D. W. Jackson, M. Lehmann, J. Knotts, and A. P. Profile, “Experiments in long-distance holographic imagery,” Appl. Opt. 8, 1581–1586 (1969).
    [Crossref]
  2. J. W. Goodman, W. H. Huntley, D. W. Jackson, and M. Lehmann, “Wavefront-reconstruction imaging through random media,” Appl. Phys. Lett. 8, 311–313 (1966).
    [Crossref]
  3. J. D. Gaskill, “Imaging through a randomly inhomogeneous medium by wavefront reconstruction,” J. Opt. Soc. Am. A 58, 600–608 (1968).
    [Crossref]
  4. J. D. Gaskill, “Atmospheric degradation of holographic images,” J. Opt. Soc. Am. 59, 308–318 (1969).
    [Crossref]
  5. J. W. Goodman, “Systems application of holography,” Proc. SPIE 0015, 1–8 (1968).
    [Crossref]
  6. J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
    [Crossref]
  7. D. L. Fried, “Limiting resolution looking down through the atmosphere,” J. Opt. Soc. Am. 56, 1380–1384 (1966).
    [Crossref]
  8. D. L. Fried, “Optical heterodyne detection of an atmospherically distorted signal wave front,” Proc. IEEE 55, 57–77 (1967).
    [Crossref]
  9. J. P. Moreland and S. A. Collins, “Optical heterodyne detection of a randomly distorted signal beam,” J. Opt. Soc. Am. 59, 10–13 (1969).
    [Crossref]
  10. R. K. Tyson, Introduction to Adaptive Optics (SPIE, 2011).
  11. M. F. Spencer and D. E. Thornton, “Signal-to-noise models for digital- holographic detection,” Proc. SPIE 1065, 1065008 (2018).
    [Crossref]
  12. 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]
  13. J. D. Barchers, D. L. Fried, and D. J. Link, “Evaluation of the performance of a shearing interferometer in strong scintillation in the absence of additive measurement noise,” Appl. Opt. 41, 3674–3684 (2002).
    [Crossref]
  14. D. L. Fried, “Branch point problem in adaptive optics,” J. Opt. Soc. Am. A 15, 2759–2768 (1998).
    [Crossref]
  15. J. D. Barchers and T. A. Rhoadarmer, “Evaluation of phase-shifting approaches for a point-diffraction interferometer with the mutual coherence function,” Appl. Opt. 41, 7499–7509 (2002).
    [Crossref]
  16. T. A. Rhoadarmer, “Development of a self-referencing interferometer wavefront sensor,” Proc. SPIE 5553, 1–15 (2004).
    [Crossref]
  17. M. J. Steinbock, M. W. Hyde, and J. D. Schmidt, “LSPV+7, a branch-point-tolerant reconstructor for strong turbulence adaptive optics,” Appl. Opt. 53, 3821–3831 (2014).
    [Crossref]
  18. T. J. Brennan and T. A. Rhoadarmer, “Performance of a woofer-tweeter deformable mirror control architecture for high-bandwidth high-spatial resolution adaptive optics,” Proc. SPIE 6306, 63060B (2006).
    [Crossref]
  19. D. J. Wheeler and J. D. Schmidt, “Coupling of Gaussian Schell-model beams into single-mode optical fibers,” J. Opt. Soc. Am. A 28, 1224–1238 (2011).
    [Crossref]
  20. M. F. Spencer, “Spatial heterodyne,” in Encyclopedia of Modern Optics, 2nd ed. (Academic, 2018), Vol. IV, pp. 369–400.
  21. D. E. Thornton, M. F. Spencer, and G. P. Perram, “Deep-turbulence wavefront sensing using digital holography in the on-axis phase shifting recording geometry,” Proc. SPIE 10410, 1041004 (2017).
    [Crossref]
  22. T. C. Poon and J. P. Liu, Introduction to Modern Digital Holography (Cambridge University, 2014).
  23. G. Nehmetallah, R. Aylo, and L. Williams, Analog and Digital Holography with Matlab (SPIE, 2015).
  24. 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 plane recording geometry,” Opt. Eng. 56, 031213 (2016).
    [Crossref]
  25. M. T. Banet, M. F. Spencer, and R. A. Raynor, “Digital-holographic detection in the off-axis pupil plane recording geometry for deep-turbulence wavefront sensing,” Appl. Opt. 57, 465–475 (2018).
    [Crossref]
  26. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2007).
  27. J. D. Schmidt, M. J. Steinbock, and E. C. Berg, “A flexible testbed for adaptive optics in strong turbulence,” Proc. SPIE 8038, 80380O (2011).
    [Crossref]
  28. T. A. Rhoadarmer and L. M. Klein, “Design of a spatially phase shifted self-referencing interferometer wave front sensor,” Proc. SPIE 6306, 63060K (2006).
    [Crossref]
  29. J. P. Liu, T. C. Poon, G. S. Jhou, and P. J. Chen, “Comparison of two-, three-, and four-exposure quadrature phase-shifting holography,” Appl. Opt. 50, 2443–2450 (2011).
    [Crossref]
  30. E. L. Dereniak and G. D. Boreman, Infrared Detectors and Systems (Wiley, 1996).
  31. T. A. Rhoadarmer and J. D. Barchers, “Noise analysis for complex field estimation using a self-referencing interferometer wave front sensor,” Proc. SPIE 4825, 215–227 (2002).
    [Crossref]
  32. J. D. Schmidt, Numerical Simulation of Optical Wave Propagation (SPIE, 2010).
  33. T. J. Brennen, P. H. Roberts, and D. C. Mann, WaveProp: A Wave Optics Simulation System for use with MATLAB, User’s Guide Version 1.3 (Optical Sciences, 2010).
  34. T. J. Brennen and P. H. Phillips, AOTools: The Adaptive Optics Toolbox for use with MATLAB, User’s Guide Version 1.4 (Optical Sciences, 2010).
  35. M. F. Spencer, I. V. Dragulin, D. S. Cargill, and M. J. Steinbock, “Digital holography wave-front sensing in the presence of strong atmospheric turbulence and thermal blooming,” Proc. SPIE 9617, 961705 (2015).
    [Crossref]
  36. M. T. Banet, M. F. Spencer, R. A. Raynor, and D. K. Marker, “Digital holography wavefront sensing in the pupil-plane recording geometry for distributed-volume atmospheric aberrations,” Proc. SPIE 9982, 998208 (2016).
    [Crossref]
  37. G. P. Perram, S. J. Cusumano, R. L. Hengehold, and S. Fiorino, An Introduction to Laser Weapon Systems (Directed Energy Professional Society, 2010).
  38. M. T. Banet and M. F. Spencer, “Spatial-heterodyne sampling requirements in the off-axis pupil plane recording geometry for deep-turbulence wavefront sensing,” Proc. SPIE 10410, 104100E (2017).
    [Crossref]
  39. M. S. Corley and T. A. Rhoadarmer, “Evaluation of phase-shifting techniques for a self-referencing interferometer wavefront sensor,” Proc. SPIE 5894, 58940R (2005).
    [Crossref]
  40. T. R. Ellis, “Shack-Hartmann and interferometric hybrid wavefront sensor,” Ph.D. dissertation (The Air Force Institute of Technology, 2011).
  41. L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media, 2nd ed. (SPIE, 2005).

