Aperture averaging of optical scintillations in the turbulent atmosphere

James H. Churnside

doi:10.1364/AO.30.001982

Applied Optics
Vol. 30,
Issue 15,
pp. 1982-1994
(1991)
•https://doi.org/10.1364/AO.30.001982

Aperture averaging of optical scintillations in the turbulent atmosphere

James H. Churnside

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
James H. Churnside, "Aperture averaging of optical scintillations in the turbulent atmosphere," Appl. Opt. 30, 1982-1994 (1991)

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

Abstract

We have developed approximate expressions for the aperture-averaging factor of optical scintillation in the turbulent atmosphere. For large apertures and weak path-integrated turbulence with a small inner scale, the variance of signal fluctuations is proportional to the −7/3 power of the ratio of the aperture diameter to the Fresnel zone size. If the inner scale is large, the variance is proportional to the −7/3 power of the ratio of the aperture diameter to the inner scale. In strong path-integrated turbulence, two scales develop. That portion of the variance associated with the smaller scale is proportional to the −2 power of the ratio of the aperture diameter to the phase coherence length. That portion of the variance associated with the larger scale is proportional to the −7/3 power of the ratio of the aperture diameter to the scattering disk. These simple approximations are within a factor of 2 of the measurements.

Full Article | PDF Article

More Like This

Aperture-averaging factor for optical scintillations of plane and spherical waves in the atmosphere

Larry C. Andrews
J. Opt. Soc. Am. A 9(4) 597-600 (1992)

Temporal averaging of atmospheric turbulence-induced optical scintillation

H. T. Yura and S. M. Beck
Opt. Express 23(17) 22867-22882 (2015)

Scintillation and aperture averaging for Gaussian beams through non-Kolmogorov maritime atmospheric turbulence channels

Mingjian Cheng, Lixin Guo, and Yixin Zhang
Opt. Express 23(25) 32606-32621 (2015)

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 (15)

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 (2)

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 (91)

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

Conditions	Formula
ϱ₀ ≥ (L/k)^1/2	$A = {[1 + 1.07 {(\frac{k D^{2}}{4 L})}^{7 / 6}]}^{- 1}$
ℓ₀ ≥ 2.73 (L/k)^1/2	$A = {[1 + 1.07 {(\frac{k D^{2}}{4 L})}^{7 / 6}]}^{- 1}$

ϱ₀ ≥ (L/k)^1/2	$A = {[1 + 2.21 {(\frac{D}{ℓ_{0}})}^{7 / 3}]}^{- 1}$
ℓ₀ > 2.73 (L/k)^1/2	$A = {[1 + 2.21 {(\frac{D}{ℓ_{0}})}^{7 / 3}]}^{- 1}$

ϱ₀ < (L/k)^1/2	$\begin{array}{l} A = \frac{σ_{I}^{2} + 1}{2 σ_{I}^{2}} {[1 + 0.908 {(\frac{D}{2 ϱ_{o}})}^{2}]}^{- 1} + \frac{σ_{I}^{2} - 1}{2 σ_{I}^{2}} {[1 + 0.162 {(\frac{k ϱ_{0} D}{2 L})}^{7 / 3}]}^{- 1} \\ ϱ_{0} = {(1.46 k^{2} L C_{n}^{2})}^{- 3 / 5} \\ σ_{I}^{2} = 1 + 1.22 {(\frac{k ϱ_{0}^{2}}{L})}^{1 / 3} \end{array}$
ℓ₀ ≤ ϱ₀

ϱ₀ < (L/k)^1/2	$\begin{array}{l} A = \frac{σ_{I}^{2} + 1}{2 σ_{I}^{2}} {[1 + {(\frac{D}{2 ϱ_{0}})}^{2}]}^{- 1} + \frac{σ_{I}^{2} - 1}{2 σ_{I}^{2}} {[1 + 1.27 {(\frac{k ϱ_{0} D}{2 L})}^{7 / 3}]}^{- 1} \\ ϱ_{0} = {(1.20 k^{2} L C_{n}^{2} L ℓ_{0}^{- 1 / 3})}^{- 1 / 2} \\ σ_{I}^{2} = 1 + 1.21 {(\frac{k ϱ_{0} ℓ_{0}}{L})}^{1 / 3} \end{array}$
ℓ₀ > ϱ₀

Conditions	Formula
ϱ₀ ≥ (L/k)^1/2	$A = {[1 + 0.214 {(\frac{k D^{2}}{4 L})}^{7 / 6}]}^{- 1}$
ℓ₀ ≥ 1.5 (L/k)^1/2	$A = {[1 + 0.214 {(\frac{k D^{2}}{4 L})}^{7 / 6}]}^{- 1}$

ϱ₀ ≥ (L/k)^1/2	$A = {[1 + 0.109 {(\frac{D}{ℓ_{0}})}^{7 / 3}]}^{- 1}$
ℓ₀ > 1.5 (L/k)^1/2	$A = {[1 + 0.109 {(\frac{D}{ℓ_{0}})}^{7 / 3}]}^{- 1}$

ϱ₀ < (L/k)^1/2	$\begin{array}{l} A = \frac{σ_{I}^{2} + 1}{2 σ_{I}^{2}} {[1 + 0.908 {(\frac{D}{2 ϱ_{o}})}^{2}]}^{- 1} + \frac{σ_{I}^{2} - 1}{2 σ_{I}^{2}} {[1 + 0.613 {(\frac{k D ϱ_{0}}{2 L})}^{7 / 3}]}^{- 1} \\ ϱ_{0} = {(0.545 k^{2} L C_{n}^{2})}^{- 3 / 5} \\ σ_{I}^{2} = 1 + 3.86 {(\frac{k ϱ_{0}^{2}}{L})}^{1 / 3} \end{array}$
ℓ₀ ≤ ϱ₀

