Abstract

Optical path-length fluctuations across a plume of heated air are investigated by various interferometric techniques. Real-time data processing yields spatial and temporal structure functions as well as histograms of optical phase differences. Histograms obtained over a large range of beam separations and beam heights above the heater show an excellent agreement with the class of one-dimensional <i>K</i> distributions. The dependence of the distribution parameters on the probe-beam separation agrees well with a simple empirical model based on four parameters: mean number and mean strength of turbulent eddies and inner and outer eddy scales. The model permits a correct prediction of the averaged intensity in the far field of the screen. Some characteristics of higher-intensity moments can be reproduced by a facet model based on <i>K</i>-distributed phase gradients.

© 1983 Optical Society of America

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1982 (2)

J. G. Walker and E. Jakeman, "Non-Gaussian light scattering by a ruffled water surface," Opt. Acta 29, 313–324 (1982).

K. Schätzel and G. Parry, "Real-time moiré-measurement of phase gradient," Opt. Acta 29, 1441–1445 (1982).

1981 (4)

E. O. Schulz-DuBois and I. Rehberg, "Structure function in lieu of correlation function," Appl. Phys. 24, 323–329 (1981).

E. Jakeman and J. G. McWhirter, "Non-Gaussian scattering by a random phase screen," Appl. Phys. B26, 125–131 (1981).

V. P. Lukin and V. V. Pokasov, "Optical wave phase fluctuations," Appl. Opt. 20, 121–135 (1981).

D. Bensimon, A. Englander, S. Shtrikman, M. Slatkine, and D. Treves, "Statistical properties of He–Ne laser radiation reflected through a turbulent atmosphere," Appl. Opt. 20, 947 (1981).

1980 (2)

K. Schätzel, "Interferometric analysis of deep random phase screens," Opt. Lett. 5, 389–391 (1980).

E. Jakeman, "On the statistics of K-distributed noise," J. Phys. A13, 31–48 (1980).

1979 (1)

B. J. Hoenders, E. Jakeman, H. P. Baltes, and B. Steinle, "Kcorrelations and facet models in diffuse scattering," Opt. Acta 26, 1307–1319 (1979).

1978 (1)

E. Jakeman and P. Pusey, "Significance of K-distributions in scattering experiments," Phys. Rev. Lett. 40, 546–550 (1978).

1977 (3)

A. Zardecki and C. Deslisle, "Higher-order statistics of light scattered by a random phase screen," Opt. Acta 24, 241–259 (1977).

G. Parry, P. N. Pusey, E. Jakeman, and J. G. McWhirter, "Focussing by a random phase screen," Opt. Commun. 22, 195–201 (1977).

J. W. Hardy, J. E. Lefebvre, and C. L. Koliopoulos, "Real-time atmospheric compensation," J. Opt. Soc. Am. 67, 360–369 (1977).

1976 (1)

1975 (4)

G. K. Born, R. Bogenberger, K. D. Erben, F. Frank, F. Mohr, and G. Sepp, "Phase front distortion of laser radiation in a turbulent atmosphere," Appl. Opt. 14, 2857–2863 (1975).

E. Jakeman and P. N. Pusey, "Non-Gaussian fluctuations in electromagnetic radiation scattered by a random phase screen, I. Theory," J. Phys. A8, 369–391 (1975).

M. J. Lavan, W. K. Chawallender, and T. F. Deyoung, "Heterodyne interferometer to determine relative optical phase changes," Rev. Sci. Instrum. 46, 525–527 (1975).

Y. Ohtsuka and I. Sasaki, "Light-beam method to process phase fluctuations of a laser light beam," Appl. Phys. 7, 265–270 (1975).

1974 (1)

Y. Ohtsuka and I. Sasaki, "Light-beat measurements of phase fluctuations of a laser-beam propagating through a turbulent atmosphere," Appl. Phys. 3, 15–20 (1974).

1973 (3)

D. Kelsall, "Optical seeing through the atmosphere by an interferometric technique," J. Opt. Soc. Am. 63, 1473–1484 (1973).

