Abstract

Optical wave propagation through long paths of extended turbulence presents unique challenges to adaptive optics (AO) systems. As scintillation and branch points develop in the beacon phase, challenges arise in accurately unwrapping the received wavefront and optimizing the reconstructed phase with respect to branch cut placement on a continuous facesheet deformable mirror. Several applications are currently restricted by these capability limits: laser communication, laser weapons, remote sensing, and ground-based astronomy. This paper presents a set of temporally evolving AO simulations comparing traditional least-squares reconstruction techniques to a complex-exponential reconstructor and several other reconstructors derived from the postprocessing congruence operation. The reconstructors’ behavior in closed-loop operation is compared and discussed, providing several insights into the fundamental strengths and limitations of each reconstructor type. This research utilizes a self-referencing interferometer (SRI) as the high-order wavefront sensor, driving a traditional linear control law in conjunction with a cooperative point source beacon. The SRI model includes practical optical considerations and frame-by-frame fiber coupling effects to allow for realistic noise modeling. The “LSPV+7” reconstructor is shown to offer the best performance in terms of Strehl ratio and correction stability—outperforming the traditional least-squares reconstructed system by an average of 120% in the studied scenarios. Utilizing a continuous facesheet deformable mirror, these reconstructors offer significant AO performance improvements in strong turbulence applications without the need for segmented deformable mirrors.

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References

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  1. D. L. Fried and J. L. Vaughn, “Branch cuts in the phase function,” Appl. Opt. 31, 2865–2882 (1992).
    [CrossRef]
  2. D. L. Fried, “Adaptive optics wave function reconstruction and phase unwrapping when branch points are present,” Opt. Commun. 200, 43–72 (2001).
    [CrossRef]
  3. J. L. Vaughn, the Optical Sciences Company, 1341 South Sunkist Street, Anaheim, California, 92806 (personal communication, Jan. 2014).
  4. D. L. Fried, “Branch point problem in adaptive optics,” J. Opt. Soc. Am. A 15, 2759–2768 (1998).
    [CrossRef]
  5. V. Aksenov, V. Banakh, and O. Tikhomirova, “Potential and vortex features of optical speckle fields and visualization of wave-front singularities,” Appl. Opt. 37, 4536–4540 (1998).
    [CrossRef]
  6. 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]
  7. J. D. Barchers, D. L. Fried, D. J. Link, G. A. Tyler, W. Moretti, T. J. Brennan, and R. Q. Fugate, “Performance of wavefront sensors in strong scintillation,” Proc. SPIE 4839, 217–227 (2003).
    [CrossRef]
  8. T. A. Rhoadarmer, “Development of a self-referencing interferometer wavefront sensor,” Proc. SPIE 5553, 112–126 (2004).
    [CrossRef]
  9. T. M. Venema and J. D. Schmidt, “Optical phase unwrapping in the presence of branch points,” Opt. Express 16, 6985–6998 (2008).
    [CrossRef]
  10. M. J. Steinbock, “Implementation of branch-point-tolerant wavefront reconstructor for strong turbulence compensation,” Master’s thesis (Air Force Institute of Technology, 2012).
  11. C. J. Pellizzari and J. D. Schmidt, “Phase unwrapping in the presence of strong turbulence,” in Proceedings of IEEE Aerospace Conference (IEEE, 2010), pp. 1–10.
  12. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).
  13. M. J. Steinbock, J. D. Schmidt, and M. W. Hyde, “Comparison of branch point tolerant wavefront reconstructors in the presence of simulated noise effects,” in Proceedings of IEEE Aerospace Conference (IEEE, 2012), pp. 1–13.
  14. M. J. Steinbock and M. W. Hyde, “Phase discrepancy induced from least squares wavefront reconstruction of wrapped phase measurements with high noise or large localized wavefront gradients,” Proc. SPIE 8517, 85170W (2012).
    [CrossRef]
  15. T. M. Venema, “Closed-loop adaptive optics control in strong atmospheric turbulence,” Ph.D. dissertation (Air Force Institute of Technology, 2008).
  16. C. Pellizzari, “Phase unwrapping in the presence of strong turbulence,” Master’s thesis (Air Force Institute of Technology, 2010).
  17. M. J. Steinbock, M. W. Hyde, J. D. Schmidt, and S. J. Cusumano, “Comparison of wavefront reconstruction techniques for extended turbulence beam projection applications,” in Advanced High-Power Lasers Meeting (Directed Energy Professional Society, CO, 2012), pp. 1–22.
  18. T. Brennan, P. Roberts, and D. Mann, WaveProp: A Wave Optics Simulation System (Optical Sciences Company, 2008).
  19. J. D. Schmidt, Numerical Simulation of Optical Wave Propagation (SPIE, 2010).
  20. J. H. Churnside, “A spectrum of refractive turbulence in the turbulent atmosphere,” J. Mod. Opt. 37, 13–16 (1990).
    [CrossRef]
  21. R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence: Evaluation and Application of Mellin Transforms (SPIE, 2007).
  22. 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]
  23. J. D. Barchers, “Control law for a high resolution self-referencing interferometer wavefront sensor used with a low resolution deformable mirror,” (SAIC, CO, 2002).
  24. R. H. Hudgin, “Wave-front reconstruction for compensated imaging,” J. Opt. Soc. Am. 67, 375–378 (1977).
    [CrossRef]
  25. Boston Micromachines, “Multi-DM,” Datasheet, (Retrieved Apr. 15, 2012 from http://www.bostonmicromachines.com/pdf/Multi-DM.pdf ).
  26. 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]
  27. 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).
  28. Goodrich Corporation, “SU320KTSW-1.7RT SU320KTSVis-1.7RT InGaAs SWIR Camera,” Datasheet, (Retrieved Nov. 9, 2012 from http://www.sensorsinc.com/downloads/SU320KTS-SU320KTSVIS.pdf ).

