D. J. Sanchez, D. W. Oesch, and P. R. Kelly, “The aggregate behavior of branch points - theoretical calculation of branch point velocity,” Proc. SPIE 8380, 83800P (2012).

[CrossRef]

D. W. Oesch, D. J. Sanchez, and C. M. Tewksbury-Christle, “Aggregate behavior of branch points--persistent pairs,” Opt. Express 20(2), 1046–1059 (2012).

[CrossRef]
[PubMed]

D. W. Oesch, D. J. Sanchez, C. M. Tewksbury-Christle, and P. R. Kelly, “The aggregate behavior of branch points - altitude and strength of atmospheric turbulence layers,” Proc. SPIE 7816, 781605 (2010).

[CrossRef]

D. W. Oesch, D. J. Sanchez, and C. L. Matson, “The aggregate behavior of branch points--measuring the number and velocity of atmospheric turbulence layers,” Opt. Express 18(21), 22377–22392 (2010).

[CrossRef]
[PubMed]

D. J. Sanchez and D. W. Oesch, “The aggregate behavior of branch points - the creation and evolution of branch points,” Proc. SPIE 7466, 746605 (2009).

[CrossRef]

D. W. Oesch, D. J. Sanchez, C. M. Tewksbury-Christle, and P. R. Kelly, “The aggregate behavior of branch points - branch point density as a characteristic of an atmospheric turbulence simulator,” Proc. SPIE 7466, 746606 (2009).

[CrossRef]

X. Qian, W. Zhu, and R. Rao, “Phase screen distribution for simulating laser propagation along an inhomogeneous atmospheric path,” Acta Phys. Sin. 58, 6633–6638 (2009).

C. Fan, Y. Wang, and Z. Gong, “Effect of branch points on adaptive optics,” High Power Laser Particle Beams 15, 435–438 (2003).

D. L. Fried, “Adaptive optics wave function reconstruction and phase unwrapping when branch points are present,” Opt. Commun. 200(1–6), 43–72 (2001).

[CrossRef]

B. Wang, A. C. Koivunen, and M. C. Roggemann, “Comparison of branch point and least squares reconstructors for laser beam transmission through the atmosphere,” Proc. SPIE 3763, 41–49 (1999).

[CrossRef]

E.-O. Le Bigot, W. J. Wild, and E. J. Kibblewhite, “Branch point reconstructors for discontinuous light phase functions,” Proc. SPIE 3381, 76–87 (1998).

[CrossRef]

V. V. Voitsekhovich, D. Kouznetsov, and D. K. Morozov, “Density of turbulence-induced phase dislocations,” Appl. Opt. 37(21), 4525–4535 (1998).

[CrossRef]
[PubMed]

D. L. Fried, “Branch point problem in adaptive optics,” J. Opt. Soc. Am. A 15(10), 2759–2768 (1998).

[CrossRef]

D. L. Fried, “Scaling laws for propagation through turbulence,” Atmos. Oceanic Opt. 11, 982–990 (1998).

B. V. Fortes and V. Lukin, “The effects of wavefront dislocations on the atmospheric adaptive optical systems performance,” Proc. SPIE 2778, 1002–1003 (1996).

V. A. Tartakovski and N. N. Mayer, “Phase dislocation and minimal phase representation of the wave function,” Atmos. Oceanic Opt. 8, 231–235 (1995).

C. A. Primmerman, T. R. Price, R. A. Humphreys, B. G. Zollars, H. T. Barclay, and J. H. Herrmann, “Atmospheric-compensation experiments in strong-scintillation conditions,” Appl. Opt. 34(12), 2081–2088 (1995).

[CrossRef]
[PubMed]

I. Freund and N. Shvartsman, “Wave-field phase singularities: The sign principle,” Phys. Rev. A 50(6), 5164–5172 (1994).

[CrossRef]
[PubMed]

N. B. Baranova, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, and B. Y. Zel’dovich, “Wave-front dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. A 73(5), 525–528 (1983).

[CrossRef]

J. F. Nye, “The motion and structure of dislocation in wavefronts,” Proc. R. Soc. London A Math. Phys. Sci. 378(1773), 219–239 (1981).

[CrossRef]

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London A Math. Phys. Sci. 336(1605), 165–190 (1974).

[CrossRef]

N. B. Baranova, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, and B. Y. Zel’dovich, “Wave-front dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. A 73(5), 525–528 (1983).