E. Jakeman and P. Pusey, "The statistics of light scattered by a random phase screen," J. Phys. A6, L88–92 (1973).

J. A. Dowling and P. M. Livingstone, "Behavior of focused beams in atmospheric turbulence: measurements and comment on the theory," J. Opt. Soc. Am. 63, 846–858 (1973).

1971 (2)

1970 (6)

1969 (1)

1968 (1)

1967 (2)

1966 (1)

Ackley, M. H.

Baltes, H. P.

B. J. Hoenders, E. Jakeman, H. P. Baltes, and B. Steinle, "Kcorrelations and facet models in diffuse scattering," Opt. Acta 26, 1307–1319 (1979).

Bensimon, D.

Bertolotti, M.

Bogenberger, R.

Born, G. K.

Bouricius, G. M. B.

Breckinridge, J. B.

Buck, A. L.

Burlamacchi, P.

Buser, R. G.

Carnevale, M.

Chawallender, W. K.

M. J. Lavan, W. K. Chawallender, and T. F. Deyoung, "Heterodyne interferometer to determine relative optical phase changes," Rev. Sci. Instrum. 46, 525–527 (1975).

Clifford, S. F.

Consortini, A.

Crosignani, B.

Deslisle, C.

A. Zardecki and C. Deslisle, "Higher-order statistics of light scattered by a random phase screen," Opt. Acta 24, 241–259 (1977).

Deyoung, T. F.

M. J. Lavan, W. K. Chawallender, and T. F. Deyoung, "Heterodyne interferometer to determine relative optical phase changes," Rev. Sci. Instrum. 46, 525–527 (1975).

DiPorto, P.

Dowling, J. A.

Englander, A.

Erben, K. D.

Frank, F.

Gradsteyn, I. S.

I. S. Gradsteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1970).

Hardy, J. W.

Herrick, R. B.

Hoenders, B. J.

B. J. Hoenders, E. Jakeman, H. P. Baltes, and B. Steinle, "Kcorrelations and facet models in diffuse scattering," Opt. Acta 26, 1307–1319 (1979).

Jakeman, E.

J. G. Walker and E. Jakeman, "Non-Gaussian light scattering by a ruffled water surface," Opt. Acta 29, 313–324 (1982).

E. Jakeman and J. G. McWhirter, "Non-Gaussian scattering by a random phase screen," Appl. Phys. B26, 125–131 (1981).

E. Jakeman, "On the statistics of K-distributed noise," J. Phys. A13, 31–48 (1980).

B. J. Hoenders, E. Jakeman, H. P. Baltes, and B. Steinle, "Kcorrelations and facet models in diffuse scattering," Opt. Acta 26, 1307–1319 (1979).

E. Jakeman and P. Pusey, "Significance of K-distributions in scattering experiments," Phys. Rev. Lett. 40, 546–550 (1978).

G. Parry, P. N. Pusey, E. Jakeman, and J. G. McWhirter, "Focussing by a random phase screen," Opt. Commun. 22, 195–201 (1977).

E. Jakeman and P. N. Pusey, "Non-Gaussian fluctuations in electromagnetic radiation scattered by a random phase screen, I. Theory," J. Phys. A8, 369–391 (1975).

E. Jakeman and P. Pusey, "The statistics of light scattered by a random phase screen," J. Phys. A6, L88–92 (1973).

Kelsall, D.

D. Kelsall, "Optical seeing through the atmosphere by an interferometric technique," J. Opt. Soc. Am. 63, 1473–1484 (1973).

Koliopoulos, C. L.

Lavan, M. J.

M. J. Lavan, W. K. Chawallender, and T. F. Deyoung, "Heterodyne interferometer to determine relative optical phase changes," Rev. Sci. Instrum. 46, 525–527 (1975).

Lefebvre, J. E.

Livingstone, P. M.

Lukin, V. P.

McWhirter, J. G.