2018 (2)

2017 (2)

M. T. Banet and M. F. Spencer, “Spatial-heterodyne sampling requirements in the off-axis pupil plane recording geometry for deep-turbulence wavefront sensing,” Proc. SPIE 10410, 104100E (2017).
[Crossref]

D. E. Thornton, M. F. Spencer, and G. P. Perram, “Deep-turbulence wavefront sensing using digital holography in the on-axis phase shifting recording geometry,” Proc. SPIE 10410, 1041004 (2017).
[Crossref]

2016 (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 plane recording geometry,” Opt. Eng. 56, 031213 (2016).
[Crossref]

M. T. Banet, M. F. Spencer, R. A. Raynor, and D. K. Marker, “Digital holography wavefront sensing in the pupil-plane recording geometry for distributed-volume atmospheric aberrations,” Proc. SPIE 9982, 998208 (2016).
[Crossref]

2015 (1)

M. F. Spencer, I. V. Dragulin, D. S. Cargill, and M. J. Steinbock, “Digital holography wave-front sensing in the presence of strong atmospheric turbulence and thermal blooming,” Proc. SPIE 9617, 961705 (2015).
[Crossref]

2014 (1)

2011 (3)

2006 (2)

T. A. Rhoadarmer and L. M. Klein, “Design of a spatially phase shifted self-referencing interferometer wave front sensor,” Proc. SPIE 6306, 63060K (2006).
[Crossref]

T. J. Brennan and T. A. Rhoadarmer, “Performance of a woofer-tweeter deformable mirror control architecture for high-bandwidth high-spatial resolution adaptive optics,” Proc. SPIE 6306, 63060B (2006).
[Crossref]

2005 (1)

M. S. Corley and T. A. Rhoadarmer, “Evaluation of phase-shifting techniques for a self-referencing interferometer wavefront sensor,” Proc. SPIE 5894, 58940R (2005).
[Crossref]

2004 (1)

T. A. Rhoadarmer, “Development of a self-referencing interferometer wavefront sensor,” Proc. SPIE 5553, 1–15 (2004).
[Crossref]

2002 (4)

1998 (1)

1969 (3)

1968 (2)

J. D. Gaskill, “Imaging through a randomly inhomogeneous medium by wavefront reconstruction,” J. Opt. Soc. Am. A 58, 600–608 (1968).
[Crossref]