[CrossRef]

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London A Math. Phys. Sci. 336(1605), 165–190 (1974).

[CrossRef]

C. Fan, Y. Wang, and Z. Gong, “Effects of different beacon wavelengths on atmospheric compensation in strong scintillation,” Appl. Opt. 43(22), 4334–4338 (2004).

[CrossRef]
[PubMed]

C. Fan, Y. Wang, and Z. Gong, “Effect of branch points on adaptive optics,” High Power Laser Particle Beams 15, 435–438 (2003).

B. V. Fortes and V. Lukin, “The effects of wavefront dislocations on the atmospheric adaptive optical systems performance,” Proc. SPIE 2778, 1002–1003 (1996).

I. Freund and N. Shvartsman, “Wave-field phase singularities: The sign principle,” Phys. Rev. A 50(6), 5164–5172 (1994).

[CrossRef]
[PubMed]

D. L. Fried, “Adaptive optics wave function reconstruction and phase unwrapping when branch points are present,” Opt. Commun. 200(1–6), 43–72 (2001).

[CrossRef]

D. L. Fried, “Branch point problem in adaptive optics,” J. Opt. Soc. Am. A 15(10), 2759–2768 (1998).

[CrossRef]

D. L. Fried, “Scaling laws for propagation through turbulence,” Atmos. Oceanic Opt. 11, 982–990 (1998).

D. L. Fried and J. L. Vaughn, “Branch cuts in the phase function,” Appl. Opt. 31(15), 2865–2882 (1992).

[CrossRef]
[PubMed]

C. Fan, Y. Wang, and Z. Gong, “Effects of different beacon wavelengths on atmospheric compensation in strong scintillation,” Appl. Opt. 43(22), 4334–4338 (2004).

[CrossRef]
[PubMed]

C. Fan, Y. Wang, and Z. Gong, “Effect of branch points on adaptive optics,” High Power Laser Particle Beams 15, 435–438 (2003).

D. J. Sanchez, D. W. Oesch, and P. R. Kelly, “The aggregate behavior of branch points - theoretical calculation of branch point velocity,” Proc. SPIE 8380, 83800P (2012).

[CrossRef]

D. W. Oesch, D. J. Sanchez, C. M. Tewksbury-Christle, and P. R. Kelly, “The aggregate behavior of branch points - altitude and strength of atmospheric turbulence layers,” Proc. SPIE 7816, 781605 (2010).

[CrossRef]

D. W. Oesch, D. J. Sanchez, C. M. Tewksbury-Christle, and P. R. Kelly, “The aggregate behavior of branch points - branch point density as a characteristic of an atmospheric turbulence simulator,” Proc. SPIE 7466, 746606 (2009).

[CrossRef]

E.-O. Le Bigot, W. J. Wild, and E. J. Kibblewhite, “Branch point reconstructors for discontinuous light phase functions,” Proc. SPIE 3381, 76–87 (1998).

[CrossRef]

B. Wang, A. C. Koivunen, and M. C. Roggemann, “Comparison of branch point and least squares reconstructors for laser beam transmission through the atmosphere,” Proc. SPIE 3763, 41–49 (1999).

[CrossRef]

E.-O. Le Bigot, W. J. Wild, and E. J. Kibblewhite, “Branch point reconstructors for discontinuous light phase functions,” Proc. SPIE 3381, 76–87 (1998).

[CrossRef]

Y. Li, “Branch point effect on adaptive correction,” Proc. SPIE 5490, 1064–1070 (2004).

[CrossRef]

B. V. Fortes and V. Lukin, “The effects of wavefront dislocations on the atmospheric adaptive optical systems performance,” Proc. SPIE 2778, 1002–1003 (1996).

N. B. Baranova, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, and B. Y. Zel’dovich, “Wave-front dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. A 73(5), 525–528 (1983).

[CrossRef]

V. A. Tartakovski and N. N. Mayer, “Phase dislocation and minimal phase representation of the wave function,” Atmos. Oceanic Opt. 8, 231–235 (1995).

J. F. Nye, “The motion and structure of dislocation in wavefronts,” Proc. R. Soc. London A Math. Phys. Sci. 378(1773), 219–239 (1981).

[CrossRef]

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London A Math. Phys. Sci. 336(1605), 165–190 (1974).