E. Jakeman and J. G. McWhirter, "Non-Gaussian scattering by a random phase screen," Appl. Phys. B26, 125–131 (1981).

G. Parry, P. N. Pusey, E. Jakeman, and J. G. McWhirter, "Focussing by a random phase screen," Opt. Commun. 22, 195–201 (1977).

Merz, J.

J. Merz, "Lichtstreuung am Phasenschirm," Diplomarbeit, Kiel (1981).

Meyer-Arendt, J. R.

Mohr, F.

Muzii, L.

Muzzi, L.

Ochs, G R.

Ohtsubo, J.

J. Ohtsubo, "Non-Gaussian speckle: a computer simulation," submitted to Appl. Opt. (1982).

Ohtsuka, Y.

Y. Ohtsuka and I. Sasaki, "Light-beam method to process phase fluctuations of a laser light beam," Appl. Phys. 7, 265–270 (1975).

Y. Ohtsuka and I. Sasaki, "Light-beat measurements of phase fluctuations of a laser-beam propagating through a turbulent atmosphere," Appl. Phys. 3, 15–20 (1974).

Parry, G.

K. Schätzel and G. Parry, "Real-time moiré-measurement of phase gradient," Opt. Acta 29, 1441–1445 (1982).

G. Parry, P. N. Pusey, E. Jakeman, and J. G. McWhirter, "Focussing by a random phase screen," Opt. Commun. 22, 195–201 (1977).

Pokasov, V. V.

Pusey, P.

E. Jakeman and P. Pusey, "Significance of K-distributions in scattering experiments," Phys. Rev. Lett. 40, 546–550 (1978).

E. Jakeman and P. Pusey, "The statistics of light scattered by a random phase screen," J. Phys. A6, L88–92 (1973).

Pusey, P. N.

G. Parry, P. N. Pusey, E. Jakeman, and J. G. McWhirter, "Focussing by a random phase screen," Opt. Commun. 22, 195–201 (1977).

E. Jakeman and P. N. Pusey, "Non-Gaussian fluctuations in electromagnetic radiation scattered by a random phase screen, I. Theory," J. Phys. A8, 369–391 (1975).

Rehberg, I.

E. O. Schulz-DuBois and I. Rehberg, "Structure function in lieu of correlation function," Appl. Phys. 24, 323–329 (1981).

Ronchi, L.

Ryzhik, I. M.

I. S. Gradsteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1970).

Sasaki, I.

Y. Ohtsuka and I. Sasaki, "Light-beam method to process phase fluctuations of a laser light beam," Appl. Phys. 7, 265–270 (1975).

Y. Ohtsuka and I. Sasaki, "Light-beat measurements of phase fluctuations of a laser-beam propagating through a turbulent atmosphere," Appl. Phys. 3, 15–20 (1974).

Schätzel, K.

K. Schätzel and G. Parry, "Real-time moiré-measurement of phase gradient," Opt. Acta 29, 1441–1445 (1982).

K. Schätzel, "Interferometric analysis of deep random phase screens," Opt. Lett. 5, 389–391 (1980).

K. Schätzel, "Fluktuationen der optischen Weglänge in turbulenten Phasenobjekten," Dissertation, Kiel (1982).

K. Schätzel, "Two-point statistics of turbulent deep random phase screens," in Proceedings of the 4th Conference on Photon Correlation Techniques in Fluid Dynamics, W. T. Mayo and A. E. Smart, eds. (Stanford U. Press, Stanford, Calif., 1980), paper 23.

Schulz-DuBois, E. O.

E. O. Schulz-DuBois and I. Rehberg, "Structure function in lieu of correlation function," Appl. Phys. 24, 323–329 (1981).

Sepp, G.

Sette, D.

Shtrikman, S.

Slatkine, M.

Steinle, B.

B. J. Hoenders, E. Jakeman, H. P. Baltes, and B. Steinle, "Kcorrelations and facet models in diffuse scattering," Opt. Acta 26, 1307–1319 (1979).

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Random Medium (McGraw-Hill, New York, 1961).

Treves, D.

Walker, J. G.

J. G. Walker and E. Jakeman, "Non-Gaussian light scattering by a ruffled water surface," Opt. Acta 29, 313–324 (1982).

Zardecki, A.

