Abstract

The effect of aberrations on the Strehl intensity is analyzed. The aberrations are assumed to be random and normally distributed. A variety of different correlation coefficients for the aberration variation are discussed, including Gaussian correlation and Kolmogorov turbulence. For weak aberrations, the Strehl ratio is independent of the correlation function. The Strehl ratio for a given root-mean-square aberration is greater for a smaller number of correlation areas. For Kolmogorov turbulence, the Strehl ratio is lower than for Gaussian correlation.

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References

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  9. P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, 1963).
  10. C. J. R. Sheppard and T. J. Connolly, J. Mod. Opt. 42, 861 (1995).
    [CrossRef]
  11. S. Gladysz, J. C. Christou, L. W. Bradford, and C. Lewis, Publ. Astron. Soc. Pac. 120, 1132 (2008).
    [CrossRef]
  12. T. S. Ross, Appl. Opt. 48, 1812 (2009).
    [CrossRef]
  13. J. W. Goodman, Opt. Commun. 14, 324 (1975).
    [CrossRef]
  14. C. J. R. Sheppard, Opt. Commun. 122, 178 (1996).
    [CrossRef]
  15. H. T. Yura and D. L. Fried, J. Opt. Soc. Am. A 15, 2107 (1998).
    [CrossRef]

2009 (1)

2008 (1)

S. Gladysz, J. C. Christou, L. W. Bradford, and C. Lewis, Publ. Astron. Soc. Pac. 120, 1132 (2008).
[CrossRef]

2000 (1)

1998 (1)

1997 (1)

R. Barakat, Pure Appl. Opt. 6, 309 (1997).
[CrossRef]

1996 (1)

C. J. R. Sheppard, Opt. Commun. 122, 178 (1996).
[CrossRef]

1995 (1)

C. J. R. Sheppard and T. J. Connolly, J. Mod. Opt. 42, 861 (1995).
[CrossRef]

1993 (1)

1992 (1)

1983 (1)

1982 (1)

V. N. Mahajan, J. Opt. Soc. Am. A 72, 1258 (1982).
[CrossRef]

1975 (1)

J. W. Goodman, Opt. Commun. 14, 324 (1975).
[CrossRef]

1947 (1)

A. Maréchal, Revue d’Optique 26, 257 (1947).

Barakat, R.

R. Barakat, Pure Appl. Opt. 6, 309 (1997).
[CrossRef]

Beckmann, P.

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, 1963).

Born, M.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, 1975).

Bradford, L. W.

S. Gladysz, J. C. Christou, L. W. Bradford, and C. Lewis, Publ. Astron. Soc. Pac. 120, 1132 (2008).
[CrossRef]

Christou, J. C.

S. Gladysz, J. C. Christou, L. W. Bradford, and C. Lewis, Publ. Astron. Soc. Pac. 120, 1132 (2008).
[CrossRef]

Connolly, T. J.

C. J. R. Sheppard and T. J. Connolly, J. Mod. Opt. 42, 861 (1995).
[CrossRef]

Fried, D. L.

Gladysz, S.

S. Gladysz, J. C. Christou, L. W. Bradford, and C. Lewis, Publ. Astron. Soc. Pac. 120, 1132 (2008).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Opt. Commun. 14, 324 (1975).
[CrossRef]

Herrmann, J.

Lewis, C.

S. Gladysz, J. C. Christou, L. W. Bradford, and C. Lewis, Publ. Astron. Soc. Pac. 120, 1132 (2008).
[CrossRef]

Mahajan, V. N.

Maréchal, A.

A. Maréchal, Revue d’Optique 26, 257 (1947).

Ross, T. S.

Sheppard, C. J. R.

C. J. R. Sheppard, Opt. Commun. 122, 178 (1996).
[CrossRef]

C. J. R. Sheppard and T. J. Connolly, J. Mod. Opt. 42, 861 (1995).
[CrossRef]

Spizzichino, A.

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, 1963).

van den Bos, A.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, 1975).

Yura, H. T.

Appl. Opt. (2)

J. Mod. Opt. (1)

C. J. R. Sheppard and T. J. Connolly, J. Mod. Opt. 42, 861 (1995).
[CrossRef]

J. Opt. Soc. Am. A (5)

Opt. Commun. (2)

J. W. Goodman, Opt. Commun. 14, 324 (1975).
[CrossRef]

C. J. R. Sheppard, Opt. Commun. 122, 178 (1996).
[CrossRef]

Publ. Astron. Soc. Pac. (1)

S. Gladysz, J. C. Christou, L. W. Bradford, and C. Lewis, Publ. Astron. Soc. Pac. 120, 1132 (2008).
[CrossRef]

Pure Appl. Opt. (1)

R. Barakat, Pure Appl. Opt. 6, 309 (1997).
[CrossRef]

Revue d’Optique (1)

A. Maréchal, Revue d’Optique 26, 257 (1947).

Other (2)

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, 1975).

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, 1963).

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Figures (2)

Fig. 1.
Fig. 1.

Strehl intensity as a function of the root mean square aberration kσ, for different number of correlation areas and different aberration correlation functions: (a) Gaussian, (b) Brownian fractal, and (c) Kolmogorov turbulence.

Fig. 2.
Fig. 2.

Normalized partially coherent part NIR of the Strehl intensity for a fractal correlation function. ν=1/3 corresponds to Kolmogorov turbulence, v=1/2 to exponential correlation, ν=1 to a marginal fractal correlation, and ν to Gaussian correlation.

Equations (34)

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I=(112k2σ2)2,
I1k2σ2,
I=exp(k2σ2)
I=1S2|SeikΦdS|2,
χ(k)=+w(h)eikhdh,
eikΦ=1SSeikhdS=χ(k).
I=1S2S2S1exp{ik[h(x1,y1)h(x2,y2)]}dx1dy1dx2dy2=exp{ik[Φ(x1,y1)Φ(x2,y2)]}.
χ2(k,k)=+W(h1,h2)exp[ik(Φ1Φ2)]dh1dh2,
I=1S2S2S1χ2(k,k)dS1dS2.
I=2πS0χ2(k,k)τdτ,
I=χ(k)χ*(k)+2πS0[χ2(k,k)χ(k)χ*(k)]τdτ.
I=χ(k)χ*(k).
w(h)=1σ2πexp(h22σ2).
χ(k)=exp(12k2σ2),
χ2(k,k)=exp{k2σ2[C(τ)1]}.
I=exp(k2σ2)(1+2πS0{exp[k2σ2C(τ)]1}τdτ)=exp(k2σ2)+IR,
I=exp(k2σ2)+k2σ22πS0C(τ)τdτ.
A=2π0C(τ)τdτ=πT2
N=S/A,
I=exp(k2σ2)+k2σ2N=exp(k2σ2)+(NIR)N.
N[m+1(mzero);2m(m0)]×[n2+1(neven);n+12(nodd)].
C(τ)=exp(τ2/T2).
I=exp(k2σ2){1+1N[Ei(k2σ2)γln(k2σ2)]},
I=exp(k2σ2)[1+1Nm=1(kσ)2mm!m].
I=exp(k2σ2)[1+k2σ2Nexp(k2σ24)].
I1Nk2σ2.
C(τ)=2Γ(ν)(ν1/2τT)νKν(2ν1/2τT),
ν=3D2,
C(τ)=exp(2τT),
I=exp(k2σ2)[1+1Nm=1(kσ)2mm!m2].
C(τ)=2π31/6γAi[(3τT)2/3],
I=exp(k2σ2)[1+k2σ2Nexp(k2σ29)].
I1Nk4σ4,
I3[Γ(13)]64π31Nk6σ6,

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