J. W. Goodman, “Systems application of holography,” Proc. SPIE 0015, 1–8 (1968).
[Crossref]

1967 (2)

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[Crossref]

D. L. Fried, “Optical heterodyne detection of an atmospherically distorted signal wave front,” Proc. IEEE 55, 57–77 (1967).
[Crossref]

1966 (2)

J. W. Goodman, W. H. Huntley, D. W. Jackson, and M. Lehmann, “Wavefront-reconstruction imaging through random media,” Appl. Phys. Lett. 8, 311–313 (1966).
[Crossref]

D. L. Fried, “Limiting resolution looking down through the atmosphere,” J. Opt. Soc. Am. 56, 1380–1384 (1966).
[Crossref]

Andrews, L. C.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media, 2nd ed. (SPIE, 2005).

Aylo, R.

G. Nehmetallah, R. Aylo, and L. Williams, Analog and Digital Holography with Matlab (SPIE, 2015).

Banet, M. T.

M. T. Banet, M. F. Spencer, and R. A. Raynor, “Digital-holographic detection in the off-axis pupil plane recording geometry for deep-turbulence wavefront sensing,” Appl. Opt. 57, 465–475 (2018).
[Crossref]

M. T. Banet and M. F. Spencer, “Spatial-heterodyne sampling requirements in the off-axis pupil plane recording geometry for deep-turbulence wavefront sensing,” Proc. SPIE 10410, 104100E (2017).
[Crossref]

M. T. Banet, M. F. Spencer, R. A. Raynor, and D. K. Marker, “Digital holography wavefront sensing in the pupil-plane recording geometry for distributed-volume atmospheric aberrations,” Proc. SPIE 9982, 998208 (2016).
[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 plane recording geometry,” Opt. Eng. 56, 031213 (2016).
[Crossref]

Barchers, J. D.

Berg, E. C.

J. D. Schmidt, M. J. Steinbock, and E. C. Berg, “A flexible testbed for adaptive optics in strong turbulence,” Proc. SPIE 8038, 80380O (2011).
[Crossref]

Boreman, G. D.

E. L. Dereniak and G. D. Boreman, Infrared Detectors and Systems (Wiley, 1996).

Brennan, T. J.

T. J. Brennan and T. A. Rhoadarmer, “Performance of a woofer-tweeter deformable mirror control architecture for high-bandwidth high-spatial resolution adaptive optics,” Proc. SPIE 6306, 63060B (2006).
[Crossref]

Brennen, T. J.

T. J. Brennen, P. H. Roberts, and D. C. Mann, WaveProp: A Wave Optics Simulation System for use with MATLAB, User’s Guide Version 1.3 (Optical Sciences, 2010).

T. J. Brennen and P. H. Phillips, AOTools: The Adaptive Optics Toolbox for use with MATLAB, User’s Guide Version 1.4 (Optical Sciences, 2010).

Cargill, D. S.

M. F. Spencer, I. V. Dragulin, D. S. Cargill, and M. J. Steinbock, “Digital holography wave-front sensing in the presence of strong atmospheric turbulence and thermal blooming,” Proc. SPIE 9617, 961705 (2015).
[Crossref]

Chen, P. J.

Collins, S. A.

Corley, M. S.

M. S. Corley and T. A. Rhoadarmer, “Evaluation of phase-shifting techniques for a self-referencing interferometer wavefront sensor,” Proc. SPIE 5894, 58940R (2005).
[Crossref]

Cusumano, S. J.

G. P. Perram, S. J. Cusumano, R. L. Hengehold, and S. Fiorino, An Introduction to Laser Weapon Systems (Directed Energy Professional Society, 2010).

Dereniak, E. L.

E. L. Dereniak and G. D. Boreman, Infrared Detectors and Systems (Wiley, 1996).

Dragulin, I. V.

M. F. Spencer, I. V. Dragulin, D. S. Cargill, and M. J. Steinbock, “Digital holography wave-front sensing in the presence of strong atmospheric turbulence and thermal blooming,” Proc. SPIE 9617, 961705 (2015).
[Crossref]

Ellis, T. R.

T. R. Ellis, “Shack-Hartmann and interferometric hybrid wavefront sensor,” Ph.D. dissertation (The Air Force Institute of Technology, 2011).

Fiorino, S.

G. P. Perram, S. J. Cusumano, R. L. Hengehold, and S. Fiorino, An Introduction to Laser Weapon Systems (Directed Energy Professional Society, 2010).

Fried, D. L.

Gaskill, J. D.

J. D. Gaskill, “Atmospheric degradation of holographic images,” J. Opt. Soc. Am. 59, 308–318 (1969).
[Crossref]

J. D. Gaskill, “Imaging through a randomly inhomogeneous medium by wavefront reconstruction,” J. Opt. Soc. Am. A 58, 600–608 (1968).
[Crossref]

Goodman, J. W.

