Abstract

Polychromatic laser light can reduce speckle noise in wavefront-sensing and imaging applications that use direct-detection schemes. To help quantify the achievable reduction in speckle, this paper investigates the accuracy and numerical efficiency of three separate wave-optics methods. Each method simulates the active illumination of extended objects with polychromatic laser light. In turn, this paper uses the Monte Carlo method, the depth-slicing method, and the spectral-slicing method, respectively, to simulate the laser-object interaction. The limitations and sampling requirements of all three methods are discussed. Further, the numerical efficiencies of the methods are compared over a range of conditions. The Monte Carlo method is found to be the most efficient, while spectral slicing is more efficient than depth slicing for well-resolved objects. Finally, Hu’s theory is used to quantify method accuracy when possible (i.e., for well-resolved objects). In general, the theory compares favorably to the simulation methods.

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  1. I. Markhvida, L. Tchvialeva, T. K. Lee, and H. Zeng, “Influence of geometry on polychromatic speckle contrast,” J. Opt. Soc. Am. A 24, 93–97 (2007).
    [Crossref]
  2. 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]
  3. J. M. Huntley, “Simple model for image-plane polychromatic speckle contrast,” Appl. Opt. 38, 2212–2215 (1999).
    [Crossref]
  4. V. Molebny, P. McManamon, O. Steinvall, T. Kobayashi, and W. Chen, “Laser radar: historical prospective—from the East to the West,” Opt. Eng. 56, 031220 (2016).
    [Crossref]
  5. P. F. McManamon, “Review of ladar: a historic, yet emerging, sensor technology with rich phenomenology,” Opt. Eng. 51, 060901 (2012).
    [Crossref]
  6. S. Sahin, Z. Tong, and O. Korotkova, “Sensing of semi-rough targets embedded in atmospheric turbulence by means of stochastic electromagnetic beams,” Opt. Commun. 283, 4512–4518 (2010).
    [Crossref]
  7. Y. Cai, O. Korotkova, H. T. Eyyuboglu, and Y. Baykal, “Active laser radar systems with stochastic electromagnetic beams in turbulent atmosphere,” Opt. Express 16, 15834–15846 (2008).
    [Crossref]
  8. R. D. Richmond and S. C. Cain, Direct-Detection LADAR Systems (SPIE, 2010).
  9. J. G. Manni and J. W. Goodman, “Versatile method for achieving 1% speckle contrast in large-venue laser projection displays using a stationary multimode optical fiber,” Opt. Express 20, 11288–11315 (2012).
    [Crossref]
  10. J. Riker, “Requirements on active (laser) tracking and imaging from a technology perspective,” Proc. SPIE 8052, 805202 (2011).
    [Crossref]
  11. 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]
  12. D. Dayton, J. Allen, R. Nolasco, G. Fertig, and M. Myers, “Comparison of fast correlation algorithms for target tracking,” Proc. SPIE 8520, 85200G (2012).
    [Crossref]
  13. R. S. Pierre, G. Holleman, M. Valley, H. Injeyan, J. Berg, G. Harpole, R. Hilyard, M. Mitchell, M. Weber, J. Zamel, T. Engler, D. Hall, R. Tinti, and J. Machan, “Active tracker laser (ATLAS),” in Advanced Solid State Lasers, C. Pollock and W. Bosenberg, eds., OSA Trends in Optics and Photonics Series (Optical Society of America, 1997), Vol. 10, paper HP4.
  14. R. K. Tyson, Introduction to Adaptive Optics (SPIE, 2000).
  15. 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]
  16. 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]
  17. M. Laurenzis, Y. Lutz, F. Christnacher, A. Matwyschuk, and J. Poyet, “Homogeneous and speckle-free laser illumination for range-gated imaging and active polarimetry,” Opt. Eng. 51, 061302 (2012).
    [Crossref]
  18. T. Iwai and T. Asakura, “Speckle reduction in coherent information processing,” in Proceedings of the IEEE (IEEE, 1996), Vol. 84, pp. 765–781.
  19. J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts & Company, 2007).
  20. J. W. Goodman, Statistical Optics (Wiley, 1985).
  21. J. C. Dainty and W. T. Welford, “Reduction of speckle in image plane hologram reconstruction by moving pupils,” Opt. Commun. 3, 289–294 (1971).
    [Crossref]
  22. J. Bures, C. Delisle, and A. Zardecki, “Détermination de la Surface de Cohérence à Partir d’une Expérience de Photocomptage,” Can. J. Phys. 50, 760–768 (1972).
    [Crossref]
  23. M. Elbaum, M. Greenbaum, and M. King, “A wavelength diversity technique for reduction of speckle size,” Opt. Commun. 5, 171–174 (1972).
    [Crossref]
  24. R. A. Sprague, “Surface roughness measurement using white light speckle,” Appl. Opt. 11, 2811–2816 (1972).
    [Crossref]
  25. N. George and A. Jain, “Speckle reduction using multiple tones of illumination,” Appl. Opt. 12, 1202–1212 (1973).
    [Crossref]
  26. H. Pedersen, “On the contrast of polychromatic speckle patterns and its dependence on surface roughness,” Opt. Acta 22, 15–24 (1975).
    [Crossref]
  27. K. Nakagawa and T. Asakura, “Average contrast of white-light image speckle patterns,” Opt. Acta 26, 951–960 (1979).
    [Crossref]
  28. H. Pedersen, “Second-order statistics of light diffracted from Gaussian, rough surfaces with applications to the roughness dependence of speckles,” Opt. Acta 22, 523–535 (1975).
    [Crossref]
  29. G. Parry, “Speckle patterns in partially coherent light,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, 1975), pp. 78–120.
  30. T. S. McKechnie, “Image-plane speckle in partially coherent illumination,” Opt. Quantum Electron. 8, 61–67 (1976).
    [Crossref]
  31. Y.-Q. Hu, “Dependence of polychromatic-speckle-pattern contrast on imaging and illumination directions,” Appl. Opt. 33, 2707–2714 (1994).
    [Crossref]
  32. L. Tchvialeva, T. K. Lee, I. Markhvida, D. I. McLean, H. Lui, and H. Zeng, “Using a zone model to incorporate the influence of geometry on polychromatic speckle contrast,” Opt. Eng. 47, 074201 (2008).
    [Crossref]
  33. L. Tchvialeva, I. Markhvida, and T. K. Lee, “Error analysis for polychromatic speckle contrast measurements,” Opt. Lasers Eng. 49, 1397–1401 (2011).
    [Crossref]
  34. N. R. Van Zandt, M. W. Hyde, S. Basu, D. G. Voelz, and X. Xiao, “Synthesizing time-evolving partially-coherent Schell-model sources,” Opt. Commun. 387, 377–384 (2017).
    [Crossref]
  35. Y. Chen, F. Wang, J. Yu, L. Liu, and Y. Cai, “Vector Hermite-Gaussian correlated Schell-model beam,” Opt. Express 24, 15232–15250 (2016).
    [Crossref]
  36. X. Chen, C. Chang, Z. Chen, Z. Lin, and J. Pu, “Generation of stochastic electromagnetic beams with complete controllable coherence,” Opt. Express 24, 21587–21596 (2016).
    [Crossref]
  37. M. W. Hyde, S. Bose-Pillai, D. G. Voelz, and X. Xiao, “Generation of vector partially coherent optical sources using phase-only spatial light modulators,” Phys. Rev. Appl. 6, 064030 (2016).
    [Crossref]
  38. M. W. Hyde, S. Bose-Pillai, X. Xiao, and D. G. Voelz, “A fast and efficient method for producing partially coherent sources,” J. Opt. 19, 025601 (2017).
    [Crossref]
  39. Y. Cai, Y. Chen, J. Yu, X. Liu, and L. Liu, “Generation of partially coherent beams,” Prog. Opt. 62, 157–223 (2017).
    [Crossref]
  40. 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]
  41. A. Deninger and T. Renner, “12 orders of coherence control,” Toptica Appl-1010 (2010), https://www.toptica.com/fileadmin/Editors_English/12_literature/quantum_technologies/12_orders_of_coherence_control.pdf .
  42. C. Zeringue, I. Dajani, S. Naderi, G. T. Moore, and C. Robin, “A theoretical study of transient stimulated Brillouin scattering in optical fibers seeded with phase-modulated light,” Opt. Express 20, 21196–21213 (2012).
    [Crossref]
  43. A. V. Harish and J. Nilsson, “Optimization of phase modulation with arbitrary waveform generators for optical spectral control and suppression of stimulated Brillouin scattering,” Opt. Express 23, 6988–6999 (2015).
    [Crossref]
  44. B. Anderson, A. Flores, R. Holten, and I. Dajani, “Comparison of phase modulation schemes for coherently combined fiber amplifiers,” Opt. Express 23, 27046–27060 (2015).
    [Crossref]
  45. N. R. Van Zandt, M. F. Spencer, M. J. Steinbock, B. M. Anderson, M. W. Hyde, and S. T. Fiorino, “Comparison of polychromatic wave-optics models,” Proc. SPIE 9982, 998209 (2016).
    [Crossref]
  46. C. Rydberg and J. Bengtsson, “Efficient numerical representation of the optical field for the propagation of partially coherent radiation with a specified spatial and temporal coherence function,” J. Opt. Soc. Am. A 23, 1616–1625 (2006).
    [Crossref]
  47. J. Schmidt, Numerical Simulation of Optical Wave Propagation with Examples in MATLAB (SPIE, 2010).
  48. G. P. Perram, S. J. Cusumano, R. L. Hengehold, and S. T. Fiorino, Introduction to Laser Weapon Systems (DEPS, 2010).
  49. D. Voelz, Computational Fourier Optics (SPIE, 2011).
  50. S. C. Coy and B. P. Venet, “Wavetrain user guide,” http://www.mza.com/doc/wavetrain/wtug/main.htm .
  51. TimeLike Systems LLC, “Lightlike user’s manual,” http://www.timelikesystems.com/htmldocs/LightLikeHelp/ .
  52. D. Link, AOSims LLC (personal communication, 6 January, 2016).
  53. J. Barchers, Nutronics Inc., 1851 Lefthand Circle, Longmont, CO, 80501 (personal communication, 2 August, 2016).
  54. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).
  55. H. Mao and D. Zhao, “Second-order intensity-moment characteristics for broadband partially coherent flat-topped beams in atmospheric turbulence,” Opt. Express 18, 1741–1755 (2010).
    [Crossref]
  56. H. Mao, X. Du, L. Chen, and D. Zhao, “Propagation of broadband Gaussian Schell-model beams in the apertured fractional Fourier transformation systems,” J. Opt. Soc. Am. A 28, 976–982 (2011).
    [Crossref]
  57. R. L. Fante, “The effect of source temporal coherence on light scintillations in weak turbulence,” J. Opt. Soc. Am. 69, 71–73 (1979).
    [Crossref]
  58. Y. Baykal, M. A. Plonus, and S. J. Wang, “The scintillations for weak atmospheric turbulence using a partially coherent source,” Radio Sci. 18, 551–556 (1983).
    [Crossref]
  59. M. Steinbock, Directed Energy Directorate, Air Force Research Laboratory (personal communication, 21 April, 2016).
  60. 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]

