Abstract

Previous studies have shown that the isoplanatic angle (θ0) can be measured by using plane-wave scintillation. The problem of measuring the isoplanatic angle in a finite distance using spherical-wave scintillation is considered in this Letter. Based on theoretical analysis and numerical evaluation, we found that by selecting suitable aperture size and aperture separations, the isoplanatic angle can be estimated through spherical-wave scintillation and covariance of irradiance in three received apertures using a point source. The error of θ0 measured by this method is less than 6% in typical turbulence models.

© 2014 Optical Society of America

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References

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2013 (1)

L.-K. Yu, Y. Wu, Z.-H. Hou, and X. Jing, Acta Opt. Sin. 33, 1201004 (2013).
[CrossRef]

2012 (1)

J. P. Bos, A. V. Sergeyev, and M. C. Roggemann, Proc. SPIE 8246, 82460N (2012).
[CrossRef]

2009 (1)

L. C. Andrews, R. L. Phillips, D. Wayne, T. Leclerc, P. Sauer, R. Crabbs, and J. Kiriazes, Proc. SPIE 7324, 732402 (2009).
[CrossRef]

2008 (1)

1997 (1)

1979 (1)

1967 (1)

Andrews, L. C.

L. C. Andrews, R. L. Phillips, D. Wayne, T. Leclerc, P. Sauer, R. Crabbs, and J. Kiriazes, Proc. SPIE 7324, 732402 (2009).
[CrossRef]

Bos, J. P.

J. P. Bos, A. V. Sergeyev, and M. C. Roggemann, Proc. SPIE 8246, 82460N (2012).
[CrossRef]

Bradford, L. W.

Crabbs, R.

L. C. Andrews, R. L. Phillips, D. Wayne, T. Leclerc, P. Sauer, R. Crabbs, and J. Kiriazes, Proc. SPIE 7324, 732402 (2009).
[CrossRef]

Fried, D. L.

Hogge, C. B.

Hou, Z.

L. Yu, H. Shen, X. Jing, Z. Hou, and Y. Wu, “Study on the measurement of θ0 using stellar scintillation,” Acta Opt. Sin. (to be published).

Hou, Z.-H.

L.-K. Yu, Y. Wu, Z.-H. Hou, and X. Jing, Acta Opt. Sin. 33, 1201004 (2013).
[CrossRef]

Jing, X.

L.-K. Yu, Y. Wu, Z.-H. Hou, and X. Jing, Acta Opt. Sin. 33, 1201004 (2013).
[CrossRef]

L. Yu, H. Shen, X. Jing, Z. Hou, and Y. Wu, “Study on the measurement of θ0 using stellar scintillation,” Acta Opt. Sin. (to be published).

Kiriazes, J.

L. C. Andrews, R. L. Phillips, D. Wayne, T. Leclerc, P. Sauer, R. Crabbs, and J. Kiriazes, Proc. SPIE 7324, 732402 (2009).
[CrossRef]

Leclerc, T.

L. C. Andrews, R. L. Phillips, D. Wayne, T. Leclerc, P. Sauer, R. Crabbs, and J. Kiriazes, Proc. SPIE 7324, 732402 (2009).
[CrossRef]

Loos, G. C.

Louthain, J. A.

Phillips, R. L.

L. C. Andrews, R. L. Phillips, D. Wayne, T. Leclerc, P. Sauer, R. Crabbs, and J. Kiriazes, Proc. SPIE 7324, 732402 (2009).
[CrossRef]

Roggemann, M. C.

J. P. Bos, A. V. Sergeyev, and M. C. Roggemann, Proc. SPIE 8246, 82460N (2012).
[CrossRef]

Sasiela, R. J.

R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence: Evaluation and Application of Mellin Transforms (Springer-Verlag, 2007).

Sauer, P.

L. C. Andrews, R. L. Phillips, D. Wayne, T. Leclerc, P. Sauer, R. Crabbs, and J. Kiriazes, Proc. SPIE 7324, 732402 (2009).
[CrossRef]

Schmidt, J. D.

Sergeyev, A. V.

J. P. Bos, A. V. Sergeyev, and M. C. Roggemann, Proc. SPIE 8246, 82460N (2012).
[CrossRef]

Shen, H.