J. W. Goodman, D. W. Jackson, M. Lehmann, J. Knotts, and A. P. Profile, “Experiments in long-distance holographic imagery,” Appl. Opt. 8, 1581–1586 (1969).
[Crossref]

J. W. Goodman, “Systems application of holography,” Proc. SPIE 0015, 1–8 (1968).
[Crossref]

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[Crossref]

J. W. Goodman, W. H. Huntley, D. W. Jackson, and M. Lehmann, “Wavefront-reconstruction imaging through random media,” Appl. Phys. Lett. 8, 311–313 (1966).
[Crossref]

Hengehold, R. L.

G. P. Perram, S. J. Cusumano, R. L. Hengehold, and S. Fiorino, An Introduction to Laser Weapon Systems (Directed Energy Professional Society, 2010).

Huntley, W. H.

J. W. Goodman, W. H. Huntley, D. W. Jackson, and M. Lehmann, “Wavefront-reconstruction imaging through random media,” Appl. Phys. Lett. 8, 311–313 (1966).
[Crossref]

Hyde, M. W.

Jackson, D. W.

J. W. Goodman, D. W. Jackson, M. Lehmann, J. Knotts, and A. P. Profile, “Experiments in long-distance holographic imagery,” Appl. Opt. 8, 1581–1586 (1969).
[Crossref]

J. W. Goodman, W. H. Huntley, D. W. Jackson, and M. Lehmann, “Wavefront-reconstruction imaging through random media,” Appl. Phys. Lett. 8, 311–313 (1966).
[Crossref]

Jhou, G. S.

Klein, L. M.

T. A. Rhoadarmer and L. M. Klein, “Design of a spatially phase shifted self-referencing interferometer wave front sensor,” Proc. SPIE 6306, 63060K (2006).
[Crossref]

Knotts, J.

Lawrence, R. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[Crossref]

Lehmann, M.

J. W. Goodman, D. W. Jackson, M. Lehmann, J. Knotts, and A. P. Profile, “Experiments in long-distance holographic imagery,” Appl. Opt. 8, 1581–1586 (1969).
[Crossref]

J. W. Goodman, W. H. Huntley, D. W. Jackson, and M. Lehmann, “Wavefront-reconstruction imaging through random media,” Appl. Phys. Lett. 8, 311–313 (1966).
[Crossref]

Link, D. J.

Liu, J. P.

Mann, D. C.

T. J. Brennen, P. H. Roberts, and D. C. Mann, WaveProp: A Wave Optics Simulation System for use with MATLAB, User’s Guide Version 1.3 (Optical Sciences, 2010).

Marker, D. K.

M. T. Banet, M. F. Spencer, R. A. Raynor, and D. K. Marker, “Digital holography wavefront sensing in the pupil-plane recording geometry for distributed-volume atmospheric aberrations,” Proc. SPIE 9982, 998208 (2016).
[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 plane recording geometry,” Opt. Eng. 56, 031213 (2016).
[Crossref]

Moreland, J. P.

Nehmetallah, G.

G. Nehmetallah, R. Aylo, and L. Williams, Analog and Digital Holography with Matlab (SPIE, 2015).

Perram, G. P.

D. E. Thornton, M. F. Spencer, and G. P. Perram, “Deep-turbulence wavefront sensing using digital holography in the on-axis phase shifting recording geometry,” Proc. SPIE 10410, 1041004 (2017).
[Crossref]

G. P. Perram, S. J. Cusumano, R. L. Hengehold, and S. Fiorino, An Introduction to Laser Weapon Systems (Directed Energy Professional Society, 2010).

Phillips, P. H.

T. J. Brennen and P. H. Phillips, AOTools: The Adaptive Optics Toolbox for use with MATLAB, User’s Guide Version 1.4 (Optical Sciences, 2010).

Phillips, R. L.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media, 2nd ed. (SPIE, 2005).

Poon, T. C.

Profile, A. P.

Raynor, R. A.

M. T. Banet, M. F. Spencer, and R. A. Raynor, “Digital-holographic detection in the off-axis pupil plane recording geometry for deep-turbulence wavefront sensing,” Appl. Opt. 57, 465–475 (2018).
[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 plane recording geometry,” Opt. Eng. 56, 031213 (2016).
[Crossref]

M. T. Banet, M. F. Spencer, R. A. Raynor, and D. K. Marker, “Digital holography wavefront sensing in the pupil-plane recording geometry for distributed-volume atmospheric aberrations,” Proc. SPIE 9982, 998208 (2016).
[Crossref]

Rhoadarmer, T. A.