2017 (3)

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

M. W. Hyde, S. Bose-Pillai, X. Xiao, and D. G. Voelz, “A fast and efficient method for producing partially coherent sources,” J. Opt. 19, 025601 (2017).
[Crossref]

Y. Cai, Y. Chen, J. Yu, X. Liu, and L. Liu, “Generation of partially coherent beams,” Prog. Opt. 62, 157–223 (2017).
[Crossref]

2016 (7)

N. R. Van Zandt, M. F. Spencer, M. J. Steinbock, B. M. Anderson, M. W. Hyde, and S. T. Fiorino, “Comparison of polychromatic wave-optics models,” Proc. SPIE 9982, 998209 (2016).
[Crossref]

M. W. Hyde, S. Bose-Pillai, D. G. Voelz, and X. Xiao, “Generation of vector partially coherent optical sources using phase-only spatial light modulators,” Phys. Rev. Appl. 6, 064030 (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]

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]

V. Molebny, P. McManamon, O. Steinvall, T. Kobayashi, and W. Chen, “Laser radar: historical prospective—from the East to the West,” Opt. Eng. 56, 031220 (2016).
[Crossref]

Y. Chen, F. Wang, J. Yu, L. Liu, and Y. Cai, “Vector Hermite-Gaussian correlated Schell-model beam,” Opt. Express 24, 15232–15250 (2016).
[Crossref]

X. Chen, C. Chang, Z. Chen, Z. Lin, and J. Pu, “Generation of stochastic electromagnetic beams with complete controllable coherence,” Opt. Express 24, 21587–21596 (2016).
[Crossref]

2015 (2)

2012 (6)

J. G. Manni and J. W. Goodman, “Versatile method for achieving 1% speckle contrast in large-venue laser projection displays using a stationary multimode optical fiber,” Opt. Express 20, 11288–11315 (2012).
[Crossref]

C. Zeringue, I. Dajani, S. Naderi, G. T. Moore, and C. Robin, “A theoretical study of transient stimulated Brillouin scattering in optical fibers seeded with phase-modulated light,” Opt. Express 20, 21196–21213 (2012).
[Crossref]

P. F. McManamon, “Review of ladar: a historic, yet emerging, sensor technology with rich phenomenology,” Opt. Eng. 51, 060901 (2012).
[Crossref]

D. Dayton, J. Allen, R. Nolasco, G. Fertig, and M. Myers, “Comparison of fast correlation algorithms for target tracking,” Proc. SPIE 8520, 85200G (2012).
[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]

M. Laurenzis, Y. Lutz, F. Christnacher, A. Matwyschuk, and J. Poyet, “Homogeneous and speckle-free laser illumination for range-gated imaging and active polarimetry,” Opt. Eng. 51, 061302 (2012).
[Crossref]

2011 (3)

J. Riker, “Requirements on active (laser) tracking and imaging from a technology perspective,” Proc. SPIE 8052, 805202 (2011).
[Crossref]

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

H. Mao, X. Du, L. Chen, and D. Zhao, “Propagation of broadband Gaussian Schell-model beams in the apertured fractional Fourier transformation systems,” J. Opt. Soc. Am. A 28, 976–982 (2011).
[Crossref]

2010 (2)

H. Mao and D. Zhao, “Second-order intensity-moment characteristics for broadband partially coherent flat-topped beams in atmospheric turbulence,” Opt. Express 18, 1741–1755 (2010).
[Crossref]

S. Sahin, Z. Tong, and O. Korotkova, “Sensing of semi-rough targets embedded in atmospheric turbulence by means of stochastic electromagnetic beams,” Opt. Commun. 283, 4512–4518 (2010).
[Crossref]

2008 (2)

L. Tchvialeva, T. K. Lee, I. Markhvida, D. I. McLean, H. Lui, and H. Zeng, “Using a zone model to incorporate the influence of geometry on polychromatic speckle contrast,” Opt. Eng. 47, 074201 (2008).
[Crossref]

