J. M. Nichols, C. C. Olson, J. V. Michalowitz, and F. Bucholtz, “A simple algorithm for generating spectrally colored non-Gaussian signals,” Prob. Eng. Mech. 25, 315–322 (2010).

[CrossRef]

J. Mendez and S. Castanedo, “A probability distribution for depth-limited extreme wave heights in a sea state,” Coastal Eng. 54, 878–882 (2007).

[CrossRef]

S. C. Pryor, M. Nielsen, R. J. Barthelmie, and J. Mann, “Can satellite sampling of off shore wind speeds realistically represent wind speed distributions? Part II: Quantifying uncertainties associated with distribution fitting methods,” J. Appl. Meteorol. Climatol. 43, 739–750 (2004).

[CrossRef]

A. Garcia-Martin, R. Gomez-Medina, J. J. Saenz, and M. Nieto-Vesperinas, “Finite-size effects in the spatial distribution of the intensity reflected from disordered media,” Phys. Rev. B 62, 9386–9389 (2000).

[CrossRef]

P. Lehmann, A. Schone, and J. Peters, “Non-Gaussian far field fluctuations in laser light scattered by a random phase screen,” Optik 95, 63–72 (1993).

M. Shinozuka and G. Deodatis, “Simulation of stochastic processes by spectral representation,” Appl. Mech. Rev. 44, 191–204 (1991).

[CrossRef]

M. Shinozuka and G. Deodatis, “Simulation of stochastic processes by spectral representation,” Appl. Mech. Rev. 44, 191–204 (1991).

[CrossRef]

M. Shinozuka and C. M. Jan, “Digital simulation of random processes and its application,” J. Sound Vib. 25, 111–128 (1972).

[CrossRef]

Y. Aizu and T. Asakura, Spatial Filtering Velocimetry, Fundamentals and Applications, Vol. 116 of Springer Ser. Opt. Sci. (Springer-Verlag, 2006).

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001), Chap. 2.

[CrossRef]

Y. Aizu and T. Asakura, Spatial Filtering Velocimetry, Fundamentals and Applications, Vol. 116 of Springer Ser. Opt. Sci. (Springer-Verlag, 2006).

S. C. Pryor, M. Nielsen, R. J. Barthelmie, and J. Mann, “Can satellite sampling of off shore wind speeds realistically represent wind speed distributions? Part II: Quantifying uncertainties associated with distribution fitting methods,” J. Appl. Meteorol. Climatol. 43, 739–750 (2004).

[CrossRef]

S. Minfen, F. H. Y. Chan, and P. J. Beadle, “A method for generating non-Gaussian noise series with specified probability distribution and power spectrum,” in ISCAS ’03. Proceedings of the 2003 International Symposium on Circuits and Systems (IEEE, 2003), Vol. 2, II-1–II-4.

[CrossRef]

P. Beckmann, Probability in Communication Engineering (Harcourt, Brace & World, 1967), Section 6.6.

P. Bratley, B. L. Fox, and L. E. Schrage, A Guide to Simulation, 2nd ed. (Springer-Verlag, 1987).

[CrossRef]

J. M. Nichols, C. C. Olson, J. V. Michalowitz, and F. Bucholtz, “A simple algorithm for generating spectrally colored non-Gaussian signals,” Prob. Eng. Mech. 25, 315–322 (2010).

[CrossRef]

J. Mendez and S. Castanedo, “A probability distribution for depth-limited extreme wave heights in a sea state,” Coastal Eng. 54, 878–882 (2007).

[CrossRef]

S. Minfen, F. H. Y. Chan, and P. J. Beadle, “A method for generating non-Gaussian noise series with specified probability distribution and power spectrum,” in ISCAS ’03. Proceedings of the 2003 International Symposium on Circuits and Systems (IEEE, 2003), Vol. 2, II-1–II-4.

[CrossRef]

M. Shinozuka and G. Deodatis, “Simulation of stochastic processes by spectral representation,” Appl. Mech. Rev. 44, 191–204 (1991).

[CrossRef]

M. Shinozuka and G. Deodatis, “Simulation of stochastic processes by spectral representation,” Appl. Mech. Rev. 44, 191–204 (1991).