ϱ₀ < (L/k)^1/2	$\begin{array}{l} A = \frac{σ_{I}^{2} + 1}{2 σ_{I}^{2}} {[1 + {(\frac{D}{2 ϱ_{0}})}^{2}]}^{- 1} + \frac{σ_{I}^{2} - 1}{2 σ_{I}^{2}} {[1 + 0.534 {(\frac{k D ϱ_{0}}{2 L})}^{7 / 3}]}^{- 1} \\ ϱ_{0} = {(0.545 k^{2} L C_{n}^{2} L ℓ_{0}^{- 1 / 3})}^{- 1 / 2} \\ σ_{I}^{2} = 1 + 2.27 {(\frac{k ϱ_{0} ℓ_{0}}{L})}^{1 / 3} \end{array}$
ℓ₀ > ϱ₀

Conditions	Formula
ϱ₀ ≥ (L/k)^1/2	$A = {[1 + 1.07 {(\frac{k D^{2}}{4 L})}^{7 / 6}]}^{- 1}$
ℓ₀ ≥ 2.73 (L/k)^1/2	$A = {[1 + 1.07 {(\frac{k D^{2}}{4 L})}^{7 / 6}]}^{- 1}$

ϱ₀ ≥ (L/k)^1/2	$A = {[1 + 2.21 {(\frac{D}{ℓ_{0}})}^{7 / 3}]}^{- 1}$
ℓ₀ > 2.73 (L/k)^1/2	$A = {[1 + 2.21 {(\frac{D}{ℓ_{0}})}^{7 / 3}]}^{- 1}$

ϱ₀ < (L/k)^1/2	$\begin{array}{l} A = \frac{σ_{I}^{2} + 1}{2 σ_{I}^{2}} {[1 + 0.908 {(\frac{D}{2 ϱ_{o}})}^{2}]}^{- 1} + \frac{σ_{I}^{2} - 1}{2 σ_{I}^{2}} {[1 + 0.162 {(\frac{k ϱ_{0} D}{2 L})}^{7 / 3}]}^{- 1} \\ ϱ_{0} = {(1.46 k^{2} L C_{n}^{2})}^{- 3 / 5} \\ σ_{I}^{2} = 1 + 1.22 {(\frac{k ϱ_{0}^{2}}{L})}^{1 / 3} \end{array}$
ℓ₀ ≤ ϱ₀

ϱ₀ < (L/k)^1/2	$\begin{array}{l} A = \frac{σ_{I}^{2} + 1}{2 σ_{I}^{2}} {[1 + {(\frac{D}{2 ϱ_{0}})}^{2}]}^{- 1} + \frac{σ_{I}^{2} - 1}{2 σ_{I}^{2}} {[1 + 1.27 {(\frac{k ϱ_{0} D}{2 L})}^{7 / 3}]}^{- 1} \\ ϱ_{0} = {(1.20 k^{2} L C_{n}^{2} L ℓ_{0}^{- 1 / 3})}^{- 1 / 2} \\ σ_{I}^{2} = 1 + 1.21 {(\frac{k ϱ_{0} ℓ_{0}}{L})}^{1 / 3} \end{array}$
ℓ₀ > ϱ₀

Conditions	Formula
ϱ₀ ≥ (L/k)^1/2	$A = {[1 + 0.214 {(\frac{k D^{2}}{4 L})}^{7 / 6}]}^{- 1}$
ℓ₀ ≥ 1.5 (L/k)^1/2	$A = {[1 + 0.214 {(\frac{k D^{2}}{4 L})}^{7 / 6}]}^{- 1}$

ϱ₀ ≥ (L/k)^1/2	$A = {[1 + 0.109 {(\frac{D}{ℓ_{0}})}^{7 / 3}]}^{- 1}$
ℓ₀ > 1.5 (L/k)^1/2	$A = {[1 + 0.109 {(\frac{D}{ℓ_{0}})}^{7 / 3}]}^{- 1}$

ϱ₀ < (L/k)^1/2	$\begin{array}{l} A = \frac{σ_{I}^{2} + 1}{2 σ_{I}^{2}} {[1 + 0.908 {(\frac{D}{2 ϱ_{o}})}^{2}]}^{- 1} + \frac{σ_{I}^{2} - 1}{2 σ_{I}^{2}} {[1 + 0.613 {(\frac{k D ϱ_{0}}{2 L})}^{7 / 3}]}^{- 1} \\ ϱ_{0} = {(0.545 k^{2} L C_{n}^{2})}^{- 3 / 5} \\ σ_{I}^{2} = 1 + 3.86 {(\frac{k ϱ_{0}^{2}}{L})}^{1 / 3} \end{array}$
ℓ₀ ≤ ϱ₀

ϱ₀ < (L/k)^1/2	$\begin{array}{l} A = \frac{σ_{I}^{2} + 1}{2 σ_{I}^{2}} {[1 + {(\frac{D}{2 ϱ_{0}})}^{2}]}^{- 1} + \frac{σ_{I}^{2} - 1}{2 σ_{I}^{2}} {[1 + 0.534 {(\frac{k D ϱ_{0}}{2 L})}^{7 / 3}]}^{- 1} \\ ϱ_{0} = {(0.545 k^{2} L C_{n}^{2} L ℓ_{0}^{- 1 / 3})}^{- 1 / 2} \\ σ_{I}^{2} = 1 + 2.27 {(\frac{k ϱ_{0} ℓ_{0}}{L})}^{1 / 3} \end{array}$
ℓ₀ > ϱ₀

Abstract

Cited By

Figures (15)

Tables (2)

Equations (91)

Applied Optics