Y. Cai, O. Korotkova, H. T. Eyyuboglu, and Y. Baykal, “Active laser radar systems with stochastic electromagnetic beams in turbulent atmosphere,” Opt. Express 16, 15834–15846 (2008).
[Crossref]

2007 (2)

2006 (1)

2003 (1)

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]

1999 (1)

1997 (1)

1994 (1)

1983 (1)

Y. Baykal, M. A. Plonus, and S. J. Wang, “The scintillations for weak atmospheric turbulence using a partially coherent source,” Radio Sci. 18, 551–556 (1983).
[Crossref]

1979 (2)

R. L. Fante, “The effect of source temporal coherence on light scintillations in weak turbulence,” J. Opt. Soc. Am. 69, 71–73 (1979).
[Crossref]

K. Nakagawa and T. Asakura, “Average contrast of white-light image speckle patterns,” Opt. Acta 26, 951–960 (1979).
[Crossref]

1976 (1)

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

1975 (2)

H. Pedersen, “Second-order statistics of light diffracted from Gaussian, rough surfaces with applications to the roughness dependence of speckles,” Opt. Acta 22, 523–535 (1975).
[Crossref]

H. Pedersen, “On the contrast of polychromatic speckle patterns and its dependence on surface roughness,” Opt. Acta 22, 15–24 (1975).
[Crossref]

1973 (1)

1972 (3)

R. A. Sprague, “Surface roughness measurement using white light speckle,” Appl. Opt. 11, 2811–2816 (1972).
[Crossref]

J. Bures, C. Delisle, and A. Zardecki, “Détermination de la Surface de Cohérence à Partir d’une Expérience de Photocomptage,” Can. J. Phys. 50, 760–768 (1972).
[Crossref]

M. Elbaum, M. Greenbaum, and M. King, “A wavelength diversity technique for reduction of speckle size,” Opt. Commun. 5, 171–174 (1972).
[Crossref]

1971 (1)

J. C. Dainty and W. T. Welford, “Reduction of speckle in image plane hologram reconstruction by moving pupils,” Opt. Commun. 3, 289–294 (1971).
[Crossref]

Allen, J.

D. Dayton, J. Allen, R. Nolasco, G. Fertig, and M. Myers, “Comparison of fast correlation algorithms for target tracking,” Proc. SPIE 8520, 85200G (2012).
[Crossref]

Anderson, B.

Anderson, B. M.

N. R. Van Zandt, M. F. Spencer, M. J. Steinbock, B. M. Anderson, M. W. Hyde, and S. T. Fiorino, “Comparison of polychromatic wave-optics models,” Proc. SPIE 9982, 998209 (2016).
[Crossref]

Asakura, T.

K. Nakagawa and T. Asakura, “Average contrast of white-light image speckle patterns,” Opt. Acta 26, 951–960 (1979).
[Crossref]

T. Iwai and T. Asakura, “Speckle reduction in coherent information processing,” in Proceedings of the IEEE (IEEE, 1996), Vol. 84, pp. 765–781.

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

Barchers, J.

J. Barchers, Nutronics Inc., 1851 Lefthand Circle, Longmont, CO, 80501 (personal communication, 2 August, 2016).

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, M. W. Hyde, S. Basu, D. G. Voelz, and X. Xiao, “Synthesizing time-evolving partially-coherent Schell-model sources,” Opt. Commun. 387, 377–384 (2017).
[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]

Baykal, Y.

Y. Cai, O. Korotkova, H. T. Eyyuboglu, and Y. Baykal, “Active laser radar systems with stochastic electromagnetic beams in turbulent atmosphere,” Opt. Express 16, 15834–15846 (2008).
[Crossref]

Y. Baykal, M. A. Plonus, and S. J. Wang, “The scintillations for weak atmospheric turbulence using a partially coherent source,” Radio Sci. 18, 551–556 (1983).
[Crossref]

Bengtsson, J.

Berg, J.

R. S. Pierre, G. Holleman, M. Valley, H. Injeyan, J. Berg, G. Harpole, R. Hilyard, M. Mitchell, M. Weber, J. Zamel, T. Engler, D. Hall, R. Tinti, and J. Machan, “Active tracker laser (ATLAS),” in Advanced Solid State Lasers, C. Pollock and W. Bosenberg, eds., OSA Trends in Optics and Photonics Series (Optical Society of America, 1997), Vol. 10, paper HP4.

Bose-Pillai, S.

M. W. Hyde, S. Bose-Pillai, X. Xiao, and D. G. Voelz, “A fast and efficient method for producing partially coherent sources,” J. Opt. 19, 025601 (2017).
[Crossref]

M. W. Hyde, S. Bose-Pillai, D. G. Voelz, and X. Xiao, “Generation of vector partially coherent optical sources using phase-only spatial light modulators,” Phys. Rev. Appl. 6, 064030 (2016).
[Crossref]

Bures, J.

J. Bures, C. Delisle, and A. Zardecki, “Détermination de la Surface de Cohérence à Partir d’une Expérience de Photocomptage,” Can. J. Phys. 50, 760–768 (1972).
[Crossref]

Bush, K. A.

Cai, Y.

Cain, S. C.

R. D. Richmond and S. C. Cain, Direct-Detection LADAR Systems (SPIE, 2010).

Chang, C.

Chen, L.

Chen, W.

V. Molebny, P. McManamon, O. Steinvall, T. Kobayashi, and W. Chen, “Laser radar: historical prospective—from the East to the West,” Opt. Eng. 56, 031220 (2016).
[Crossref]

Chen, X.

Chen, Y.

Y. Cai, Y. Chen, J. Yu, X. Liu, and L. Liu, “Generation of partially coherent beams,” Prog. Opt. 62, 157–223 (2017).
[Crossref]

Y. Chen, F. Wang, J. Yu, L. Liu, and Y. Cai, “Vector Hermite-Gaussian correlated Schell-model beam,” Opt. Express 24, 15232–15250 (2016).
[Crossref]

Chen, Z.

Christnacher, F.

M. Laurenzis, Y. Lutz, F. Christnacher, A. Matwyschuk, and J. Poyet, “Homogeneous and speckle-free laser illumination for range-gated imaging and active polarimetry,” Opt. Eng. 51, 061302 (2012).
[Crossref]

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]

G. P. Perram, S. J. Cusumano, R. L. Hengehold, and S. T. Fiorino, Introduction to Laser Weapon Systems (DEPS, 2010).

Dainty, J. C.

J. C. Dainty and W. T. Welford, “Reduction of speckle in image plane hologram reconstruction by moving pupils,” Opt. Commun. 3, 289–294 (1971).
[Crossref]

Dajani, I.

Dayton, D.

D. Dayton, J. Allen, R. Nolasco, G. Fertig, and M. Myers, “Comparison of fast correlation algorithms for target tracking,” Proc. SPIE 8520, 85200G (2012).
[Crossref]

Delisle, C.

J. Bures, C. Delisle, and A. Zardecki, “Détermination de la Surface de Cohérence à Partir d’une Expérience de Photocomptage,” Can. J. Phys. 50, 760–768 (1972).
[Crossref]

Du, X.

Elbaum, M.

M. Elbaum, M. Greenbaum, and M. King, “A wavelength diversity technique for reduction of speckle size,” Opt. Commun. 5, 171–174 (1972).
[Crossref]

Engler, T.