[CrossRef]

P. Bratley, B. L. Fox, and L. E. Schrage, A Guide to Simulation, 2nd ed. (Springer-Verlag, 1987).

[CrossRef]

A. Garcia-Martin, R. Gomez-Medina, J. J. Saenz, and M. Nieto-Vesperinas, “Finite-size effects in the spatial distribution of the intensity reflected from disordered media,” Phys. Rev. B 62, 9386–9389 (2000).

[CrossRef]

A. Garcia-Martin, R. Gomez-Medina, J. J. Saenz, and M. Nieto-Vesperinas, “Finite-size effects in the spatial distribution of the intensity reflected from disordered media,” Phys. Rev. B 62, 9386–9389 (2000).

[CrossRef]

J. W. Goodman, “Speckle with a finite number of steps,” Appl. Opt. 47, A111–A118 (2008).

[CrossRef]
[PubMed]

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications, (Roberts, 2006), Section 3.2.2.

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts, 2006), Section 3.6.

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts, 2006).

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001), Chap. 2.

[CrossRef]

M. Shinozuka and C. M. Jan, “Digital simulation of random processes and its application,” J. Sound Vib. 25, 111–128 (1972).

[CrossRef]

H. Satoh, K. Sekiya, T. Kawakami, Y. Kuratomi, B. Katagiri, Y. Suzuki, and T. Uchida, “On the effect of small moving diffusers to the speckle reduction in laser projection displays,” in IDW ’09—Proceedings of the 16th International Display Workshops (2009), pp. 1361–1364.

H. Satoh, K. Sekiya, T. Kawakami, Y. Kuratomi, B. Katagiri, Y. Suzuki, and T. Uchida, “On the effect of small moving diffusers to the speckle reduction in laser projection displays,” in IDW ’09—Proceedings of the 16th International Display Workshops (2009), pp. 1361–1364.

D. V. Kiesewetter, “Numerical simulation of a speckle pattern formed by radiation of optical vortices in a multimode optical fibre,” Quantum Electron. 38, 172–180 (2008).

[CrossRef]

H. Satoh, K. Sekiya, T. Kawakami, Y. Kuratomi, B. Katagiri, Y. Suzuki, and T. Uchida, “On the effect of small moving diffusers to the speckle reduction in laser projection displays,” in IDW ’09—Proceedings of the 16th International Display Workshops (2009), pp. 1361–1364.

P. Lehmann, A. Schone, and J. Peters, “Non-Gaussian far field fluctuations in laser light scattered by a random phase screen,” Optik 95, 63–72 (1993).

S. C. Pryor, M. Nielsen, R. J. Barthelmie, and J. Mann, “Can satellite sampling of off shore wind speeds realistically represent wind speed distributions? Part II: Quantifying uncertainties associated with distribution fitting methods,” J. Appl. Meteorol. Climatol. 43, 739–750 (2004).

[CrossRef]

J. Mendez and S. Castanedo, “A probability distribution for depth-limited extreme wave heights in a sea state,” Coastal Eng. 54, 878–882 (2007).

[CrossRef]

J. M. Nichols, C. C. Olson, J. V. Michalowitz, and F. Bucholtz, “A simple algorithm for generating spectrally colored non-Gaussian signals,” Prob. Eng. Mech. 25, 315–322 (2010).

[CrossRef]

S. Minfen, F. H. Y. Chan, and P. J. Beadle, “A method for generating non-Gaussian noise series with specified probability distribution and power spectrum,” in ISCAS ’03. Proceedings of the 2003 International Symposium on Circuits and Systems (IEEE, 2003), Vol. 2, II-1–II-4.

[CrossRef]

J. M. Nichols, C. C. Olson, J. V. Michalowitz, and F. Bucholtz, “A simple algorithm for generating spectrally colored non-Gaussian signals,” Prob. Eng. Mech. 25, 315–322 (2010).

[CrossRef]

S. C. Pryor, M. Nielsen, R. J. Barthelmie, and J. Mann, “Can satellite sampling of off shore wind speeds realistically represent wind speed distributions? Part II: Quantifying uncertainties associated with distribution fitting methods,” J. Appl. Meteorol. Climatol. 43, 739–750 (2004).