[CrossRef]

D. J. Sanchez, D. W. Oesch, and P. R. Kelly, “The aggregate behavior of branch points - theoretical calculation of branch point velocity,” Proc. SPIE 8380, 83800P (2012).

[CrossRef]

D. W. Oesch, D. J. Sanchez, and C. M. Tewksbury-Christle, “Aggregate behavior of branch points--persistent pairs,” Opt. Express 20(2), 1046–1059 (2012).

[CrossRef]
[PubMed]

D. J. Sanchez and D. W. Oesch, “Localization of angular momentum in optical waves propagating through turbulence,” Opt. Express 19(25), 25388–25396 (2011).

[CrossRef]
[PubMed]

D. J. Sanchez and D. W. Oesch, “Orbital angular momentum in optical waves propagating through distributed turbulence,” Opt. Express 19(24), 24596–24608 (2011).

[CrossRef]
[PubMed]

D. W. Oesch, D. J. Sanchez, C. M. Tewksbury-Christle, and P. R. Kelly, “The aggregate behavior of branch points - altitude and strength of atmospheric turbulence layers,” Proc. SPIE 7816, 781605 (2010).

[CrossRef]

D. W. Oesch, D. J. Sanchez, and C. L. Matson, “The aggregate behavior of branch points--measuring the number and velocity of atmospheric turbulence layers,” Opt. Express 18(21), 22377–22392 (2010).

[CrossRef]
[PubMed]

D. W. Oesch, D. J. Sanchez, C. M. Tewksbury-Christle, and P. R. Kelly, “The aggregate behavior of branch points - branch point density as a characteristic of an atmospheric turbulence simulator,” Proc. SPIE 7466, 746606 (2009).

[CrossRef]

D. J. Sanchez and D. W. Oesch, “The aggregate behavior of branch points - the creation and evolution of branch points,” Proc. SPIE 7466, 746605 (2009).

[CrossRef]

N. B. Baranova, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, and B. Y. Zel’dovich, “Wave-front dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. A 73(5), 525–528 (1983).

[CrossRef]

X. Qian, W. Zhu, and R. Rao, “Phase screen distribution for simulating laser propagation along an inhomogeneous atmospheric path,” Acta Phys. Sin. 58, 6633–6638 (2009).

B. Wang, A. C. Koivunen, and M. C. Roggemann, “Comparison of branch point and least squares reconstructors for laser beam transmission through the atmosphere,” Proc. SPIE 3763, 41–49 (1999).

[CrossRef]

D. J. Sanchez, D. W. Oesch, and P. R. Kelly, “The aggregate behavior of branch points - theoretical calculation of branch point velocity,” Proc. SPIE 8380, 83800P (2012).

[CrossRef]

D. W. Oesch, D. J. Sanchez, and C. M. Tewksbury-Christle, “Aggregate behavior of branch points--persistent pairs,” Opt. Express 20(2), 1046–1059 (2012).

[CrossRef]
[PubMed]

D. J. Sanchez and D. W. Oesch, “Localization of angular momentum in optical waves propagating through turbulence,” Opt. Express 19(25), 25388–25396 (2011).

[CrossRef]
[PubMed]

D. J. Sanchez and D. W. Oesch, “Orbital angular momentum in optical waves propagating through distributed turbulence,” Opt. Express 19(24), 24596–24608 (2011).

[CrossRef]
[PubMed]

D. W. Oesch, D. J. Sanchez, C. M. Tewksbury-Christle, and P. R. Kelly, “The aggregate behavior of branch points - altitude and strength of atmospheric turbulence layers,” Proc. SPIE 7816, 781605 (2010).

[CrossRef]

D. W. Oesch, D. J. Sanchez, and C. L. Matson, “The aggregate behavior of branch points--measuring the number and velocity of atmospheric turbulence layers,” Opt. Express 18(21), 22377–22392 (2010).

[CrossRef]
[PubMed]

D. W. Oesch, D. J. Sanchez, C. M. Tewksbury-Christle, and P. R. Kelly, “The aggregate behavior of branch points - branch point density as a characteristic of an atmospheric turbulence simulator,” Proc. SPIE 7466, 746606 (2009).

[CrossRef]

D. J. Sanchez and D. W. Oesch, “The aggregate behavior of branch points - the creation and evolution of branch points,” Proc. SPIE 7466, 746605 (2009).

