Beam-intensity fluctuations in atmospheric turbulence

J. Carl Leader

doi:10.1364/JOSA.71.000542

Journal of the Optical Society of America
Vol. 71,
Issue 5,
pp. 542-558
(1981)
•https://doi.org/10.1364/JOSA.71.000542

Beam-intensity fluctuations in atmospheric turbulence

J. Carl Leader

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
J. Carl Leader, "Beam-intensity fluctuations in atmospheric turbulence," J. Opt. Soc. Am. 71, 542-558 (1981)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article

Abstract

An expression is derived for the intensity correlation function of a partially coherent beam wave of arbitrary size and focus propagating through weak atmospheric turbulence. Because the derivation employs the quadratic structure function (QSF) approximation, it describes only long-term beam-wander effects. Calculated covariance results agree well with measured data and substantiate the importance of beam-wander effects on focused beam statistics. Illustrative results show the effects of the phase deviation, size, and phase curvature of the source as well as the strength of turbulence and range. The weak-turbulence formulas are used to calculate strong-turbulence statistics by iterative recalculation of the coherence parameters of the beam in a succession of weakly turbulent path intervals. Successively calculated values of the beam-phase deviation and correlation length effectively provide wave-tilt correlation information that is missing in the original QSF approximation. The iterative solution for the normalized beam-intensity variance saturates and asymptotically approaches unity in a manner predicted by other theories. Calculated covariance functions also exhibit the initial rapid falloff and subsequent long coherence tail typical of saturated covariance behavior. Some magnitude discrepancies between calculated results and reported measurements are apparent for strong turbulence conditions. The iteration analysis predicts that log-amplitude fluctuations are diminished for increasingly strong turbulence and that saturated conditions arise solely from phase effects, in agreement with Fante’s conclusions [ R, L. Fante, Radio Sci. 15, 757 ( 1980)].

Full Article | PDF Article

More Like This

Intensity fluctuations resulting from partially coherent light propagating through atmospheric turbulence

J. Carl Leader
J. Opt. Soc. Am. 69(1) 73-84 (1979)

Receiver-aperture averaging effects for the intensity fluctuation of a beam wave in the turbulent atmosphere

S. J. Wang, Y. Baykal, and M. A. Plonus
J. Opt. Soc. Am. 73(6) 831-837 (1983)

Probability distribution of intensity fluctuations of arbitrary-type laser beams in the turbulent atmosphere

V. P. Aksenov, V. V. Dudorov, V. V. Kolosov, and V. Yu. Venediktov
Opt. Express 27(17) 24705-24716 (2019)

Previous Article Next Article

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (17)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (4)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (65)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

x = \| ${\overset{⇀}{r}}_{mn}$ \| ≪ (λ R)^½	x ≫ (λR)^½
D_S(x) (ρ₁⁻² + Aρ_S⁻²) x²	2ρ₁⁻² x²
D_χ_S(x) Aρ_χ_S⁻² x²	7.46 <χ²>
D₁(x) 2ρ₁⁻² x²	2ρ₁⁻² x² + 2 <χ²>