R. S. Pierre, G. Holleman, M. Valley, H. Injeyan, J. Berg, G. Harpole, R. Hilyard, M. Mitchell, M. Weber, J. Zamel, T. Engler, D. Hall, R. Tinti, and J. Machan, “Active tracker laser (ATLAS),” in Advanced Solid State Lasers, C. Pollock and W. Bosenberg, eds., OSA Trends in Optics and Photonics Series (Optical Society of America, 1997), Vol. 10, paper HP4.

Eyyuboglu, H. T.

Fante, R. L.

Fertig, G.

D. Dayton, J. Allen, R. Nolasco, G. Fertig, and M. Myers, “Comparison of fast correlation algorithms for target tracking,” Proc. SPIE 8520, 85200G (2012).
[Crossref]

Fiorino, S. T.

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, M. F. Spencer, M. J. Steinbock, B. M. Anderson, M. W. Hyde, and S. T. Fiorino, “Comparison of polychromatic wave-optics models,” Proc. SPIE 9982, 998209 (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]

G. P. Perram, S. J. Cusumano, R. L. Hengehold, and S. T. Fiorino, Introduction to Laser Weapon Systems (DEPS, 2010).

Flores, A.

George, N.

Goodman, J. W.

Greenbaum, M.

M. Elbaum, M. Greenbaum, and M. King, “A wavelength diversity technique for reduction of speckle size,” Opt. Commun. 5, 171–174 (1972).
[Crossref]

Hall, D.

R. S. Pierre, G. Holleman, M. Valley, H. Injeyan, J. Berg, G. Harpole, R. Hilyard, M. Mitchell, M. Weber, J. Zamel, T. Engler, D. Hall, R. Tinti, and J. Machan, “Active tracker laser (ATLAS),” in Advanced Solid State Lasers, C. Pollock and W. Bosenberg, eds., OSA Trends in Optics and Photonics Series (Optical Society of America, 1997), Vol. 10, paper HP4.

Harish, A. V.

Harpole, G.

R. S. Pierre, G. Holleman, M. Valley, H. Injeyan, J. Berg, G. Harpole, R. Hilyard, M. Mitchell, M. Weber, J. Zamel, T. Engler, D. Hall, R. Tinti, and J. Machan, “Active tracker laser (ATLAS),” in Advanced Solid State Lasers, C. Pollock and W. Bosenberg, eds., OSA Trends in Optics and Photonics Series (Optical Society of America, 1997), Vol. 10, paper HP4.

Hengehold, R. L.

G. P. Perram, S. J. Cusumano, R. L. Hengehold, and S. T. Fiorino, Introduction to Laser Weapon Systems (DEPS, 2010).

Hilyard, R.

R. S. Pierre, G. Holleman, M. Valley, H. Injeyan, J. Berg, G. Harpole, R. Hilyard, M. Mitchell, M. Weber, J. Zamel, T. Engler, D. Hall, R. Tinti, and J. Machan, “Active tracker laser (ATLAS),” in Advanced Solid State Lasers, C. Pollock and W. Bosenberg, eds., OSA Trends in Optics and Photonics Series (Optical Society of America, 1997), Vol. 10, paper HP4.

Holleman, G.

R. S. Pierre, G. Holleman, M. Valley, H. Injeyan, J. Berg, G. Harpole, R. Hilyard, M. Mitchell, M. Weber, J. Zamel, T. Engler, D. Hall, R. Tinti, and J. Machan, “Active tracker laser (ATLAS),” in Advanced Solid State Lasers, C. Pollock and W. Bosenberg, eds., OSA Trends in Optics and Photonics Series (Optical Society of America, 1997), Vol. 10, paper HP4.

Holten, R.

Hu, Y.-Q.

Huntley, J. M.

Hyde, M. W.

M. W. Hyde, S. Bose-Pillai, X. Xiao, and D. G. Voelz, “A fast and efficient method for producing partially coherent sources,” J. Opt. 19, 025601 (2017).
[Crossref]

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

M. W. Hyde, S. Bose-Pillai, D. G. Voelz, and X. Xiao, “Generation of vector partially coherent optical sources using phase-only spatial light modulators,” Phys. Rev. Appl. 6, 064030 (2016).
[Crossref]

N. R. Van Zandt, M. F. Spencer, M. J. Steinbock, B. M. Anderson, M. W. Hyde, and S. T. Fiorino, “Comparison of polychromatic wave-optics models,” Proc. SPIE 9982, 998209 (2016).
[Crossref]

Idell, P. S.

Injeyan, H.

R. S. Pierre, G. Holleman, M. Valley, H. Injeyan, J. Berg, G. Harpole, R. Hilyard, M. Mitchell, M. Weber, J. Zamel, T. Engler, D. Hall, R. Tinti, and J. Machan, “Active tracker laser (ATLAS),” in Advanced Solid State Lasers, C. Pollock and W. Bosenberg, eds., OSA Trends in Optics and Photonics Series (Optical Society of America, 1997), Vol. 10, paper HP4.

Iwai, T.

T. Iwai and T. Asakura, “Speckle reduction in coherent information processing,” in Proceedings of the IEEE (IEEE, 1996), Vol. 84, pp. 765–781.

Jain, A.

King, M.

M. Elbaum, M. Greenbaum, and M. King, “A wavelength diversity technique for reduction of speckle size,” Opt. Commun. 5, 171–174 (1972).
[Crossref]

Klein, L.

Kobayashi, T.

V. Molebny, P. McManamon, O. Steinvall, T. Kobayashi, and W. Chen, “Laser radar: historical prospective—from the East to the West,” Opt. Eng. 56, 031220 (2016).
[Crossref]

Korotkova, O.

S. Sahin, Z. Tong, and O. Korotkova, “Sensing of semi-rough targets embedded in atmospheric turbulence by means of stochastic electromagnetic beams,” Opt. Commun. 283, 4512–4518 (2010).
[Crossref]

Y. Cai, O. Korotkova, H. T. Eyyuboglu, and Y. Baykal, “Active laser radar systems with stochastic electromagnetic beams in turbulent atmosphere,” Opt. Express 16, 15834–15846 (2008).
[Crossref]

Laurenzis, M.

M. Laurenzis, Y. Lutz, F. Christnacher, A. Matwyschuk, and J. Poyet, “Homogeneous and speckle-free laser illumination for range-gated imaging and active polarimetry,” Opt. Eng. 51, 061302 (2012).
[Crossref]

Lee, T. K.

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

L. Tchvialeva, T. K. Lee, I. Markhvida, D. I. McLean, H. Lui, and H. Zeng, “Using a zone model to incorporate the influence of geometry on polychromatic speckle contrast,” Opt. Eng. 47, 074201 (2008).
[Crossref]

I. Markhvida, L. Tchvialeva, T. K. Lee, and H. Zeng, “Influence of geometry on polychromatic speckle contrast,” J. Opt. Soc. Am. A 24, 93–97 (2007).
[Crossref]

Lin, Z.

Link, D.

D. Link, AOSims LLC (personal communication, 6 January, 2016).

Liu, L.

Y. Cai, Y. Chen, J. Yu, X. Liu, and L. Liu, “Generation of partially coherent beams,” Prog. Opt. 62, 157–223 (2017).
[Crossref]

Y. Chen, F. Wang, J. Yu, L. Liu, and Y. Cai, “Vector Hermite-Gaussian correlated Schell-model beam,” Opt. Express 24, 15232–15250 (2016).
[Crossref]

Liu, X.

Y. Cai, Y. Chen, J. Yu, X. Liu, and L. Liu, “Generation of partially coherent beams,” Prog. Opt. 62, 157–223 (2017).
[Crossref]

Lui, H.