2012 (1)

M. J. Steinbock and M. W. Hyde, “Phase discrepancy induced from least squares wavefront reconstruction of wrapped phase measurements with high noise or large localized wavefront gradients,” Proc. SPIE 8517, 85170W (2012).
[CrossRef]

2011 (2)

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]

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]

2008 (1)

2004 (1)

T. A. Rhoadarmer, “Development of a self-referencing interferometer wavefront sensor,” Proc. SPIE 5553, 112–126 (2004).
[CrossRef]

2003 (1)

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

2002 (2)

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]

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).

2001 (1)

D. L. Fried, “Adaptive optics wave function reconstruction and phase unwrapping when branch points are present,” Opt. Commun. 200, 43–72 (2001).
[CrossRef]

1998 (2)

1992 (1)

1990 (1)

J. H. Churnside, “A spectrum of refractive turbulence in the turbulent atmosphere,” J. Mod. Opt. 37, 13–16 (1990).
[CrossRef]

1977 (1)

Aksenov, V.

Banakh, V.

Barchers, J. D.

J. D. Barchers, D. L. Fried, D. J. Link, G. A. Tyler, W. Moretti, T. J. Brennan, and R. Q. Fugate, “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]

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).

J. D. Barchers, “Control law for a high resolution self-referencing interferometer wavefront sensor used with a low resolution deformable mirror,” (SAIC, CO, 2002).

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]

Brennan, T.

T. Brennan, P. Roberts, and D. Mann, WaveProp: A Wave Optics Simulation System (Optical Sciences Company, 2008).

Brennan, T. J.

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

Churnside, J. H.

J. H. Churnside, “A spectrum of refractive turbulence in the turbulent atmosphere,” J. Mod. Opt. 37, 13–16 (1990).
[CrossRef]

Cusumano, S. J.

M. J. Steinbock, M. W. Hyde, J. D. Schmidt, and S. J. Cusumano, “Comparison of wavefront reconstruction techniques for extended turbulence beam projection applications,” in Advanced High-Power Lasers Meeting (Directed Energy Professional Society, CO, 2012), pp. 1–22.

Fried, D. L.

J. D. Barchers, D. L. Fried, D. J. Link, G. A. Tyler, W. Moretti, T. J. Brennan, and R. Q. Fugate, “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, “Adaptive optics wave function reconstruction and phase unwrapping when branch points are present,” Opt. Commun. 200, 43–72 (2001).
[CrossRef]

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

D. L. Fried and J. L. Vaughn, “Branch cuts in the phase function,” Appl. Opt. 31, 2865–2882 (1992).
[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, “Performance of wavefront sensors in strong scintillation,” Proc. SPIE 4839, 217–227 (2003).
[CrossRef]

Ghiglia, D. C.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

Hudgin, R. H.