[CrossRef]

A. Garcia-Martin, R. Gomez-Medina, J. J. Saenz, and M. Nieto-Vesperinas, “Finite-size effects in the spatial distribution of the intensity reflected from disordered media,” Phys. Rev. B 62, 9386–9389 (2000).

[CrossRef]

J. M. Nichols, C. C. Olson, J. V. Michalowitz, and F. Bucholtz, “A simple algorithm for generating spectrally colored non-Gaussian signals,” Prob. Eng. Mech. 25, 315–322 (2010).

[CrossRef]

P. Lehmann, A. Schone, and J. Peters, “Non-Gaussian far field fluctuations in laser light scattered by a random phase screen,” Optik 95, 63–72 (1993).

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001), Chap. 2.

[CrossRef]

S. C. Pryor, M. Nielsen, R. J. Barthelmie, and J. Mann, “Can satellite sampling of off shore wind speeds realistically represent wind speed distributions? Part II: Quantifying uncertainties associated with distribution fitting methods,” J. Appl. Meteorol. Climatol. 43, 739–750 (2004).

[CrossRef]

S. O. Rice, “Mathematical analysis of random noise,” in Selected Papers on Noise and Stochastic Processes (Dover, 1954).

R. W. Rubinstein, Simulation and the Monte Carlo Method(Wiley, 1981).

[CrossRef]

A. Garcia-Martin, R. Gomez-Medina, J. J. Saenz, and M. Nieto-Vesperinas, “Finite-size effects in the spatial distribution of the intensity reflected from disordered media,” Phys. Rev. B 62, 9386–9389 (2000).

[CrossRef]

H. Satoh, K. Sekiya, T. Kawakami, Y. Kuratomi, B. Katagiri, Y. Suzuki, and T. Uchida, “On the effect of small moving diffusers to the speckle reduction in laser projection displays,” in IDW ’09—Proceedings of the 16th International Display Workshops (2009), pp. 1361–1364.

P. Lehmann, A. Schone, and J. Peters, “Non-Gaussian far field fluctuations in laser light scattered by a random phase screen,” Optik 95, 63–72 (1993).

P. Bratley, B. L. Fox, and L. E. Schrage, A Guide to Simulation, 2nd ed. (Springer-Verlag, 1987).

[CrossRef]

H. Satoh, K. Sekiya, T. Kawakami, Y. Kuratomi, B. Katagiri, Y. Suzuki, and T. Uchida, “On the effect of small moving diffusers to the speckle reduction in laser projection displays,” in IDW ’09—Proceedings of the 16th International Display Workshops (2009), pp. 1361–1364.

M. Shinozuka and G. Deodatis, “Simulation of stochastic processes by spectral representation,” Appl. Mech. Rev. 44, 191–204 (1991).

[CrossRef]

M. Shinozuka and G. Deodatis, “Simulation of stochastic processes by spectral representation,” Appl. Mech. Rev. 44, 191–204 (1991).

[CrossRef]

F. Yamazaki and M. Shinozuka, “Digital generation of non-Gaussian stochastic fields,” J. Eng. Mech. Div., Am. Soc. Civ. Eng. 114, 1183–1197 (1988).

[CrossRef]

M. Shinozuka and C. M. Jan, “Digital simulation of random processes and its application,” J. Sound Vib. 25, 111–128 (1972).

[CrossRef]

H. Satoh, K. Sekiya, T. Kawakami, Y. Kuratomi, B. Katagiri, Y. Suzuki, and T. Uchida, “On the effect of small moving diffusers to the speckle reduction in laser projection displays,” in IDW ’09—Proceedings of the 16th International Display Workshops (2009), pp. 1361–1364.

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translations, 1971).

H. Satoh, K. Sekiya, T. Kawakami, Y. Kuratomi, B. Katagiri, Y. Suzuki, and T. Uchida, “On the effect of small moving diffusers to the speckle reduction in laser projection displays,” in IDW ’09—Proceedings of the 16th International Display Workshops (2009), pp. 1361–1364.

F. Yamazaki and M. Shinozuka, “Digital generation of non-Gaussian stochastic fields,” J. Eng. Mech. Div., Am. Soc. Civ. Eng. 114, 1183–1197 (1988).