L. Tchvialeva, T. K. Lee, I. Markhvida, D. I. McLean, H. Lui, and H. Zeng, “Using a zone model to incorporate the influence of geometry on polychromatic speckle contrast,” Opt. Eng. 47, 074201 (2008).
[Crossref]

Lutz, Y.

M. Laurenzis, Y. Lutz, F. Christnacher, A. Matwyschuk, and J. Poyet, “Homogeneous and speckle-free laser illumination for range-gated imaging and active polarimetry,” Opt. Eng. 51, 061302 (2012).
[Crossref]

Machan, J.

R. S. Pierre, G. Holleman, M. Valley, H. Injeyan, J. Berg, G. Harpole, R. Hilyard, M. Mitchell, M. Weber, J. Zamel, T. Engler, D. Hall, R. Tinti, and J. Machan, “Active tracker laser (ATLAS),” in Advanced Solid State Lasers, C. Pollock and W. Bosenberg, eds., OSA Trends in Optics and Photonics Series (Optical Society of America, 1997), Vol. 10, paper HP4.

Manni, J. G.

Mao, H.

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

Markhvida, I.

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

L. Tchvialeva, T. K. Lee, I. Markhvida, D. I. McLean, H. Lui, and H. Zeng, “Using a zone model to incorporate the influence of geometry on polychromatic speckle contrast,” Opt. Eng. 47, 074201 (2008).
[Crossref]

I. Markhvida, L. Tchvialeva, T. K. Lee, and H. Zeng, “Influence of geometry on polychromatic speckle contrast,” J. Opt. Soc. Am. A 24, 93–97 (2007).
[Crossref]

Matwyschuk, A.

M. Laurenzis, Y. Lutz, F. Christnacher, A. Matwyschuk, and J. Poyet, “Homogeneous and speckle-free laser illumination for range-gated imaging and active polarimetry,” Opt. Eng. 51, 061302 (2012).
[Crossref]

McCrae, J. E.

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]

McLean, D. I.

L. Tchvialeva, T. K. Lee, I. Markhvida, D. I. McLean, H. Lui, and H. Zeng, “Using a zone model to incorporate the influence of geometry on polychromatic speckle contrast,” Opt. Eng. 47, 074201 (2008).
[Crossref]

McManamon, P.

V. Molebny, P. McManamon, O. Steinvall, T. Kobayashi, and W. Chen, “Laser radar: historical prospective—from the East to the West,” Opt. Eng. 56, 031220 (2016).
[Crossref]

McManamon, P. F.

P. F. McManamon, “Review of ladar: a historic, yet emerging, sensor technology with rich phenomenology,” Opt. Eng. 51, 060901 (2012).
[Crossref]

Mitchell, M.

R. S. Pierre, G. Holleman, M. Valley, H. Injeyan, J. Berg, G. Harpole, R. Hilyard, M. Mitchell, M. Weber, J. Zamel, T. Engler, D. Hall, R. Tinti, and J. Machan, “Active tracker laser (ATLAS),” in Advanced Solid State Lasers, C. Pollock and W. Bosenberg, eds., OSA Trends in Optics and Photonics Series (Optical Society of America, 1997), Vol. 10, paper HP4.

Molebny, V.

V. Molebny, P. McManamon, O. Steinvall, T. Kobayashi, and W. Chen, “Laser radar: historical prospective—from the East to the West,” Opt. Eng. 56, 031220 (2016).
[Crossref]

Moloney, J.

Moore, G. T.

Myers, M.

D. Dayton, J. Allen, R. Nolasco, G. Fertig, and M. Myers, “Comparison of fast correlation algorithms for target tracking,” Proc. SPIE 8520, 85200G (2012).
[Crossref]

Naderi, S.

Nakagawa, K.

K. Nakagawa and T. Asakura, “Average contrast of white-light image speckle patterns,” Opt. Acta 26, 951–960 (1979).
[Crossref]

Nilsson, J.

Nolasco, R.

D. Dayton, J. Allen, R. Nolasco, G. Fertig, and M. Myers, “Comparison of fast correlation algorithms for target tracking,” Proc. SPIE 8520, 85200G (2012).
[Crossref]

Parry, G.

G. Parry, “Speckle patterns in partially coherent light,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, 1975), pp. 78–120.

Pedersen, H.

H. Pedersen, “Second-order statistics of light diffracted from Gaussian, rough surfaces with applications to the roughness dependence of speckles,” Opt. Acta 22, 523–535 (1975).
[Crossref]

H. Pedersen, “On the contrast of polychromatic speckle patterns and its dependence on surface roughness,” Opt. Acta 22, 15–24 (1975).
[Crossref]

Peleg, A.

Perram, G. P.

G. P. Perram, S. J. Cusumano, R. L. Hengehold, and S. T. Fiorino, Introduction to Laser Weapon Systems (DEPS, 2010).

Pierre, R. S.

R. S. Pierre, G. Holleman, M. Valley, H. Injeyan, J. Berg, G. Harpole, R. Hilyard, M. Mitchell, M. Weber, J. Zamel, T. Engler, D. Hall, R. Tinti, and J. Machan, “Active tracker laser (ATLAS),” in Advanced Solid State Lasers, C. Pollock and W. Bosenberg, eds., OSA Trends in Optics and Photonics Series (Optical Society of America, 1997), Vol. 10, paper HP4.

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]

Plonus, M. A.

Y. Baykal, M. A. Plonus, and S. J. Wang, “The scintillations for weak atmospheric turbulence using a partially coherent source,” Radio Sci. 18, 551–556 (1983).
[Crossref]

Polynkin, P.

Poyet, J.

M. Laurenzis, Y. Lutz, F. Christnacher, A. Matwyschuk, and J. Poyet, “Homogeneous and speckle-free laser illumination for range-gated imaging and active polarimetry,” Opt. Eng. 51, 061302 (2012).
[Crossref]

Pu, J.

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

Rhoadarmer, T.

Richmond, R. D.

R. D. Richmond and S. C. Cain, Direct-Detection LADAR Systems (SPIE, 2010).

Riker, J.

J. Riker, “Requirements on active (laser) tracking and imaging from a technology perspective,” Proc. SPIE 8052, 805202 (2011).
[Crossref]

Robin, C.

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]

Rydberg, C.

Sahin, S.

S. Sahin, Z. Tong, and O. Korotkova, “Sensing of semi-rough targets embedded in atmospheric turbulence by means of stochastic electromagnetic beams,” Opt. Commun. 283, 4512–4518 (2010).
[Crossref]

Schmidt, J.

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

Spencer, M. F.

N. R. Van Zandt, M. F. Spencer, M. J. Steinbock, B. M. Anderson, M. W. Hyde, and S. T. Fiorino, “Comparison of polychromatic wave-optics models,” Proc. SPIE 9982, 998209 (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]

Sprague, R. A.

Steinbock, M.

M. Steinbock, Directed Energy Directorate, Air Force Research Laboratory (personal communication, 21 April, 2016).

Steinbock, M. J.

N. R. Van Zandt, M. F. Spencer, M. J. Steinbock, B. M. Anderson, M. W. Hyde, and S. T. Fiorino, “Comparison of polychromatic wave-optics models,” Proc. SPIE 9982, 998209 (2016).
[Crossref]

Steinvall, O.

V. Molebny, P. McManamon, O. Steinvall, T. Kobayashi, and W. Chen, “Laser radar: historical prospective—from the East to the West,” Opt. Eng. 56, 031220 (2016).
[Crossref]

Tchvialeva, L.