Hyde, M. W.

M. J. Steinbock and M. W. Hyde, “Phase discrepancy induced from least squares wavefront reconstruction of wrapped phase measurements with high noise or large localized wavefront gradients,” Proc. SPIE 8517, 85170W (2012).
[CrossRef]

M. J. Steinbock, J. D. Schmidt, and M. W. Hyde, “Comparison of branch point tolerant wavefront reconstructors in the presence of simulated noise effects,” in Proceedings of IEEE Aerospace Conference (IEEE, 2012), pp. 1–13.

M. J. Steinbock, M. W. Hyde, J. D. Schmidt, and S. J. Cusumano, “Comparison of wavefront reconstruction techniques for extended turbulence beam projection applications,” in Advanced High-Power Lasers Meeting (Directed Energy Professional Society, CO, 2012), pp. 1–22.

Link, D. J.

J. D. Barchers, D. L. Fried, D. J. Link, G. A. Tyler, W. Moretti, T. J. Brennan, and R. Q. Fugate, “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]

Mann, D.

T. Brennan, P. Roberts, and D. Mann, WaveProp: A Wave Optics Simulation System (Optical Sciences Company, 2008).

Moretti, W.

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

Pellizzari, C.

C. Pellizzari, “Phase unwrapping in the presence of strong turbulence,” Master’s thesis (Air Force Institute of Technology, 2010).

Pellizzari, C. J.

C. J. Pellizzari and J. D. Schmidt, “Phase unwrapping in the presence of strong turbulence,” in Proceedings of IEEE Aerospace Conference (IEEE, 2010), pp. 1–10.

Pritt, M. D.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

Rhoadarmer, T. A.

T. A. Rhoadarmer, “Development of a self-referencing interferometer wavefront sensor,” Proc. SPIE 5553, 112–126 (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).

Roberts, P.

T. Brennan, P. Roberts, and D. Mann, WaveProp: A Wave Optics Simulation System (Optical Sciences Company, 2008).

Sasiela, R. J.

R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence: Evaluation and Application of Mellin Transforms (SPIE, 2007).

Schmidt, J. D.

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]

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]

T. M. Venema and J. D. Schmidt, “Optical phase unwrapping in the presence of branch points,” Opt. Express 16, 6985–6998 (2008).
[CrossRef]

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

M. J. Steinbock, M. W. Hyde, J. D. Schmidt, and S. J. Cusumano, “Comparison of wavefront reconstruction techniques for extended turbulence beam projection applications,” in Advanced High-Power Lasers Meeting (Directed Energy Professional Society, CO, 2012), pp. 1–22.

M. J. Steinbock, J. D. Schmidt, and M. W. Hyde, “Comparison of branch point tolerant wavefront reconstructors in the presence of simulated noise effects,” in Proceedings of IEEE Aerospace Conference (IEEE, 2012), pp. 1–13.

C. J. Pellizzari and J. D. Schmidt, “Phase unwrapping in the presence of strong turbulence,” in Proceedings of IEEE Aerospace Conference (IEEE, 2010), pp. 1–10.

Steinbock, M. J.

M. J. Steinbock and M. W. Hyde, “Phase discrepancy induced from least squares wavefront reconstruction of wrapped phase measurements with high noise or large localized wavefront gradients,” Proc. SPIE 8517, 85170W (2012).
[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]

M. J. Steinbock, M. W. Hyde, J. D. Schmidt, and S. J. Cusumano, “Comparison of wavefront reconstruction techniques for extended turbulence beam projection applications,” in Advanced High-Power Lasers Meeting (Directed Energy Professional Society, CO, 2012), pp. 1–22.

M. J. Steinbock, J. D. Schmidt, and M. W. Hyde, “Comparison of branch point tolerant wavefront reconstructors in the presence of simulated noise effects,” in Proceedings of IEEE Aerospace Conference (IEEE, 2012), pp. 1–13.