[CrossRef]

N. B. Baranova, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, and B. Y. Zel’dovich, “Wave-front dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. A 73(5), 525–528 (1983).

[CrossRef]

I. Freund and N. Shvartsman, “Wave-field phase singularities: The sign principle,” Phys. Rev. A 50(6), 5164–5172 (1994).

[CrossRef]
[PubMed]

V. A. Tartakovski and N. N. Mayer, “Phase dislocation and minimal phase representation of the wave function,” Atmos. Oceanic Opt. 8, 231–235 (1995).

D. W. Oesch, D. J. Sanchez, and C. M. Tewksbury-Christle, “Aggregate behavior of branch points--persistent pairs,” Opt. Express 20(2), 1046–1059 (2012).

[CrossRef]
[PubMed]

D. W. Oesch, D. J. Sanchez, C. M. Tewksbury-Christle, and P. R. Kelly, “The aggregate behavior of branch points - altitude and strength of atmospheric turbulence layers,” Proc. SPIE 7816, 781605 (2010).

[CrossRef]

D. W. Oesch, D. J. Sanchez, C. M. Tewksbury-Christle, and P. R. Kelly, “The aggregate behavior of branch points - branch point density as a characteristic of an atmospheric turbulence simulator,” Proc. SPIE 7466, 746606 (2009).

[CrossRef]

B. Wang, A. C. Koivunen, and M. C. Roggemann, “Comparison of branch point and least squares reconstructors for laser beam transmission through the atmosphere,” Proc. SPIE 3763, 41–49 (1999).

[CrossRef]

C. Fan, Y. Wang, and Z. Gong, “Effects of different beacon wavelengths on atmospheric compensation in strong scintillation,” Appl. Opt. 43(22), 4334–4338 (2004).

[CrossRef]
[PubMed]

C. Fan, Y. Wang, and Z. Gong, “Effect of branch points on adaptive optics,” High Power Laser Particle Beams 15, 435–438 (2003).

E.-O. Le Bigot, W. J. Wild, and E. J. Kibblewhite, “Branch point reconstructors for discontinuous light phase functions,” Proc. SPIE 3381, 76–87 (1998).

[CrossRef]

N. B. Baranova, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, and B. Y. Zel’dovich, “Wave-front dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. A 73(5), 525–528 (1983).

[CrossRef]

X. Qian, W. Zhu, and R. Rao, “Phase screen distribution for simulating laser propagation along an inhomogeneous atmospheric path,” Acta Phys. Sin. 58, 6633–6638 (2009).

X. Qian, W. Zhu, and R. Rao, “Phase screen distribution for simulating laser propagation along an inhomogeneous atmospheric path,” Acta Phys. Sin. 58, 6633–6638 (2009).

V. V. Voitsekhovich, D. Kouznetsov, and D. K. Morozov, “Density of turbulence-induced phase dislocations,” Appl. Opt. 37(21), 4525–4535 (1998).

[CrossRef]
[PubMed]

R. Rao, “Statistics of the fractal structure and phase singularity of a plane light wave propagation in atmospheric turbulence,” Appl. Opt. 47(2), 269–276 (2008).

[CrossRef]
[PubMed]

D. L. Fried and J. L. Vaughn, “Branch cuts in the phase function,” Appl. Opt. 31(15), 2865–2882 (1992).

[CrossRef]
[PubMed]

C. Fan, Y. Wang, and Z. Gong, “Effects of different beacon wavelengths on atmospheric compensation in strong scintillation,” Appl. Opt. 43(22), 4334–4338 (2004).

[CrossRef]
[PubMed]

C. A. Primmerman, T. R. Price, R. A. Humphreys, B. G. Zollars, H. T. Barclay, and J. H. Herrmann, “Atmospheric-compensation experiments in strong-scintillation conditions,” Appl. Opt. 34(12), 2081–2088 (1995).

[CrossRef]
[PubMed]

V. A. Tartakovski and N. N. Mayer, “Phase dislocation and minimal phase representation of the wave function,” Atmos. Oceanic Opt. 8, 231–235 (1995).

D. L. Fried, “Scaling laws for propagation through turbulence,” Atmos. Oceanic Opt. 11, 982–990 (1998).

C. Fan, Y. Wang, and Z. Gong, “Effect of branch points on adaptive optics,” High Power Laser Particle Beams 15, 435–438 (2003).