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

L. Tchvialeva, T. K. Lee, I. Markhvida, D. I. McLean, H. Lui, and H. Zeng, “Using a zone model to incorporate the influence of geometry on polychromatic speckle contrast,” Opt. Eng. 47, 074201 (2008).
[Crossref]

I. Markhvida, L. Tchvialeva, T. K. Lee, and H. Zeng, “Influence of geometry on polychromatic speckle contrast,” J. Opt. Soc. Am. A 24, 93–97 (2007).
[Crossref]

Tinti, R.

R. S. Pierre, G. Holleman, M. Valley, H. Injeyan, J. Berg, G. Harpole, R. Hilyard, M. Mitchell, M. Weber, J. Zamel, T. Engler, D. Hall, R. Tinti, and J. Machan, “Active tracker laser (ATLAS),” in Advanced Solid State Lasers, C. Pollock and W. Bosenberg, eds., OSA Trends in Optics and Photonics Series (Optical Society of America, 1997), Vol. 10, paper HP4.

Tong, Z.

S. Sahin, Z. Tong, and O. Korotkova, “Sensing of semi-rough targets embedded in atmospheric turbulence by means of stochastic electromagnetic beams,” Opt. Commun. 283, 4512–4518 (2010).
[Crossref]

Tyson, R. K.

R. K. Tyson, Introduction to Adaptive Optics (SPIE, 2000).

Valley, M.

R. S. Pierre, G. Holleman, M. Valley, H. Injeyan, J. Berg, G. Harpole, R. Hilyard, M. Mitchell, M. Weber, J. Zamel, T. Engler, D. Hall, R. Tinti, and J. Machan, “Active tracker laser (ATLAS),” in Advanced Solid State Lasers, C. Pollock and W. Bosenberg, eds., OSA Trends in Optics and Photonics Series (Optical Society of America, 1997), Vol. 10, paper HP4.

Van Zandt, N. R.

N. R. Van Zandt, M. W. Hyde, S. Basu, D. G. Voelz, and X. Xiao, “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, M. F. Spencer, M. J. Steinbock, B. M. Anderson, M. W. Hyde, and S. T. Fiorino, “Comparison of polychromatic wave-optics models,” Proc. SPIE 9982, 998209 (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.

M. W. Hyde, S. Bose-Pillai, X. Xiao, and D. G. Voelz, “A fast and efficient method for producing partially coherent sources,” J. Opt. 19, 025601 (2017).
[Crossref]

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

M. W. Hyde, S. Bose-Pillai, D. G. Voelz, and X. Xiao, “Generation of vector partially coherent optical sources using phase-only spatial light modulators,” Phys. Rev. Appl. 6, 064030 (2016).
[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]

Wang, F.

Wang, S. J.

Y. Baykal, M. A. Plonus, and S. J. Wang, “The scintillations for weak atmospheric turbulence using a partially coherent source,” Radio Sci. 18, 551–556 (1983).
[Crossref]

Weber, M.

R. S. Pierre, G. Holleman, M. Valley, H. Injeyan, J. Berg, G. Harpole, R. Hilyard, M. Mitchell, M. Weber, J. Zamel, T. Engler, D. Hall, R. Tinti, and J. Machan, “Active tracker laser (ATLAS),” in Advanced Solid State Lasers, C. Pollock and W. Bosenberg, eds., OSA Trends in Optics and Photonics Series (Optical Society of America, 1997), Vol. 10, paper HP4.

Welford, W. T.

J. C. Dainty and W. T. Welford, “Reduction of speckle in image plane hologram reconstruction by moving pupils,” Opt. Commun. 3, 289–294 (1971).
[Crossref]

Wolf, E.

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

Xiao, X.

M. W. Hyde, S. Bose-Pillai, X. Xiao, and D. G. Voelz, “A fast and efficient method for producing partially coherent sources,” J. Opt. 19, 025601 (2017).
[Crossref]

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

M. W. Hyde, S. Bose-Pillai, D. G. Voelz, and X. Xiao, “Generation of vector partially coherent optical sources using phase-only spatial light modulators,” Phys. Rev. Appl. 6, 064030 (2016).
[Crossref]

Yu, J.

Y. Cai, Y. Chen, J. Yu, X. Liu, and L. Liu, “Generation of partially coherent beams,” Prog. Opt. 62, 157–223 (2017).
[Crossref]

Y. Chen, F. Wang, J. Yu, L. Liu, and Y. Cai, “Vector Hermite-Gaussian correlated Schell-model beam,” Opt. Express 24, 15232–15250 (2016).
[Crossref]

Zamel, J.

R. S. Pierre, G. Holleman, M. Valley, H. Injeyan, J. Berg, G. Harpole, R. Hilyard, M. Mitchell, M. Weber, J. Zamel, T. Engler, D. Hall, R. Tinti, and J. Machan, “Active tracker laser (ATLAS),” in Advanced Solid State Lasers, C. Pollock and W. Bosenberg, eds., OSA Trends in Optics and Photonics Series (Optical Society of America, 1997), Vol. 10, paper HP4.

Zardecki, A.

J. Bures, C. Delisle, and A. Zardecki, “Détermination de la Surface de Cohérence à Partir d’une Expérience de Photocomptage,” Can. J. Phys. 50, 760–768 (1972).
[Crossref]

Zeng, H.

L. Tchvialeva, T. K. Lee, I. Markhvida, D. I. McLean, H. Lui, and H. Zeng, “Using a zone model to incorporate the influence of geometry on polychromatic speckle contrast,” Opt. Eng. 47, 074201 (2008).
[Crossref]

I. Markhvida, L. Tchvialeva, T. K. Lee, and H. Zeng, “Influence of geometry on polychromatic speckle contrast,” J. Opt. Soc. Am. A 24, 93–97 (2007).
[Crossref]

Zeringue, C.

Zhao, D.

Appl. Opt. (5)

Can. J. Phys. (1)

J. Bures, C. Delisle, and A. Zardecki, “Détermination de la Surface de Cohérence à Partir d’une Expérience de Photocomptage,” Can. J. Phys. 50, 760–768 (1972).
[Crossref]

J. Opt. (1)

M. W. Hyde, S. Bose-Pillai, X. Xiao, and D. G. Voelz, “A fast and efficient method for producing partially coherent sources,” J. Opt. 19, 025601 (2017).
[Crossref]

J. Opt. Soc. Am. (1)

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

Opt. Acta (3)

H. Pedersen, “On the contrast of polychromatic speckle patterns and its dependence on surface roughness,” Opt. Acta 22, 15–24 (1975).
[Crossref]

K. Nakagawa and T. Asakura, “Average contrast of white-light image speckle patterns,” Opt. Acta 26, 951–960 (1979).
[Crossref]

H. Pedersen, “Second-order statistics of light diffracted from Gaussian, rough surfaces with applications to the roughness dependence of speckles,” Opt. Acta 22, 523–535 (1975).
[Crossref]

Opt. Commun. (4)

M. Elbaum, M. Greenbaum, and M. King, “A wavelength diversity technique for reduction of speckle size,” Opt. Commun. 5, 171–174 (1972).
[Crossref]

J. C. Dainty and W. T. Welford, “Reduction of speckle in image plane hologram reconstruction by moving pupils,” Opt. Commun. 3, 289–294 (1971).
[Crossref]

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

S. Sahin, Z. Tong, and O. Korotkova, “Sensing of semi-rough targets embedded in atmospheric turbulence by means of stochastic electromagnetic beams,” Opt. Commun. 283, 4512–4518 (2010).
[Crossref]

Opt. Eng. (8)

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]

V. Molebny, P. McManamon, O. Steinvall, T. Kobayashi, and W. Chen, “Laser radar: historical prospective—from the East to the West,” Opt. Eng. 56, 031220 (2016).
[Crossref]