T. A. Rhoadarmer and L. M. Klein, “Design of a spatially phase shifted self-referencing interferometer wave front sensor,” Proc. SPIE 6306, 63060K (2006).
[Crossref]

T. J. Brennan and T. A. Rhoadarmer, “Performance of a woofer-tweeter deformable mirror control architecture for high-bandwidth high-spatial resolution adaptive optics,” Proc. SPIE 6306, 63060B (2006).
[Crossref]

M. S. Corley and T. A. Rhoadarmer, “Evaluation of phase-shifting techniques for a self-referencing interferometer wavefront sensor,” Proc. SPIE 5894, 58940R (2005).
[Crossref]

T. A. Rhoadarmer, “Development of a self-referencing interferometer wavefront sensor,” Proc. SPIE 5553, 1–15 (2004).
[Crossref]

T. A. Rhoadarmer and J. D. Barchers, “Noise analysis for complex field estimation using a self-referencing interferometer wave front sensor,” Proc. SPIE 4825, 215–227 (2002).
[Crossref]

J. D. Barchers and T. A. Rhoadarmer, “Evaluation of phase-shifting approaches for a point-diffraction interferometer with the mutual coherence function,” Appl. Opt. 41, 7499–7509 (2002).
[Crossref]

Roberts, P. H.

T. J. Brennen, P. H. Roberts, and D. C. Mann, WaveProp: A Wave Optics Simulation System for use with MATLAB, User’s Guide Version 1.3 (Optical Sciences, 2010).

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2007).

Schmidt, J. D.

Spencer, M. F.

M. F. Spencer and D. E. Thornton, “Signal-to-noise models for digital- holographic detection,” Proc. SPIE 1065, 1065008 (2018).
[Crossref]

M. T. Banet, M. F. Spencer, and R. A. Raynor, “Digital-holographic detection in the off-axis pupil plane recording geometry for deep-turbulence wavefront sensing,” Appl. Opt. 57, 465–475 (2018).
[Crossref]

D. E. Thornton, M. F. Spencer, and G. P. Perram, “Deep-turbulence wavefront sensing using digital holography in the on-axis phase shifting recording geometry,” Proc. SPIE 10410, 1041004 (2017).
[Crossref]

M. T. Banet and M. F. Spencer, “Spatial-heterodyne sampling requirements in the off-axis pupil plane recording geometry for deep-turbulence wavefront sensing,” Proc. SPIE 10410, 104100E (2017).
[Crossref]

M. T. Banet, M. F. Spencer, R. A. Raynor, and D. K. Marker, “Digital holography wavefront sensing in the pupil-plane recording geometry for distributed-volume atmospheric aberrations,” Proc. SPIE 9982, 998208 (2016).
[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 plane recording geometry,” Opt. Eng. 56, 031213 (2016).
[Crossref]

M. F. Spencer, I. V. Dragulin, D. S. Cargill, and M. J. Steinbock, “Digital holography wave-front sensing in the presence of strong atmospheric turbulence and thermal blooming,” Proc. SPIE 9617, 961705 (2015).
[Crossref]

M. F. Spencer, “Spatial heterodyne,” in Encyclopedia of Modern Optics, 2nd ed. (Academic, 2018), Vol. IV, pp. 369–400.

Steinbock, M. J.

M. F. Spencer, I. V. Dragulin, D. S. Cargill, and M. J. Steinbock, “Digital holography wave-front sensing in the presence of strong atmospheric turbulence and thermal blooming,” Proc. SPIE 9617, 961705 (2015).
[Crossref]

M. J. Steinbock, M. W. Hyde, and J. D. Schmidt, “LSPV+7, a branch-point-tolerant reconstructor for strong turbulence adaptive optics,” Appl. Opt. 53, 3821–3831 (2014).
[Crossref]

J. D. Schmidt, M. J. Steinbock, and E. C. Berg, “A flexible testbed for adaptive optics in strong turbulence,” Proc. SPIE 8038, 80380O (2011).
[Crossref]

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2007).

Thornton, D. E.

M. F. Spencer and D. E. Thornton, “Signal-to-noise models for digital- holographic detection,” Proc. SPIE 1065, 1065008 (2018).
[Crossref]

D. E. Thornton, M. F. Spencer, and G. P. Perram, “Deep-turbulence wavefront sensing using digital holography in the on-axis phase shifting recording geometry,” Proc. SPIE 10410, 1041004 (2017).
[Crossref]

Tyson, R. K.

R. K. Tyson, Introduction to Adaptive Optics (SPIE, 2011).

Wheeler, D. J.

Williams, L.