D. L. Fried, “Branch point problem in adaptive optics,” J. Opt. Soc. Am. A 15(10), 2759–2768 (1998).

[CrossRef]

N. B. Baranova, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, and B. Y. Zel’dovich, “Wave-front dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. A 73(5), 525–528 (1983).

[CrossRef]

M. Chen and F. S. Roux, “Accelerating the annihilation of an optical vortex dipole in a Gaussian beam,” J. Opt. Soc. Am. A 25(6), 1279–1286 (2008).

[CrossRef]
[PubMed]

F. S. Roux, “Anomalous transient behavior from an inhomogeneous initial optical vortex density,” J. Opt. Soc. Am. A 28(4), 621–626 (2011).

[CrossRef]
[PubMed]

D. L. Fried, “Adaptive optics wave function reconstruction and phase unwrapping when branch points are present,” Opt. Commun. 200(1–6), 43–72 (2001).

[CrossRef]

D. W. Oesch, D. J. Sanchez, and C. L. Matson, “The aggregate behavior of branch points--measuring the number and velocity of atmospheric turbulence layers,” Opt. Express 18(21), 22377–22392 (2010).

[CrossRef]
[PubMed]

D. W. Oesch, D. J. Sanchez, and C. M. Tewksbury-Christle, “Aggregate behavior of branch points--persistent pairs,” Opt. Express 20(2), 1046–1059 (2012).

[CrossRef]
[PubMed]

D. J. Sanchez and D. W. Oesch, “Localization of angular momentum in optical waves propagating through turbulence,” Opt. Express 19(25), 25388–25396 (2011).

[CrossRef]
[PubMed]

D. J. Sanchez and D. W. Oesch, “Orbital angular momentum in optical waves propagating through distributed turbulence,” Opt. Express 19(24), 24596–24608 (2011).

[CrossRef]
[PubMed]

I. Freund and N. Shvartsman, “Wave-field phase singularities: The sign principle,” Phys. Rev. A 50(6), 5164–5172 (1994).

[CrossRef]
[PubMed]

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London A Math. Phys. Sci. 336(1605), 165–190 (1974).

[CrossRef]

J. F. Nye, “The motion and structure of dislocation in wavefronts,” Proc. R. Soc. London A Math. Phys. Sci. 378(1773), 219–239 (1981).

[CrossRef]

B. V. Fortes and V. Lukin, “The effects of wavefront dislocations on the atmospheric adaptive optical systems performance,” Proc. SPIE 2778, 1002–1003 (1996).

E.-O. Le Bigot, W. J. Wild, and E. J. Kibblewhite, “Branch point reconstructors for discontinuous light phase functions,” Proc. SPIE 3381, 76–87 (1998).

[CrossRef]

B. Wang, A. C. Koivunen, and M. C. Roggemann, “Comparison of branch point and least squares reconstructors for laser beam transmission through the atmosphere,” Proc. SPIE 3763, 41–49 (1999).

[CrossRef]

Y. Li, “Branch point effect on adaptive correction,” Proc. SPIE 5490, 1064–1070 (2004).

[CrossRef]

D. J. Sanchez and D. W. Oesch, “The aggregate behavior of branch points - the creation and evolution of branch points,” Proc. SPIE 7466, 746605 (2009).

[CrossRef]

D. W. Oesch, D. J. Sanchez, C. M. Tewksbury-Christle, and P. R. Kelly, “The aggregate behavior of branch points - branch point density as a characteristic of an atmospheric turbulence simulator,” Proc. SPIE 7466, 746606 (2009).

[CrossRef]

D. W. Oesch, D. J. Sanchez, C. M. Tewksbury-Christle, and P. R. Kelly, “The aggregate behavior of branch points - altitude and strength of atmospheric turbulence layers,” Proc. SPIE 7816, 781605 (2010).

[CrossRef]

D. J. Sanchez, D. W. Oesch, and P. R. Kelly, “The aggregate behavior of branch points - theoretical calculation of branch point velocity,” Proc. SPIE 8380, 83800P (2012).

[CrossRef]

D. W. Oesch, D. J. Sanchez, and P. R. Kelly, “Optical vortex density in Rytov saturated atmospheric turbulence,” in FiO (2012), FW3A. 3.

R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence: Evaluation and Application of Mellin Transforms, 2nd ed. (SPIE, 2007).

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