A. Zardecki and C. Deslisle, "Higher-order statistics of light scattered by a random phase screen," Opt. Acta 24, 241–259 (1977).

Appl. Opt. (9)

Appl. Phys. (4)

E. Jakeman and J. G. McWhirter, "Non-Gaussian scattering by a random phase screen," Appl. Phys. B26, 125–131 (1981).

Y. Ohtsuka and I. Sasaki, "Light-beat measurements of phase fluctuations of a laser-beam propagating through a turbulent atmosphere," Appl. Phys. 3, 15–20 (1974).

Y. Ohtsuka and I. Sasaki, "Light-beam method to process phase fluctuations of a laser light beam," Appl. Phys. 7, 265–270 (1975).

E. O. Schulz-DuBois and I. Rehberg, "Structure function in lieu of correlation function," Appl. Phys. 24, 323–329 (1981).

J. Opt. Soc. Am. (9)

J. Phys. (3)

E. Jakeman, "On the statistics of K-distributed noise," J. Phys. A13, 31–48 (1980).

E. Jakeman and P. Pusey, "The statistics of light scattered by a random phase screen," J. Phys. A6, L88–92 (1973).

E. Jakeman and P. N. Pusey, "Non-Gaussian fluctuations in electromagnetic radiation scattered by a random phase screen, I. Theory," J. Phys. A8, 369–391 (1975).

Opt. Acta (4)

A. Zardecki and C. Deslisle, "Higher-order statistics of light scattered by a random phase screen," Opt. Acta 24, 241–259 (1977).

B. J. Hoenders, E. Jakeman, H. P. Baltes, and B. Steinle, "Kcorrelations and facet models in diffuse scattering," Opt. Acta 26, 1307–1319 (1979).

J. G. Walker and E. Jakeman, "Non-Gaussian light scattering by a ruffled water surface," Opt. Acta 29, 313–324 (1982).

K. Schätzel and G. Parry, "Real-time moiré-measurement of phase gradient," Opt. Acta 29, 1441–1445 (1982).

Opt. Commun. (1)

G. Parry, P. N. Pusey, E. Jakeman, and J. G. McWhirter, "Focussing by a random phase screen," Opt. Commun. 22, 195–201 (1977).

Opt. Lett. (1)

Phys. Lett. (1)

G. K. Born, "Phase front distortion of a laser beam by atmospheric turbulence," Phys. Lett. 33A, 397–398 (1970).

Phys. Rev. Lett. (1)

E. Jakeman and P. Pusey, "Significance of K-distributions in scattering experiments," Phys. Rev. Lett. 40, 546–550 (1978).

Rev. Sci. Instrum. (2)

M. J. Lavan, W. K. Chawallender, and T. F. Deyoung, "Heterodyne interferometer to determine relative optical phase changes," Rev. Sci. Instrum. 46, 525–527 (1975).

G. M. B. Bouricius and S. F. Clifford, "An optical interferometer using polarization coding to obtain quadrature phase components," Rev. Sci. Instrum. 41, 1800–1803 (1970).

Other (7)

H. P. Baltes, ed., Inverse Source Problems (Springer-Verlag, Berlin, 1978).

J. Ohtsubo, "Non-Gaussian speckle: a computer simulation," submitted to Appl. Opt. (1982).

J. Merz, "Lichtstreuung am Phasenschirm," Diplomarbeit, Kiel (1981).

V. I. Tatarski, Wave Propagation in a Random Medium (McGraw-Hill, New York, 1961).

K. Schätzel, "Fluktuationen der optischen Weglänge in turbulenten Phasenobjekten," Dissertation, Kiel (1982).

K. Schätzel, "Two-point statistics of turbulent deep random phase screens," in Proceedings of the 4th Conference on Photon Correlation Techniques in Fluid Dynamics, W. T. Mayo and A. E. Smart, eds. (Stanford U. Press, Stanford, Calif., 1980), paper 23.

I. S. Gradsteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1970).

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