G. Nehmetallah, R. Aylo, and L. Williams, Analog and Digital Holography with Matlab (SPIE, 2015).

Appl. Opt. (7)

Appl. Phys. Lett. (2)

J. W. Goodman, W. H. Huntley, D. W. Jackson, and M. Lehmann, “Wavefront-reconstruction imaging through random media,” Appl. Phys. Lett. 8, 311–313 (1966).
[Crossref]

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[Crossref]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (3)

Opt. Eng. (1)

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 plane recording geometry,” Opt. Eng. 56, 031213 (2016).
[Crossref]

Proc. IEEE (1)

D. L. Fried, “Optical heterodyne detection of an atmospherically distorted signal wave front,” Proc. IEEE 55, 57–77 (1967).
[Crossref]

Proc. SPIE (12)

T. A. Rhoadarmer, “Development of a self-referencing interferometer wavefront sensor,” Proc. SPIE 5553, 1–15 (2004).
[Crossref]

T. J. Brennan and T. A. Rhoadarmer, “Performance of a woofer-tweeter deformable mirror control architecture for high-bandwidth high-spatial resolution adaptive optics,” Proc. SPIE 6306, 63060B (2006).
[Crossref]

J. W. Goodman, “Systems application of holography,” Proc. SPIE 0015, 1–8 (1968).
[Crossref]

D. E. Thornton, M. F. Spencer, and G. P. Perram, “Deep-turbulence wavefront sensing using digital holography in the on-axis phase shifting recording geometry,” Proc. SPIE 10410, 1041004 (2017).
[Crossref]

T. A. Rhoadarmer and J. D. Barchers, “Noise analysis for complex field estimation using a self-referencing interferometer wave front sensor,” Proc. SPIE 4825, 215–227 (2002).
[Crossref]

J. D. Schmidt, M. J. Steinbock, and E. C. Berg, “A flexible testbed for adaptive optics in strong turbulence,” Proc. SPIE 8038, 80380O (2011).
[Crossref]

T. A. Rhoadarmer and L. M. Klein, “Design of a spatially phase shifted self-referencing interferometer wave front sensor,” Proc. SPIE 6306, 63060K (2006).
[Crossref]

M. F. Spencer, I. V. Dragulin, D. S. Cargill, and M. J. Steinbock, “Digital holography wave-front sensing in the presence of strong atmospheric turbulence and thermal blooming,” Proc. SPIE 9617, 961705 (2015).
[Crossref]

M. T. Banet, M. F. Spencer, R. A. Raynor, and D. K. Marker, “Digital holography wavefront sensing in the pupil-plane recording geometry for distributed-volume atmospheric aberrations,” Proc. SPIE 9982, 998208 (2016).
[Crossref]

M. T. Banet and M. F. Spencer, “Spatial-heterodyne sampling requirements in the off-axis pupil plane recording geometry for deep-turbulence wavefront sensing,” Proc. SPIE 10410, 104100E (2017).
[Crossref]

M. S. Corley and T. A. Rhoadarmer, “Evaluation of phase-shifting techniques for a self-referencing interferometer wavefront sensor,” Proc. SPIE 5894, 58940R (2005).
[Crossref]

M. F. Spencer and D. E. Thornton, “Signal-to-noise models for digital- holographic detection,” Proc. SPIE 1065, 1065008 (2018).
[Crossref]

Other (12)

T. R. Ellis, “Shack-Hartmann and interferometric hybrid wavefront sensor,” Ph.D. dissertation (The Air Force Institute of Technology, 2011).

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media, 2nd ed. (SPIE, 2005).

G. P. Perram, S. J. Cusumano, R. L. Hengehold, and S. Fiorino, An Introduction to Laser Weapon Systems (Directed Energy Professional Society, 2010).

E. L. Dereniak and G. D. Boreman, Infrared Detectors and Systems (Wiley, 1996).

J. D. Schmidt, Numerical Simulation of Optical Wave Propagation (SPIE, 2010).

T. J. Brennen, P. H. Roberts, and D. C. Mann, WaveProp: A Wave Optics Simulation System for use with MATLAB, User’s Guide Version 1.3 (Optical Sciences, 2010).

T. J. Brennen and P. H. Phillips, AOTools: The Adaptive Optics Toolbox for use with MATLAB, User’s Guide Version 1.4 (Optical Sciences, 2010).

T. C. Poon and J. P. Liu, Introduction to Modern Digital Holography (Cambridge University, 2014).

G. Nehmetallah, R. Aylo, and L. Williams, Analog and Digital Holography with Matlab (SPIE, 2015).

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2007).