α_mn	$\begin{array}{l} ∣ {\overset{⇀}{r}}_{13} ∣ < L_{m} \\ ∣ {\overset{⇀}{r}}_{14} ∣ < L_{m} \end{array}$	$\begin{array}{l} ∣ {\overset{⇀}{r}}_{13} ∣ < L_{m} \\ ∣ {\overset{⇀}{r}}_{24} ∣ > L_{m} \end{array}$	$\begin{array}{l} ∣ {\overset{⇀}{r}}_{13} ∣ > L_{m} \\ ∣ {\overset{⇀}{r}}_{24} ∣ < L_{m} \end{array}$	$\begin{array}{l} ∣ {\overset{⇀}{r}}_{13} ∣ > L_{m} \\ ∣ {\overset{⇀}{r}}_{24} ∣ > L_{m} \end{array}$	β_mn	$\begin{array}{l} ∣ {\overset{⇀}{r}}_{13} ∣ < L_{m} \\ ∣ {\overset{⇀}{r}}_{24} ∣ < L_{m} \end{array}$	$\begin{array}{l} ∣ {\overset{⇀}{r}}_{13} ∣ < L_{m} \\ ∣ {\overset{⇀}{r}}_{24} ∣ > L_{m} \end{array}$	$\begin{array}{l} ∣ {\overset{⇀}{r}}_{13} ∣ > L_{m} \\ ∣ {\overset{⇀}{r}}_{24} ∣ < L_{m} \end{array}$	$\begin{array}{l} ∣ {\overset{⇀}{r}}_{13} ∣ > L_{m} \\ ∣ {\overset{⇀}{r}}_{24} ∣ > L_{m} \end{array}$
α₂₂	0	iAρ_χ_s⁻²	− iAρ_χ_s⁻²	0	β₂₂	0	iAρ_χ_s⁻² cos ²θ	iAρ_χ_s⁻² cos ²θ	0
α₃₃	0	iAρ_χ_s⁻²	−iAρ_χ_s⁻²	0	β₃₃	0	iAρ_χ_s⁻² cos ²θ	iAρ_χ_s⁻² cos ²θ	0
α₄₄	4ρ₁⁻²	4ρ₁⁻²	4ρ₁⁻²	4ρ₁⁻²	β₄₄	4ρ₁⁻² cos ²θ	4ρ₁⁻² cos ²θ	4ρ₁⁻² cos ²θ	4ρ₁⁻² cos ²θ
α₁₄	$i \frac{k}{2 R}$	$i \frac{k}{2 R}$	$i \frac{k}{2 R}$	$i \frac{k}{2 R}$	β₁₄	$i \frac{k}{2 R}$	$i \frac{k}{2 R}$	$i \frac{k}{2 R}$	$i \frac{k}{2 R}$
α₂₃	$- i (2 A {ρ_{χ_{S}}}^{- 2} - \frac{k}{2 R})$	$- i (A {ρ_{χ_{S}}}^{- 2} - \frac{k}{2 R})$	$- i (A {ρ_{χ_{S}}}^{- 2} - \frac{k}{2 R})$	$i \frac{k}{2 R}$	β₂₃	$- i (2 A {ρ_{χ_{S}}}^{- 2} {cos}^{2} θ - \frac{k}{2 R})$	$- i (A {ρ_{χ_{S}}}^{- 2} {cos}^{2} θ - \frac{k}{2 R})$	$- i (A {ρ_{χ_{S}}}^{- 2} {cos}^{2} θ - \frac{k}{2 R})$	$i \frac{k}{2 R}$
α₂₀	0	$\frac{- i}{2} R β C {ρ_{χ_{S}}}^{- 2}$	$\frac{+ i}{2} R β C {ρ_{χ_{S}}}^{- 2}$	0	β₂₀	0	$\frac{i}{2} R δ C {ρ_{χ_{S}}}^{- 2} {cos}^{2} θ$	$\frac{- i}{2} R δ C {ρ_{χ_{S}}}^{- 2} {cos}^{2} θ$	0
α₃₀	$i [- R β C {ρ_{χ_{S}}}^{- 2} + \frac{k}{2} β]$	$\frac{i}{2} [- R β C {ρ_{χ_{S}}}^{- 2} + k β]$	$\frac{i}{2} [- R β C {ρ_{χ_{S}}}^{- 2} + k β]$	$i \frac{k}{2} β$	β₃₀	$i [R δ C {ρ_{χ_{S}}}^{- 2} - \frac{k}{2} δ] cos θ$	$\frac{i}{2} [R δ C {ρ_{χ_{S}}}^{- 2} - k δ] cos θ$	$\frac{i}{2} [R δ C {ρ_{χ_{S}}}^{- 2} - k δ] cos θ$	$- i \frac{k}{2} δ cos θ$
α₄₀	0	0	0	0	β₄₀	ik sin θ	ik sin θ	ik sin θ	ik sin θ
α₀₀	0	$7.46 < χ^{2} > \frac{i}{2}$	$- 7.46 < χ^{2} > \frac{i}{2}$	0	β₀₀	0	$7.46 < χ^{2} > \frac{i}{2}$	$- 7.46 < χ^{2} > \frac{i}{2}$	0

