Abstract

We start by studying light propagation through a Lau-like arrangement—two Ronchi grids out of phase by half a period—within a turbulent medium. We show that degradation produced by the turbulence can be estimated in terms of the spacing between grids, the number of lines per millimeter, and C2, the structure constant of the medium. We also propose a way to evaluate the structure constant in an experimental arrangement in the laboratory.

© 1999 Optical Society of America

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References

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  1. J. W. Goodman, Statistical Optics (Wiley, New York, 1985), p. 207.
  2. V. U. Zavorotny, V. I. Klyatskin, V. I. Tatarskii, “Strong fluctuations of the intensity of electromagnetic waves in randomly inhomogeneous media,” Sov. Phys. JETP 46, 252–260 (1977).
  3. R. Dashen, “Path integrals for waves in random media,” J. Math. Phys. 20, 894–920 (1979).
    [CrossRef]
  4. V. I. Tatarskii, V. U. Zavorotny, “Strong fluctuations in light propagation in a randomly inhomogeneous medium,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1980), Vol. 18, pp. 207–376.
  5. M. I. Charnotskii, J. Gozani, V. I. Tatarskii, V. U. Zavorotny, “Wave propagation theories in random media based on the path-integral approach,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1993), Vol. 32, pp. 205–266.
  6. M. I. Charnotskii, “Asymptotic analysis of the flux fluctuations averaging and finite size source scintillations in random media,” Waves Random Media 1, 123–243 (1991).
    [CrossRef]
  7. M. I. Charnotskii, “Turbulence effects on the imaging of an object with a sharp edge: asymptotic technique and aperture-plane statistics,” J. Opt. Soc. Am. A 13, 1094–1105 (1996).
    [CrossRef]
  8. V. I. Tatarskii, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).
  9. V. U. Zavorotny, “Origin of intensity fluctuations in the image of an incoherent source observed through a turbulent medium,” Opt. Spectrosc. 65(4), 575–576 (1988).
  10. A. Consortini, Y. Y. Sun, Lin Shi Ping, G. Conforti, “A mixed method for measuring the inner scale of atmospheric turbulence,” J. Mod. Opt. 37, 1555–1560 (1990).
    [CrossRef]
  11. A. Consortini, G. Fusco, F. Rigal, A. Agabi, Y. Y. Sun, “Experiment of thin beam propagation through atmospheric turbulence in the laboratory,” in Optics for Science and New Technologies, G.-S. Chang, G.-H. Lee, S.-Y. Lee, C. H. Nam, eds., Proc. SPIE2778, 1012–1013 (1996).

1996 (1)

1991 (1)

M. I. Charnotskii, “Asymptotic analysis of the flux fluctuations averaging and finite size source scintillations in random media,” Waves Random Media 1, 123–243 (1991).
[CrossRef]

1990 (1)

A. Consortini, Y. Y. Sun, Lin Shi Ping, G. Conforti, “A mixed method for measuring the inner scale of atmospheric turbulence,” J. Mod. Opt. 37, 1555–1560 (1990).
[CrossRef]

1988 (1)

V. U. Zavorotny, “Origin of intensity fluctuations in the image of an incoherent source observed through a turbulent medium,” Opt. Spectrosc. 65(4), 575–576 (1988).

1979 (1)

R. Dashen, “Path integrals for waves in random media,” J. Math. Phys. 20, 894–920 (1979).
[CrossRef]

1977 (1)

V. U. Zavorotny, V. I. Klyatskin, V. I. Tatarskii, “Strong fluctuations of the intensity of electromagnetic waves in randomly inhomogeneous media,” Sov. Phys. JETP 46, 252–260 (1977).

Agabi, A.

A. Consortini, G. Fusco, F. Rigal, A. Agabi, Y. Y. Sun, “Experiment of thin beam propagation through atmospheric turbulence in the laboratory,” in Optics for Science and New Technologies, G.-S. Chang, G.-H. Lee, S.-Y. Lee, C. H. Nam, eds., Proc. SPIE2778, 1012–1013 (1996).

Charnotskii, M. I.

M. I. Charnotskii, “Turbulence effects on the imaging of an object with a sharp edge: asymptotic technique and aperture-plane statistics,” J. Opt. Soc. Am. A 13, 1094–1105 (1996).
[CrossRef]

M. I. Charnotskii, “Asymptotic analysis of the flux fluctuations averaging and finite size source scintillations in random media,” Waves Random Media 1, 123–243 (1991).
[CrossRef]

M. I. Charnotskii, J. Gozani, V. I. Tatarskii, V. U. Zavorotny, “Wave propagation theories in random media based on the path-integral approach,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1993), Vol. 32, pp. 205–266.