L. Yu, H. Shen, X. Jing, Z. Hou, and Y. Wu, “Study on the measurement of θ0 using stellar scintillation,” Acta Opt. Sin. (to be published).

Walters, D. L.

Wayne, D.

L. C. Andrews, R. L. Phillips, D. Wayne, T. Leclerc, P. Sauer, R. Crabbs, and J. Kiriazes, Proc. SPIE 7324, 732402 (2009).
[CrossRef]

Wu, Y.

L.-K. Yu, Y. Wu, Z.-H. Hou, and X. Jing, Acta Opt. Sin. 33, 1201004 (2013).
[CrossRef]

L. Yu, H. Shen, X. Jing, Z. Hou, and Y. Wu, “Study on the measurement of θ0 using stellar scintillation,” Acta Opt. Sin. (to be published).

Yu, L.

L. Yu, H. Shen, X. Jing, Z. Hou, and Y. Wu, “Study on the measurement of θ0 using stellar scintillation,” Acta Opt. Sin. (to be published).

Yu, L.-K.

L.-K. Yu, Y. Wu, Z.-H. Hou, and X. Jing, Acta Opt. Sin. 33, 1201004 (2013).
[CrossRef]

Acta Opt. Sin. (1)

L.-K. Yu, Y. Wu, Z.-H. Hou, and X. Jing, Acta Opt. Sin. 33, 1201004 (2013).
[CrossRef]

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

Opt. Express (1)

Proc. SPIE (2)

J. P. Bos, A. V. Sergeyev, and M. C. Roggemann, Proc. SPIE 8246, 82460N (2012).
[CrossRef]

L. C. Andrews, R. L. Phillips, D. Wayne, T. Leclerc, P. Sauer, R. Crabbs, and J. Kiriazes, Proc. SPIE 7324, 732402 (2009).
[CrossRef]

Other (2)

R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence: Evaluation and Application of Mellin Transforms (Springer-Verlag, 2007).

L. Yu, H. Shen, X. Jing, Z. Hou, and Y. Wu, “Study on the measurement of θ0 using stellar scintillation,” Acta Opt. Sin. (to be published).

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Figures (5)

Fig. 1.
Fig. 1.

Normalized path-weighting function Ws(u) for plane waves, spherical waves, and distributed beacons (dashed–dotted line) with diameter Ds=D, when Fresnel number FN=1.

Fig. 2.
Fig. 2.

Normalized path-weighting function Ws(u) for a point beacon with various Fresnel numbers: FN=1, FN=9, FN=25.

Fig. 3.
Fig. 3.

Normalized path-weighting function WC(u) for a point beacon with various displacements of two apertures: d=D, d=1.5D, d=2D.

Fig. 4.
Fig. 4.

Normalized integrated path-weighting function WInt(u) for a point beacon with various Fresnel numbers: FN=0.5, FN=1, FN=2.

Fig. 5.
Fig. 5.

Error of θ0 EInt with FN=1 versus the point beacon height in three typical turbulence models: H-V5/7, HAP, and Greenwood [8].

Equations (14)

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θ0=[2.91k20LCn2(z)z5/3dz]3/5,
θ0=[2.91k2L8/301Cn2(uL)u5/3du]3/5.
W0(u)u5/3.
σχA2=0.132π2k2L01duCn2(uL)Ws(u),
Ws(u)=0κF(γκ)κ11/3sin2(κ2γuL2k)dκ.
Fa(γκ)=[4J1(γκD/2)/γκD]2,
Fs(γκ)=[4J1(κDsu)/κDsu]2,
Ws(u)=D5/30κ8/3[2J1(γκ/2)γκ/2]2dκ[2J1(κuDs/2D)κuDs/2D]2sin2(κ2γu4πFN),
Cs(d)/S¯2=exp[4CχA(d)]1,
σs2/S¯2=exp[4σχA2(d)]1,
CχA(d)=0.132π2k2L01duCn2(uL)Wc(u),
Wc=(u,d)=Ws(u)J0(γκd).
WInt(u)=i=1NaiWi(u)u5/3.
EInt=[01Cn2(uh)WInt(u)du01Cn2(uh)u5/3du]0.61,

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