R. K. Tyson, Introduction to Adaptive Optics (SPIE, 2011).

M. F. Spencer, “Spatial heterodyne,” in Encyclopedia of Modern Optics, 2nd ed. (Academic, 2018), Vol. IV, pp. 369–400.

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 (10)

Fig. 1.
Fig. 1. Illustration of digital holography in the on-axis PSRG. Note that we need phase-shifting optics (PSO) to implement our phase-shifting strategy (cf. Fig. 2).
Fig. 2.
Fig. 2. Example of the PSO needed for the four-step method. This example also contains an illustration of the directional dependence of the π -phase shift upon reflection from a beam splitter (BS).
Fig. 3.
Fig. 3. Illustration of how digital holography in the on-axis PSRG allows us to access the wrapped-phase function. Here, we use the interference of light to create multiple holograms by mixing a phase-shifted reference beam with a signal beam. Note that the number of shifts or measurements required by the phase-shifting strategy is dependent on the phase-shifting method being used (here, we illustrate the four-step method). After we record the hologram irradiances with a FPA, we perform a straightforward calculation to obtain the wrapped-phase function from an estimate of complex-optical field [cf. Eq. (12) along with Eqs. (3)–(5)].
Fig. 4.
Fig. 4. (a) Irradiance and (b) wrapped phase for the simulated signal-beam truth for one realization of the turbulence (cf. Scenario 5 in Table 2).
Fig. 5.
Fig. 5. (a) Irradiance and (b) wrapped phase for the simulated signal-beam estimate for one realization of turbulence (cf. Scenario 5 in Table 2).
Fig. 6.
Fig. 6. Numerical field-estimated Strehl ratio S F versus the numerical SNR S / N with a comparison to theory. Shown here are the Monte Carlo averages from 40 independent realizations of turbulence and 30 independent realizations of noise for all of the scenarios given in Table 2 and the three separate phase-shifting strategies of interest in this paper. Note that N p = 256 for all of these results.
Fig. 7.
Fig. 7. Numerical field-estimated Strehl ratio S F versus the signal strength m ¯ S with a comparison to theory. Shown here are the Monte Carlo averages from 40 independent realizations of turbulence and 30 independent realizations of noise for Scenario 1 and Scenario 5 in Table 2 and the three separate phase-shifting strategies of interest in this paper. Note that N p = 256 for all of these results. Also note that the open circles represent the results from Scenario 1, whereas the plus signs represent the results from Scenario 5.
Fig. 8.
Fig. 8. Relative percent difference ( Δ S F ) between the theoretical and numerical field-estimated Strehl ratios for (a) Scenario 1 and (b) Scenario 5 from Table 2. We plot the results as a function of the FPA sampling N p and mean signal strength m ¯ S for the four-step method [cf. Eq. (23)]. Shown here are the Monte Carlo averages from 40 independent realizations of turbulence and 30 independent realizations of noise.
Fig. 9.
Fig. 9. Numerical field-estimated Strehl ratio S F versus the mean number of incident photoelectrons m ¯ i for digital holography in the on-axis PSRG and the SRI with 100%, 10%, and 1% fiber-coupling efficiency. Here, the solid lines represent the theoretical results for the four-step method [cf. Eq. (23) for digital holography in the on-axis PSRG and Eq. (32) for the SRI]. The open circles represent the numerical results for Scenario 1, whereas the x’s represent the numerical results for Scenario 5 (cf. Table 2). Shown here are the Monte Carlo averages from 40 independent realizations of turbulence and 30 independent realizations of noise.
Fig. 10.
Fig. 10. Numerical SNR S / N versus the mean number of incident photoelectrons m ¯ i for digital holography in the on-axis PSRG and the SRI with 100%, 10%, and 1% fiber-coupling efficiency. Here, the solid lines represent the theoretical results for the four-step method [cf. Eq. (19) for digital holography in the on-axis PSRG and Eq. (31) for the SRI). The open circles represent the numerical results for Scenario 1, whereas the x’s represent the numerical results for Scenario 5 (cf. Table 2). Shown here are the Monte Carlo averages from 40 independent realizations of turbulence and 30 independent realizations of noise.

Tables (2)

Tables Icon

Table 1. Simulation Parameters Used in the Wave-Optics Simulations

Tables Icon

Table 2. Turbulence Parameters Used for Five-Distinct Scenarios

Equations (44)