M. J. Steinbock, “Implementation of branch-point-tolerant wavefront reconstructor for strong turbulence compensation,” Master’s thesis (Air Force Institute of Technology, 2012).

Tikhomirova, O.

Tyler, G. A.

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

Vaughn, J. L.

D. L. Fried and J. L. Vaughn, “Branch cuts in the phase function,” Appl. Opt. 31, 2865–2882 (1992).
[CrossRef]

J. L. Vaughn, the Optical Sciences Company, 1341 South Sunkist Street, Anaheim, California, 92806 (personal communication, Jan. 2014).

Venema, T. M.

T. M. Venema and J. D. Schmidt, “Optical phase unwrapping in the presence of branch points,” Opt. Express 16, 6985–6998 (2008).
[CrossRef]

T. M. Venema, “Closed-loop adaptive optics control in strong atmospheric turbulence,” Ph.D. dissertation (Air Force Institute of Technology, 2008).

Wheeler, D. J.

Appl. Opt. (3)

J. Mod. Opt. (1)

J. H. Churnside, “A spectrum of refractive turbulence in the turbulent atmosphere,” J. Mod. Opt. 37, 13–16 (1990).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Commun. (1)

D. L. Fried, “Adaptive optics wave function reconstruction and phase unwrapping when branch points are present,” Opt. Commun. 200, 43–72 (2001).
[CrossRef]

Opt. Express (1)

Proc. SPIE (5)

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

T. A. Rhoadarmer, “Development of a self-referencing interferometer wavefront sensor,” Proc. SPIE 5553, 112–126 (2004).
[CrossRef]

M. J. Steinbock and M. W. Hyde, “Phase discrepancy induced from least squares wavefront reconstruction of wrapped phase measurements with high noise or large localized wavefront gradients,” Proc. SPIE 8517, 85170W (2012).
[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).

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]

Other (14)

J. D. Barchers, “Control law for a high resolution self-referencing interferometer wavefront sensor used with a low resolution deformable mirror,” (SAIC, CO, 2002).

Boston Micromachines, “Multi-DM,” Datasheet, (Retrieved Apr. 15, 2012 from http://www.bostonmicromachines.com/pdf/Multi-DM.pdf ).

Goodrich Corporation, “SU320KTSW-1.7RT SU320KTSVis-1.7RT InGaAs SWIR Camera,” Datasheet, (Retrieved Nov. 9, 2012 from http://www.sensorsinc.com/downloads/SU320KTS-SU320KTSVIS.pdf ).

T. M. Venema, “Closed-loop adaptive optics control in strong atmospheric turbulence,” Ph.D. dissertation (Air Force Institute of Technology, 2008).

C. Pellizzari, “Phase unwrapping in the presence of strong turbulence,” Master’s thesis (Air Force Institute of Technology, 2010).

M. J. Steinbock, M. W. Hyde, J. D. Schmidt, and S. J. Cusumano, “Comparison of wavefront reconstruction techniques for extended turbulence beam projection applications,” in Advanced High-Power Lasers Meeting (Directed Energy Professional Society, CO, 2012), pp. 1–22.

T. Brennan, P. Roberts, and D. Mann, WaveProp: A Wave Optics Simulation System (Optical Sciences Company, 2008).

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

J. L. Vaughn, the Optical Sciences Company, 1341 South Sunkist Street, Anaheim, California, 92806 (personal communication, Jan. 2014).

R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence: Evaluation and Application of Mellin Transforms (SPIE, 2007).

M. J. Steinbock, “Implementation of branch-point-tolerant wavefront reconstructor for strong turbulence compensation,” Master’s thesis (Air Force Institute of Technology, 2012).

C. J. Pellizzari and J. D. Schmidt, “Phase unwrapping in the presence of strong turbulence,” in Proceedings of IEEE Aerospace Conference (IEEE, 2010), pp. 1–10.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

M. J. Steinbock, J. D. Schmidt, and M. W. Hyde, “Comparison of branch point tolerant wavefront reconstructors in the presence of simulated noise effects,” in Proceedings of IEEE Aerospace Conference (IEEE, 2012), pp. 1–13.

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Figures (12)

Fig. 1.
Fig. 1.

Effect of varying h in calculating ϕrot for the same rotational field input. In (a) h=0 rad, (b) h=π/2 rad, (c) h=π rad, and (d) h=3π/2 rad.