Conforti, G.

A. Consortini, Y. Y. Sun, Lin Shi Ping, G. Conforti, “A mixed method for measuring the inner scale of atmospheric turbulence,” J. Mod. Opt. 37, 1555–1560 (1990).
[CrossRef]

Consortini, A.

A. Consortini, Y. Y. Sun, Lin Shi Ping, G. Conforti, “A mixed method for measuring the inner scale of atmospheric turbulence,” J. Mod. Opt. 37, 1555–1560 (1990).
[CrossRef]

A. Consortini, G. Fusco, F. Rigal, A. Agabi, Y. Y. Sun, “Experiment of thin beam propagation through atmospheric turbulence in the laboratory,” in Optics for Science and New Technologies, G.-S. Chang, G.-H. Lee, S.-Y. Lee, C. H. Nam, eds., Proc. SPIE2778, 1012–1013 (1996).

Dashen, R.

R. Dashen, “Path integrals for waves in random media,” J. Math. Phys. 20, 894–920 (1979).
[CrossRef]

Fusco, G.

A. Consortini, G. Fusco, F. Rigal, A. Agabi, Y. Y. Sun, “Experiment of thin beam propagation through atmospheric turbulence in the laboratory,” in Optics for Science and New Technologies, G.-S. Chang, G.-H. Lee, S.-Y. Lee, C. H. Nam, eds., Proc. SPIE2778, 1012–1013 (1996).

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), p. 207.

Gozani, J.

M. I. Charnotskii, J. Gozani, V. I. Tatarskii, V. U. Zavorotny, “Wave propagation theories in random media based on the path-integral approach,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1993), Vol. 32, pp. 205–266.

Klyatskin, V. I.

V. U. Zavorotny, V. I. Klyatskin, V. I. Tatarskii, “Strong fluctuations of the intensity of electromagnetic waves in randomly inhomogeneous media,” Sov. Phys. JETP 46, 252–260 (1977).

Ping, Lin Shi

A. Consortini, Y. Y. Sun, Lin Shi Ping, G. Conforti, “A mixed method for measuring the inner scale of atmospheric turbulence,” J. Mod. Opt. 37, 1555–1560 (1990).
[CrossRef]

Rigal, F.

A. Consortini, G. Fusco, F. Rigal, A. Agabi, Y. Y. Sun, “Experiment of thin beam propagation through atmospheric turbulence in the laboratory,” in Optics for Science and New Technologies, G.-S. Chang, G.-H. Lee, S.-Y. Lee, C. H. Nam, eds., Proc. SPIE2778, 1012–1013 (1996).

Sun, Y. Y.

A. Consortini, Y. Y. Sun, Lin Shi Ping, G. Conforti, “A mixed method for measuring the inner scale of atmospheric turbulence,” J. Mod. Opt. 37, 1555–1560 (1990).
[CrossRef]

A. Consortini, G. Fusco, F. Rigal, A. Agabi, Y. Y. Sun, “Experiment of thin beam propagation through atmospheric turbulence in the laboratory,” in Optics for Science and New Technologies, G.-S. Chang, G.-H. Lee, S.-Y. Lee, C. H. Nam, eds., Proc. SPIE2778, 1012–1013 (1996).

Tatarskii, V. I.

V. U. Zavorotny, V. I. Klyatskin, V. I. Tatarskii, “Strong fluctuations of the intensity of electromagnetic waves in randomly inhomogeneous media,” Sov. Phys. JETP 46, 252–260 (1977).

M. I. Charnotskii, J. Gozani, V. I. Tatarskii, V. U. Zavorotny, “Wave propagation theories in random media based on the path-integral approach,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1993), Vol. 32, pp. 205–266.

V. I. Tatarskii, V. U. Zavorotny, “Strong fluctuations in light propagation in a randomly inhomogeneous medium,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1980), Vol. 18, pp. 207–376.

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

Zavorotny, V. U.

V. U. Zavorotny, “Origin of intensity fluctuations in the image of an incoherent source observed through a turbulent medium,” Opt. Spectrosc. 65(4), 575–576 (1988).

V. U. Zavorotny, V. I. Klyatskin, V. I. Tatarskii, “Strong fluctuations of the intensity of electromagnetic waves in randomly inhomogeneous media,” Sov. Phys. JETP 46, 252–260 (1977).