P. F. McManamon, “Review of ladar: a historic, yet emerging, sensor technology with rich phenomenology,” Opt. Eng. 51, 060901 (2012).
[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]

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]

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]

M. Laurenzis, Y. Lutz, F. Christnacher, A. Matwyschuk, and J. Poyet, “Homogeneous and speckle-free laser illumination for range-gated imaging and active polarimetry,” Opt. Eng. 51, 061302 (2012).
[Crossref]

L. Tchvialeva, T. K. Lee, I. Markhvida, D. I. McLean, H. Lui, and H. Zeng, “Using a zone model to incorporate the influence of geometry on polychromatic speckle contrast,” Opt. Eng. 47, 074201 (2008).
[Crossref]

Opt. Express (8)

Y. Chen, F. Wang, J. Yu, L. Liu, and Y. Cai, “Vector Hermite-Gaussian correlated Schell-model beam,” Opt. Express 24, 15232–15250 (2016).
[Crossref]

X. Chen, C. Chang, Z. Chen, Z. Lin, and J. Pu, “Generation of stochastic electromagnetic beams with complete controllable coherence,” Opt. Express 24, 21587–21596 (2016).
[Crossref]

Y. Cai, O. Korotkova, H. T. Eyyuboglu, and Y. Baykal, “Active laser radar systems with stochastic electromagnetic beams in turbulent atmosphere,” Opt. Express 16, 15834–15846 (2008).
[Crossref]

J. G. Manni and J. W. Goodman, “Versatile method for achieving 1% speckle contrast in large-venue laser projection displays using a stationary multimode optical fiber,” Opt. Express 20, 11288–11315 (2012).
[Crossref]

H. Mao and D. Zhao, “Second-order intensity-moment characteristics for broadband partially coherent flat-topped beams in atmospheric turbulence,” Opt. Express 18, 1741–1755 (2010).
[Crossref]

C. Zeringue, I. Dajani, S. Naderi, G. T. Moore, and C. Robin, “A theoretical study of transient stimulated Brillouin scattering in optical fibers seeded with phase-modulated light,” Opt. Express 20, 21196–21213 (2012).
[Crossref]

A. V. Harish and J. Nilsson, “Optimization of phase modulation with arbitrary waveform generators for optical spectral control and suppression of stimulated Brillouin scattering,” Opt. Express 23, 6988–6999 (2015).
[Crossref]

B. Anderson, A. Flores, R. Holten, and I. Dajani, “Comparison of phase modulation schemes for coherently combined fiber amplifiers,” Opt. Express 23, 27046–27060 (2015).
[Crossref]

Opt. Lasers Eng. (1)

L. Tchvialeva, I. Markhvida, and T. K. Lee, “Error analysis for polychromatic speckle contrast measurements,” Opt. Lasers 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]

Phys. Rev. Appl. (1)

M. W. Hyde, S. Bose-Pillai, D. G. Voelz, and X. Xiao, “Generation of vector partially coherent optical sources using phase-only spatial light modulators,” Phys. Rev. Appl. 6, 064030 (2016).
[Crossref]

Proc. SPIE (3)

J. Riker, “Requirements on active (laser) tracking and imaging from a technology perspective,” Proc. SPIE 8052, 805202 (2011).
[Crossref]

D. Dayton, J. Allen, R. Nolasco, G. Fertig, and M. Myers, “Comparison of fast correlation algorithms for target tracking,” Proc. SPIE 8520, 85200G (2012).
[Crossref]

N. R. Van Zandt, M. F. Spencer, M. J. Steinbock, B. M. Anderson, M. W. Hyde, and S. T. Fiorino, “Comparison of polychromatic wave-optics models,” Proc. SPIE 9982, 998209 (2016).
[Crossref]

Prog. Opt. (1)

Y. Cai, Y. Chen, J. Yu, X. Liu, and L. Liu, “Generation of partially coherent beams,” Prog. Opt. 62, 157–223 (2017).
[Crossref]

Radio Sci. (1)

Y. Baykal, M. A. Plonus, and S. J. Wang, “The scintillations for weak atmospheric turbulence using a partially coherent source,” Radio Sci. 18, 551–556 (1983).
[Crossref]

Other (17)

M. Steinbock, Directed Energy Directorate, Air Force Research Laboratory (personal communication, 21 April, 2016).

A. Deninger and T. Renner, “12 orders of coherence control,” Toptica Appl-1010 (2010), https://www.toptica.com/fileadmin/Editors_English/12_literature/quantum_technologies/12_orders_of_coherence_control.pdf .

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

G. P. Perram, S. J. Cusumano, R. L. Hengehold, and S. T. Fiorino, Introduction to Laser Weapon Systems (DEPS, 2010).

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

S. C. Coy and B. P. Venet, “Wavetrain user guide,” http://www.mza.com/doc/wavetrain/wtug/main.htm .

TimeLike Systems LLC, “Lightlike user’s manual,” http://www.timelikesystems.com/htmldocs/LightLikeHelp/ .

D. Link, AOSims LLC (personal communication, 6 January, 2016).

J. Barchers, Nutronics Inc., 1851 Lefthand Circle, Longmont, CO, 80501 (personal communication, 2 August, 2016).

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

G. Parry, “Speckle patterns in partially coherent light,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, 1975), pp. 78–120.

R. S. Pierre, G. Holleman, M. Valley, H. Injeyan, J. Berg, G. Harpole, R. Hilyard, M. Mitchell, M. Weber, J. Zamel, T. Engler, D. Hall, R. Tinti, and J. Machan, “Active tracker laser (ATLAS),” in Advanced Solid State Lasers, C. Pollock and W. Bosenberg, eds., OSA Trends in Optics and Photonics Series (Optical Society of America, 1997), Vol. 10, paper HP4.

R. K. Tyson, Introduction to Adaptive Optics (SPIE, 2000).

T. Iwai and T. Asakura, “Speckle reduction in coherent information processing,” in Proceedings of the IEEE (IEEE, 1996), Vol. 84, pp. 765–781.

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

J. W. Goodman, Statistical Optics (Wiley, 1985).

R. D. Richmond and S. C. Cain, Direct-Detection LADAR Systems (SPIE, 2010).

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Figures (14)