Fig. 2.
Fig. 2.

Normalized histograms showing PDFs of hopt for turbulence conditions of (a) σχ2=0.04, d/r0=1; (b) σχ2=1, d/r0=1/2; and (c) σχ2=1, d/r0=1 averaged over 10 turbulence realizations for each case.

Fig. 3.
Fig. 3.

Ensemble averaged autocorrelation of hopt over time for LSPV+200 corrected propagations, showing almost delta-correlation in time between hopt values.

Fig. 4.
Fig. 4.

AFIT’s AO system, from which the simulations are modeled. In this work, the SH WFS is not utilized.

Fig. 5.
Fig. 5.

Higher-order correction dataflow from raw SRI measurements to DM commands.

Fig. 6.
Fig. 6.

WFS to DM geometry. The fine grid outlines the 33×33 SRI subaperture array. The blue dots show actively controlled DM actuator positions. The red circle outlines the active beam area. Surrounding actuators are slaved to adjacent “master” actuators.

Fig. 7.
Fig. 7.

Field-estimated Strehl ratios for the PCO-based reconstructors over a range of SNR. Each data point is averaged over the 20 turbulence realizations, and all 6561 frames in time for each realization. The error bars mark the spread of σ¯S, which should not be confused with the uncertainty bounds of the data points.

Fig. 8.
Fig. 8.

Residual wavefront errors using the LSPV+7 reconstructor for (a) SNR=120 and (b) SNR=16 in the reduced beam-space of the AO optical system. Both snapshots are from the same frame of the same turbulence seed. Note the large wavefront errors on the top and right edges of the pupil in the SNR=120 case, which are not present in the SNR=16 case.

Fig. 9.
Fig. 9.

Field-estimated Strehl ratios for Pellizzari’s LSPV variants over a range of SNR. Each data point is averaged over the 20 turbulence realizations and all 6561 frames in time for each realization. The error bars mark the spread of σ¯S, which should not be confused with the uncertainty bounds of the data points.

Fig. 10.
Fig. 10.

Field-estimated Strehl ratios for the least-squares, LSPV+7, and SPhase reconstructors over a range of SNR. Each data point is averaged over the 20 turbulence realizations and all 6561 frames in time for each realization. The error bars mark the spread of σ¯S, which should not be confused with the uncertainty bounds of the data points.

Fig. 11.
Fig. 11.

Strehl ratios over an equivalent turbulence realization for the (a) LSPV+7 and (b) SPhase reconstructors.

Fig. 12.
Fig. 12.

Weak turbulence field-estimated Strehl ratios for several reconstructors over a range of SNR. Each data point is averaged over the 10 turbulence realizations and all 6561 frames in time for each realization. The error bars mark the spread of σ¯S, which should not be confused with the uncertainty bounds of the data points.

Equations (19)

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

ϕ=ϕirr+ϕrot.
ϕ^rot=Wππ[ϕϕirr]=Wππ[ϕSRIϕLS],
ϕ^PCO=ϕLS+Wππ[ϕSRIϕLS+h].
hk=h¯+2πkN:k=0,1,2,,N1,
hopthk:argmink[IWCL(ϕrot,k)].
σχ2=0.124k7/6L11/6Cn2=1,
r0,sw=[0.423k2Cn2(38)L]3/5=3cm.
NF=(D/2)2λL=3.
fg=0.254k6/5v[Cn2L]3/5=20Hz
ck+1=αck+KDC(1α)ek,
σsys=σshot2+σread2+σquan2.
σshot2=K¯=ηqeNsplit[TintApx(Is+ηcIr)],
σread2=(183pe)2.
σquan2=112LSB2=112(183pe)2,
SNR=K¯(σshot2+σread2+σquan2)1/2=K¯[K¯+(183pe)2+112(183pe)2]1/2.
S=|U(x,y)dxdy|2A|U(x,y)|2dxdy,
S=|mean[U(x,y)]|2mean[|U(x,y)|2],
S¯=1NtNfi=1Ntj=1NfSi,j,
σ¯S=1Nti=1Nt[(1Nfj=1NfSi,j2)(1Nfj=1NfSi,j)2]1/2,

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