Integral number	α₁₁	α₂₂	α₃₃	α₄₄	α₀₀	α₁₄	α₂₃	α₂₄	α₃₄
1	L_A⁻²	L_A⁻²	L_A⁻² + 2ρ_u⁻²	L_A⁻² + 2ρ_u⁻²	−σ_ϕ² + ln χ⁺	$- \frac{k}{2 L_{ϕ}}$	$- \frac{k}{2 L_{ϕ}}$	0	0
2	L_A⁻²	L_A⁻² + 2ρ_u⁻²	L_A⁻²	L_A⁻² + 2ρ_u⁻²	−σ_ϕ² + ln χ⁺	$- \frac{k}{2 L_{ϕ}}$	$- \frac{k}{2 L_{ϕ}}$	0	0
3	L_A⁻²	L_A⁻² + 2ρ_u⁻²	L_A⁻² + 2ρ_u⁻²	L_A⁻²	−σ_ϕ² + ln χ⁺	$- \frac{k}{2 L_{ϕ}}$	$- \frac{k}{2 L_{ϕ}}$	0	0
4	L_A⁻²	L_A⁻²	L_A⁻² + 2ρ_u⁻²	L_A⁻² + 2ρ_u⁻²	$- {σ_{ϕ}}^{2} + \frac{1}{2} ln χ^{+}$	$- \frac{k}{2 L_{ϕ}}$	$- \frac{k}{2 L_{ϕ}}$	0	−ρ_u⁻²
5	L_A⁻²	L_A⁻²	L_A⁻² + 2ρ_u⁻²	L_A⁻² + 2ρ_u⁻²	$- {σ_{ϕ}}^{2} + \frac{1}{2} ln χ^{+}$	$- \frac{k}{2 L_{ϕ}}$	$- \frac{k}{2 L_{ϕ}}$	0	+ρ_u⁻²
6	L_A⁻²	L_A⁻² + 2ρ_u⁻²	L_A⁻²	L_A⁻² + 2ρ_u⁻²	$- {σ_{ϕ}}^{2} + \frac{1}{2} ln χ^{+}$	$- \frac{k}{2 L_{ϕ}}$	$- \frac{k}{2 L_{ϕ}}$	−ρ_u⁻²	0
7	L_A⁻²	L_A⁻² + 2ρ_u⁻²	L_A⁻²	L_A⁻² + 2ρ_u⁻²	$- {σ_{ϕ}}^{2} + \frac{1}{2} ln χ^{+}$	$- \frac{k}{2 L_{ϕ}}$	$- \frac{k}{2 L_{ϕ}}$	+ρ_u⁻²	0
8	L_A⁻²	L_A⁻² + 2ρ_u⁻²	L_A⁻² + 2ρ_u⁻²	L_A⁻²	$- {σ_{ϕ}}^{2} + \frac{1}{2} ln χ^{-}$	$- \frac{k}{2 L_{ϕ}}$	$- \frac{k}{2 L_{ϕ}} - {ρ_{u}}^{- 2}$	0	0
9	L_A⁻²	L_A⁻² + 2ρ_u⁻²	L_A⁻² + 2ρ_u⁻²	L_A⁻²	$- {σ_{ϕ}}^{2} + \frac{1}{2} ln χ^{-}$	$- \frac{k}{2 L_{ϕ}}$	$- \frac{k}{2 L_{ϕ}} + {ρ_{u}}^{- 2}$	0	0
10	L_A⁻²	L_A⁻²	L_A⁻²	L_A⁻²	−σ_ϕ²	$- \frac{k}{2 L_{ϕ}}$	$- \frac{k}{2 L_{ϕ}}$	0	0

Propagation Coefficients
$∣ {\overset{⇀}{r}}_{13} ∣ \begin{array}{l} < L_{M} = + \\ > L_{m} = - \end{array}$	$∣ {\overset{⇀}{r}}_{24} ∣ \begin{array}{l} < L_{M} = + \\ > L_{m} = - \end{array}$	$A_{1} = \frac{1}{2} (α_{22} + α_{33}) - α_{23}$	$A_{2} = \frac{1}{2} (α_{22} + α_{33}) + α_{23}$	B₁ = −(β₂₀ + β₃₀)	B₂ = β₃₀ − β₂₀
+	+	$i (2 A {ρ_{χ_{S}}}^{- 2} - \frac{k}{2 R})$	$- i (2 A {ρ_{χ_{S}}}^{- 2} - \frac{k}{2 R})$	$- i ({ρ_{χ_{S}}}^{- 2} CP δ - \frac{k δ}{2})$	$- i ({ρ_{χ_{S}}}^{- 2} CP δ - \frac{k δ}{2})$
+	−	$i (2 A {ρ_{χ_{S}}}^{- 2} - \frac{k}{2 R})$	$i \frac{k}{2 R}$	$- i ({ρ_{χ_{S}}}^{- 2} CP δ - \frac{k δ}{2})$	$- i \frac{k δ}{2}$
−	+	$- i \frac{k}{2 R}$	$- i (2 A {ρ_{χ_{S}}}^{- 2} - \frac{k}{2 R})$	$i \frac{k δ}{2}$	$i ({ρ_{χ_{S}}}^{- 2} CP δ - \frac{k δ}{2})$
−	−	$- i \frac{k}{2 R}$	$i \frac{k}{2 R}$	$i \frac{k δ}{2}$	$- i \frac{k δ}{2}$
Source Coefficients for Integral Number 10
All ±	All ±	${L_{A}}^{- 2} + i \frac{k}{2 L_{ϕ}}$	${L_{A}}^{- 2} - i \frac{k}{2 L_{ϕ}}$	0	0

x = \| ${\overset{⇀}{r}}_{mn}$ \| ≪ (λ R)^½	x ≫ (λR)^½
D_S(x) (ρ₁⁻² + Aρ_S⁻²) x²	2ρ₁⁻² x²
D_χ_S(x) Aρ_χ_S⁻² x²	7.46 <χ²>
D₁(x) 2ρ₁⁻² x²	2ρ₁⁻² x² + 2 <χ²>

Abstract

Cited By

Figures (17)

Tables (4)

Equations (65)

Journal of the Optical Society of America