M. I. Charnotskii, J. Gozani, V. I. Tatarskii, V. U. Zavorotny, “Wave propagation theories in random media based on the path-integral approach,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1993), Vol. 32, pp. 205–266.

V. I. Tatarskii, V. U. Zavorotny, “Strong fluctuations in light propagation in a randomly inhomogeneous medium,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1980), Vol. 18, pp. 207–376.

J. Math. Phys. (1)

R. Dashen, “Path integrals for waves in random media,” J. Math. Phys. 20, 894–920 (1979).
[CrossRef]

J. Mod. Opt. (1)

A. Consortini, Y. Y. Sun, Lin Shi Ping, G. Conforti, “A mixed method for measuring the inner scale of atmospheric turbulence,” J. Mod. Opt. 37, 1555–1560 (1990).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Spectrosc. (1)

V. U. Zavorotny, “Origin of intensity fluctuations in the image of an incoherent source observed through a turbulent medium,” Opt. Spectrosc. 65(4), 575–576 (1988).

Sov. Phys. JETP (1)

V. U. Zavorotny, V. I. Klyatskin, V. I. Tatarskii, “Strong fluctuations of the intensity of electromagnetic waves in randomly inhomogeneous media,” Sov. Phys. JETP 46, 252–260 (1977).

Waves Random Media (1)

M. I. Charnotskii, “Asymptotic analysis of the flux fluctuations averaging and finite size source scintillations in random media,” Waves Random Media 1, 123–243 (1991).
[CrossRef]

Other (5)

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

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), p. 207.

V. I. Tatarskii, V. U. Zavorotny, “Strong fluctuations in light propagation in a randomly inhomogeneous medium,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1980), Vol. 18, pp. 207–376.

M. I. Charnotskii, J. Gozani, V. I. Tatarskii, V. U. Zavorotny, “Wave propagation theories in random media based on the path-integral approach,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1993), Vol. 32, pp. 205–266.

A. Consortini, G. Fusco, F. Rigal, A. Agabi, Y. Y. Sun, “Experiment of thin beam propagation through atmospheric turbulence in the laboratory,” in Optics for Science and New Technologies, G.-S. Chang, G.-H. Lee, S.-Y. Lee, C. H. Nam, eds., Proc. SPIE2778, 1012–1013 (1996).

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Figures (1)

Fig. 1
Fig. 1

Optical system employed here: two grids separated a distance L with equal amplitude transmittance functions. A1 is the outgoing intensity distribution, A2 is the transmittance function (both with period 2d), and I is the intensity distribution at a screen located at z=l.

Equations (18)

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tα(x)=12+1πn=0(-1)n+1(2n+1)cos(2n+1)πd(x+α),
A1(r)=A0t0(eˇx·r)SD×D(r),
whereSD×D=1ifr-D2,D2×-D2,D20otherwise,
I(R)=d2rA1(r)|Gtot(R, l; r,-L)|2,
Gtot(R, l; r,-L)
=d2rG0(R, l; r, 0)A2(r)G(r, 0; r,-L).
G0(r, z; r, z)=-ik2π|z-z|expik(r-r)22|z-z|.
I(R)=A0k4(2π)2l2L2D×Dd2rt0(eˇx·r)×D×Dd2Rd2rtdeˇx·R-r2×tdeˇxR+r2exp-ikfr·R×exp-ikRl+rL·rgR-r2, r, L×g*R+r2, r, L,
I(R)=A0k4(2π)2l2L2D×Dd2rt0(eˇx·r)D×Dd2rCt(r)×expikRl+rL·r,
Iˆ(κ)=A0k2(2π)2L2tˆ0D×D-lLκCtlkκ×Θ(2)12D+lkκΘ(2)12D-lkκ,
l=L/s,
Ig(R)=I0Dλ22q2(p/q+1)d3π8-4π(-1)p/2+p/q+1×n=01(2n+1)2cos(2n+1)πdpqeˇx·R.
V=(p/q+1)16Nl[1+2(-1)p/2+p/q+1].
g(r, r, L)=2πiLkD2vδ0Lv(ξ)dξ×expik20Lv2(ξ)dξ×expik20Lz, rzL+r1-zL+zLv(ξ)dξ.
Iˆ(κ)=A0k2(2π)2L2tˆ0D×D-lLκCtlkκexp-D(lkκ)2×Θ(2)12D+lkκΘ(2)12D-lkκ,
D(μ)=2μ-2πcosπμ2Γμ+12Γ-μ2k2C2,
En=exp-D(μ)2λL2dμ(2n+1)μ
=exp-D(μ)2pμdμ(2n+1)μ.

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