Abstract

An exact expression is derived for the Strehl ratio as a function of the minimum root-mean-square aberration value that may produce it. The result is applicable to any aperture and is shown to imply a similar expression for the Strehl ratio as a function of the minimum amplitude range of the aberration.

© 2000 Optical Society of America

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References

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  1. J. Strutt ( Rayleigh), in Scientific Papers (Cambridge U. Press, Cambridge, UK, 1899), Vol. 1, Chap. 62, pp. 428–436.
  2. A. Maréchal, “Étude des effets combinés de la diffraction et des aberrations géométriques sur l’image d’un point lumineux,” Rev. Opt. Théorique Instrum. 26, 257–277 (1947).
  3. M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1997).
  4. A. van den Bos, “Rayleigh wave-front criterion: comment,” J. Opt. Soc. Am. A 16, 2307–2309 (1999).
    [CrossRef]

1999 (1)

1947 (1)

A. Maréchal, “Étude des effets combinés de la diffraction et des aberrations géométriques sur l’image d’un point lumineux,” Rev. Opt. Théorique Instrum. 26, 257–277 (1947).

Born, M.

M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1997).

Maréchal, A.

A. Maréchal, “Étude des effets combinés de la diffraction et des aberrations géométriques sur l’image d’un point lumineux,” Rev. Opt. Théorique Instrum. 26, 257–277 (1947).

Rayleigh,

J. Strutt ( Rayleigh), in Scientific Papers (Cambridge U. Press, Cambridge, UK, 1899), Vol. 1, Chap. 62, pp. 428–436.

Strutt, J.

J. Strutt ( Rayleigh), in Scientific Papers (Cambridge U. Press, Cambridge, UK, 1899), Vol. 1, Chap. 62, pp. 428–436.

van den Bos, A.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1997).

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

Rev. Opt. Théorique Instrum. (1)

A. Maréchal, “Étude des effets combinés de la diffraction et des aberrations géométriques sur l’image d’un point lumineux,” Rev. Opt. Théorique Instrum. 26, 257–277 (1947).

Other (2)

M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1997).

J. Strutt ( Rayleigh), in Scientific Papers (Cambridge U. Press, Cambridge, UK, 1899), Vol. 1, Chap. 62, pp. 428–436.

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Equations (13)

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f(x1, y1)f(x2, y2)exp[j2π{g(x1, y1)
-g(x2, y2)}]dx1dy1dx2dy2,
S=f(ξ1, η1)f(ξ2, η2)exp[j2π{g(ξ1, η1)-g(ξ2, η2)}]dξ1dη1dξ2dη2,
S=(1-α)2+α2+2α(1-α)cos 2πΓ.
S=0.5(cos 2πΓ+1)
S=0.5[1-β(1-β)(1-cos 2πγ)+(1-β)cos 2πΓ+β cos 2π(Γ-γ)].
σ=0.5Γ,
σ2=0.25Γ2=0.25[Δ2+2βγΔ+β(2-β)γ2]=const,
S=0.25[1+β2+(1-β)2+2β(1-β)cos 2πγ+2β cos 2π(Δ+γ)+2(1-β)cos 2πΔ].
dSdγγ=0=0,
d2Sdγ2γ=0=2π2β(1-β)2sin 2πΓ2πΓ-cos 2πΓ-1.
S=0.5(cos 4πσ+1),
S(1-2π2σ2)2.

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