[CrossRef]

M. Shinozuka and G. Deodatis, “Simulation of stochastic processes by spectral representation,” Appl. Mech. Rev. 44, 191–204 (1991).

[CrossRef]

M. Shinozuka and G. Deodatis, “Simulation of stochastic processes by spectral representation,” Appl. Mech. Rev. 44, 191–204 (1991).

[CrossRef]

J. Mendez and S. Castanedo, “A probability distribution for depth-limited extreme wave heights in a sea state,” Coastal Eng. 54, 878–882 (2007).

[CrossRef]

S. C. Pryor, M. Nielsen, R. J. Barthelmie, and J. Mann, “Can satellite sampling of off shore wind speeds realistically represent wind speed distributions? Part II: Quantifying uncertainties associated with distribution fitting methods,” J. Appl. Meteorol. Climatol. 43, 739–750 (2004).

[CrossRef]

F. Yamazaki and M. Shinozuka, “Digital generation of non-Gaussian stochastic fields,” J. Eng. Mech. Div., Am. Soc. Civ. Eng. 114, 1183–1197 (1988).

[CrossRef]

M. Shinozuka and C. M. Jan, “Digital simulation of random processes and its application,” J. Sound Vib. 25, 111–128 (1972).

[CrossRef]

P. Lehmann, A. Schone, and J. Peters, “Non-Gaussian far field fluctuations in laser light scattered by a random phase screen,” Optik 95, 63–72 (1993).

A. Garcia-Martin, R. Gomez-Medina, J. J. Saenz, and M. Nieto-Vesperinas, “Finite-size effects in the spatial distribution of the intensity reflected from disordered media,” Phys. Rev. B 62, 9386–9389 (2000).

[CrossRef]

J. M. Nichols, C. C. Olson, J. V. Michalowitz, and F. Bucholtz, “A simple algorithm for generating spectrally colored non-Gaussian signals,” Prob. Eng. Mech. 25, 315–322 (2010).

[CrossRef]

D. V. Kiesewetter, “Numerical simulation of a speckle pattern formed by radiation of optical vortices in a multimode optical fibre,” Quantum Electron. 38, 172–180 (2008).

[CrossRef]

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts, 2006), Section 3.6.

H. Satoh, K. Sekiya, T. Kawakami, Y. Kuratomi, B. Katagiri, Y. Suzuki, and T. Uchida, “On the effect of small moving diffusers to the speckle reduction in laser projection displays,” in IDW ’09—Proceedings of the 16th International Display Workshops (2009), pp. 1361–1364.

Wolfram Mathematica, Version 7 (Cambridge University, 2008).

P. Bratley, B. L. Fox, and L. E. Schrage, A Guide to Simulation, 2nd ed. (Springer-Verlag, 1987).

[CrossRef]

R. W. Rubinstein, Simulation and the Monte Carlo Method(Wiley, 1981).

[CrossRef]

S. O. Rice, “Mathematical analysis of random noise,” in Selected Papers on Noise and Stochastic Processes (Dover, 1954).

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts, 2006).

P. Beckmann, Probability in Communication Engineering (Harcourt, Brace & World, 1967), Section 6.6.

S. Minfen, F. H. Y. Chan, and P. J. Beadle, “A method for generating non-Gaussian noise series with specified probability distribution and power spectrum,” in ISCAS ’03. Proceedings of the 2003 International Symposium on Circuits and Systems (IEEE, 2003), Vol. 2, II-1–II-4.

[CrossRef]

Y. Aizu and T. Asakura, Spatial Filtering Velocimetry, Fundamentals and Applications, Vol. 116 of Springer Ser. Opt. Sci. (Springer-Verlag, 2006).

In this regard we note, for ν=1/2, Eq. becomes an exponential, whose first and second derivative evaluated at the origin are −1 and 1, respectively, and thus cannot be representative of a real physical process.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001), Chap. 2.

[CrossRef]

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translations, 1971).

The CDF of the Rice–Nakagami distribution can be expressed in terms of a Marcum Q function, which are tabulated, but not supported, to the best of our knowledge, by any commercial commuter programs such as Mathematica and MATLAB.

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications, (Roberts, 2006), Section 3.2.2.