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

i H ( δ ) = | U S + U R e j δ | 2 = | U S | 2 + | U R | 2 + U S U R * e j δ + U S * U R e j δ ,
i H ( 0 ) = | U S | 2 + | U R | 2 + U S U R * + U S * U R , i H ( π / 2 ) = | U S | 2 + | U R | 2 + j U S U R * j U S * U R , i H ( π ) = | U S | 2 + | U R | 2 U S U R * U S * U R , i H ( 3 π / 2 ) = | U S | 2 + | U R | 2 j U S U R * + j U S * U R .
4 U R * U S = ( i H ( 0 ) i H ( π ) ) j ( i H ( π / 2 ) i H ( 3 π / 2 ) )
4 U R * U S = ( 1 + j ) ( i H ( 0 ) i H ( π / 2 ) ) + ( j 1 ) ( i H ( π ) i H ( π / 2 ) )
2 U R * U S = ( i H ( 0 ) | U S | 2 | U R | 2 ) j ( i H ( π / 2 ) | U S | 2 | U R | 2 )
2 | U S | 2 = i H ( 0 ) + i H ( π / 2 ) { [ 2 | U R | 2 + i H ( 0 ) + i H ( π / 2 ) ] 2 2 [ 4 | U R | 4 + ( i H ( 0 ) ) 2 + ( i H ( π / 2 ) ) 2 ] } 1 / 2 .
i ^ H ( δ ) ( n x p , m y p ) = 1 w x w y i H ( δ ) ( x , y ) rect ( x n x p w x ) rect ( y m y p w y ) d x d y ,
rect ( x ) = { 1 0 | x | < 0.5 0.5 | x | = 0.5 0 | x | > 0.5
m ¯ H ( δ ) ( n x p , m y p ) = η τ w x w y h ν i ^ H ( δ ) ( n x p , m y p ) = η τ h ν i H ( δ ) ( n x p , m y p ) * * rect ( n x p w x ) rect ( m y p w y ) ,
m ¯ R = η τ w x w y h ν | U R | 2 ,
m ¯ S ( n x p , m y p ) = η τ h ν | U S ( n x p , m y p ) | 2 * * rect ( n x p w x ) rect ( m y p w y ) .
U ^ S ( s ) ( n x p , m y p ) = κ s η τ h ν U R * U S ( n x p , m y p ) * * rect ( n x p w x ) rect ( m y p w y ) ,
σ n 2 = m ¯ R + σ r 2 ,
m ¯ H + N ( δ ) ( n x p , m y p ) = m ¯ H ( δ ) ( n x p , m y p ) + σ n n k ( n x p , m y p ) ,
U ^ S + N ( s ) ( n x p , m y p ) = U ^ S ( s ) ( n x p , m y p ) + ζ σ n N k ( n x p , m y p ) ,
S / N ( s ) = | U ^ S ( s ) ( x , y ) | 2 V { U ^ S + N ( s ) ( x , y ) } ,
| U ^ S ( s ) ( x , y ) | 2 = κ 2 s m ¯ R m ¯ S ,
V { U ^ S + N ( s ) ( x , y ) } = ζ σ n 2 .
S / N ( 4 ) = m ¯ R m ¯ S m ¯ R + σ r 2
S / N ( 3 ) = 2 3 m ¯ R m ¯ S m ¯ R + σ r 2
S / N ( 2 ) = 1 2 m ¯ R m ¯ S m ¯ R + σ r 2
S F ( s ) = 1 1 + 1 S / N ( s ) .
S F ( 4 ) = m ¯ R m ¯ S m ¯ R m ¯ S + m ¯ R + σ r 2
S F ( 3 ) = 2 m ¯ R m ¯ S 2 m ¯ R m ¯ S + 3 ( m ¯ R + σ r 2 ) ,
S F ( 2 ) = m ¯ R m ¯ S m ¯ R m ¯ S + 2 ( m ¯ R + σ r 2 ) ,
σ χ s w 2 = 0.124 k 7 / 6 z 11 / 6 C n 2
r 0 s w = 0.33 ( λ 2 z C n 2 ) 3 / 5 ,
S F = | U S ( x , y ) U ^ S + N * ( x , y ) | 2 | U S ( x , y ) | 2 | U ^ S + N ( x , y ) | 2 ,
S / N = | U ^ S + N | 2 | U ^ N | 2 Var { U ^ N } ,
Δ S F = S F S F ( 4 ) S F ( 4 ) × 100 ,
S / N S R I ( 4 ) = 1 4 m ¯ S 2 m ¯ S / 2 + σ r 2 ,
S F , S R I ( 4 ) = m ¯ S 2 m ¯ S 2 + 2 m ¯ S + 4 σ r 2 ,
| U , V | 2 U , U V , V ,
1 | U , V | 2 U , U V , V ,
U , V = i , j = 1 m , n U i j V i j * ,
U V * = 1 m n i , j = 1 m , n U i j V i j * = 1 m n U , V .
S F = | U ^ S ( x , y ) U ^ S + N * ( x , y ) | 2 | U ^ S ( x , y ) | 2 | U ^ S + N ( x , y ) | 2 .
S F = 1 1 + 1 S / N
U ^ S + N ( x , y ) = U ^ S ( x , y ) + σ n 2 N k ( x , y ) ,
| U ^ S ( x , y ) U ^ S + N * ( x , y ) | 2 = | | U ^ S ( x , y ) | 2 | 2 ,
| U ^ S + N ( x , y ) | 2 = | U ^ S ( x , y ) | 2 + σ n 2 ,
S F = | | U ^ S ( x , y ) | 2 | 2 | U ^ S ( x , y ) | 2 ( | U ^ S ( x , y ) | 2 + σ n 2 ) .
S F = 1 1 + σ n 2 | U ^ S ( x , y ) | 2 ,
S / N = | U ^ S ( x , y ) | 2 σ n 2 .

Metrics