Fig. 1.
Fig. 1. Polychromatic illumination of a planar object (a.k.a. target) at a 45° slope. Image-plane speckle is mitigated by the four coherence regions within a single resolution cell on the object.
Fig. 2.
Fig. 2. Example of the Monte Carlo polychromatic simulation method. Images (a), (b), and (c) show the speckle patterns from three random realizations of the object’s roughness. Image (d) is the average of the first three. It is a partially speckled image of the object with the proper ensemble-average speckle strength. The center wavelength is 1.064 μm.
Fig. 3.
Fig. 3. Example of the depth-slicing polychromatic simulation method. Images (a), (b), and (c) show the speckle irradiance from the first three depth slices of a square object. The last image, (d), is the incoherent sum of all slice images. It approximates the partially speckled image of the object. The center wavelength is 1.064 μm.
Fig. 4.
Fig. 4. Gaussian source spectrum broken up into discrete wavelengths for spectral-slicing simulation. The bandwidth shown here produces a coherence length of 1 cm. The center wavelength is 1.064 μm. This spectrum is normalized to integrate to 1.
Fig. 5.
Fig. 5. Example speckle patterns at three consecutive wavelengths in the discrete spectrum (a)–(c), and the weighted sum of the images from all wavelengths (d). Note that the speckle pattern changes slightly from one wavelength to the next due to changes in the laser-object interaction. Also, the wavelength spacing is exaggerated for this figure to accentuate the changes in the speckle pattern.
Fig. 6.
Fig. 6. Aperture positions within the speckle field at two slightly different wavelengths. Owing to the wavelength difference, some of the area of the speckle field never falls within the aperture. Also, there are three regions that contribute to the image-plane speckle pattern. Region 1 is the area of overlap. It is captured by the aperture at both wavelengths. On the other hand, regions 2 and 3 are only captured by the aperture at wavelength 1 and 2, respectively.
Fig. 7.
Fig. 7. Partially overlapping aperture positions for a spectral-slicing simulation with n slices. Each aperture position overlaps only with adjacent positions. In total, there are 2 n 1 distinct regions, each of which contributes a complex field component to the image-plane speckle.
Fig. 8.
Fig. 8. Comparison of speckle contrast results from the spectral-slicing simulation method with the discrete theory ( n = 6 ) and Hu’s theory ( n = ). Agreement is quite good. For the range of fractional overlap shown here (0 to 0.5), the discretization errors are rather large, ranging from 25% down to 7.5%.
Fig. 9.
Fig. 9. Comparison of spectral-slicing simulation results with theory for n = 16 and any degree of overlap. Agreement is excellent. Further, both theory and simulation reach the correct values for the two extreme cases of no overlap ( C = 1 / 16 = 0.25 ) and total overlap (monochromatic; C = 1 ). The three curves with M < 16 show the trend of increasing accuracy as more terms are added to Eq. (22). The vertical-dashed black lines indicate the first three points at which another term must be added to maintain accuracy.
Fig. 10.
Fig. 10. Spectral-slicing simulation error versus the fractional area of overlap in aperture position from one wavelength sample to the next. These results assume the common case of a circular aperture and Gaussian spectrum. Numerically measured, area-predicted, and curve-fitted results are shown. All three agree quite well until about 15% error. Beyond that point, the curve-fitted result more closely matches the data.
Fig. 11.
Fig. 11. Numerical efficiency comparison for well-resolved objects. All plots show the number of propagations needed per speckle image versus both speckle contrast and object width. Width is expressed in terms of the target Fresnel number. The plots represent the (a) Monte Carlo, (b) depth-slicing, and (c) spectral-slicing methods. Note that Monte Carlo is the most efficient, while depth slicing is less efficient than spectral slicing for object widths of about 8 λ / D or wider because increased object width (and depth) requires more depth slices.
Fig. 12.
Fig. 12. Numerical efficiency comparison for small objects. Here, the plot format matches that of Fig. 11. Again, the (a) Monte Carlo, (b) depth-slicing, and (c) spectral-slicing methods are shown. For very small objects, the Monte Carlo and depth-slicing methods are nearly equally efficient, and both are much more efficient than spectral slicing, which loses significant efficiency as the object width shrinks (assuming constant speckle contrast).
Fig. 13.
Fig. 13. Comparison of the simulation methods with theory for the 10-km range. Spectral-slicing results are virtually indistinguishable from the theoretical curve. Monte Carlo and depth slicing also agree well with only small errors.
Fig. 14.
Fig. 14. Comparison of the simulation methods with theory for the 3-km range. Once again, the spectral-slicing curve nearly overlaps the theoretical curve. Depth slicing also agrees very well, though it is a little low for contrast between about 0.75 and 0.95. In that same range, the Monte Carlo results are a bit high.

Equations (24)

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C 2 ( θ i m , θ i l l ) = [ 1 / S ( λ ) d λ ] 2 d λ 1 d λ 2 S ( λ 1 ) S ( λ 2 ) exp ( 4 π 2 σ 2 ( cos ( θ i m ) + cos ( θ i l l ) ) 2 ( 1 / λ 2 1 / λ 1 ) 2 ) × | H ( λ 1 R ( x sin ( θ i l l ) λ 1 cos ( θ i m ) ) , λ 1 R y ) H * ( λ 2 R ( x sin ( θ i l l ) λ 2 cos ( θ i m ) tan ( θ i m ) λ 1 + tan ( θ i m ) λ 2 ) , λ 2 R y ) d x d y | 2 | H ( λ 1 R x , λ 1 R y ) | 2 d x d y | H ( λ 2 R x , λ 2 R y ) | 2 d x d y ,
C = σ I I ¯ ,
N = 2 tan ( θ ) 1.75 λ R D l c ,
N eff = { 1 N erf ( π N ) 1 π N 2 [ 1 exp ( π N 2 ) ] } 1 ,
C = 1 N eff .
N F = D T λ R ,
N F = D W speckle ,
N F = T r diff .
C = m = 1 M I ¯ m 2 m = 1 M I ¯ m ,
Δ x max = l c 2 tan ( θ ) ,
C = n n = 1 n .
I 2 = [ | A 1 + A 2 | 2 + | A 2 + A 3 + A 4 | 2 + + | A 2 n 4 + A 2 n 3 + A 2 n 2 | 2 + | A 2 n 2 + A 2 n 1 | 2 ] 2 ,
I 2 = [ I 1 + 2 I 2 + I 3 + 2 I 4 + + 2 I 2 n 2 + I 2 n 1 ] 2 + + 2 I 1 I 2 + 2 I 2 I 3 + 2 I 3 I 4 + 2 I 2 I 4 + + 2 I 2 n 2 I 2 n 1 ,
I ¯ 2 = ( I ¯ 1 + 2 I ¯ 2 + I ¯ 3 + 2 I ¯ 4 + + 2 I ¯ 2 n 2 + I ¯ 2 n 1 ) 2 ,
σ I 2 = I 2 I ¯ 2 = [ I 1 + 2 I 2 + I 3 + 2 I 4 + + 2 I 2 n 2 + I 2 n 1 ] 2 + + 2 I 1 I 2 + 2 I 2 I 3 + 2 I 3 I 4 + 2 I 2 I 4 + + 2 I 2 n 2 I 2 n 1 ( I ¯ 1 + 2 I ¯ 2 + I ¯ 3 + 2 I ¯ 4 + + 2 I ¯ 2 n 2 + I ¯ 2 n 1 ) 2 .
σ I 2 = I ¯ 1 2 + 4 I ¯ 2 2 + I ¯ 3 2 + 4 I ¯ 4 2 + + 4 I ¯ 2 n 2 2 + I ¯ 2 n 1 2 + 2 I ¯ 1 I ¯ 2 + 2 I ¯ 2 I ¯ 3 + 2 I ¯ 2 I ¯ 4 + 2 I ¯ 3 I ¯ 4 + + 2 I ¯ 2 n 2 I ¯ 2 n 1 .
I ¯ 1 = 1 x , I ¯ 2 = x , I ¯ 3 = 1 2 x , I ¯ 4 = x , I ¯ 2 n 1 = 1 x .
σ I 2 = 2 ( 1 x ) 2 + 4 ( n 1 ) x 2 + ( n 2 ) ( 1 2 x ) 2 + 4 x ( 1 x ) + 2 ( n 2 ) ( 2 x ( 1 2 x ) + x 2 ) .
σ I 2 = 2 ( n 1 ) x 2 + n .
C = σ I 2 I ¯ total = 2 ( n 1 ) x 2 + n n ,
C = 2 ( n 2 ) x 2 2 + 2 ( n 1 ) x 1 2 + n n ,
C = n + m = 1 M 2 ( n m ) x m 2 n , M n ,
A miss = d D π ( D / 2 ) 2 + real [ D 2 / 2 cos 1 ( d / D ) 1 / 2 d D 2 d 2 ] ,
Q = 34.14    s 2 ,

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