Experimental verification of the limits of optical channel intensity reciprocity

Dirk Giggenbach; William Cowley; Ken Grant; Nicolas Perlot

doi:10.1364/AO.51.003145

Applied Optics
Vol. 51,
Issue 16,
pp. 3145-3152
(2012)
•https://doi.org/10.1364/AO.51.003145

Experimental verification of the limits of optical channel intensity reciprocity

Dirk Giggenbach, William Cowley, Ken Grant, and Nicolas Perlot

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Dirk Giggenbach, William Cowley, Ken Grant, and Nicolas Perlot, "Experimental verification of the limits of optical channel intensity reciprocity," Appl. Opt. 51, 3145-3152 (2012)

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Abstract

Optical data links through the atmosphere suffer from turbulence-induced signal scintillation. In a coaxially-symmetric bidirectional link scenario, the variations of the axial intensities at both ends are correlated. This relation can be used as an inherent feedback mechanism, with negligible delay, to enhance the capacity of the transmission system. By experiment, we show the correlation coefficient of both received signals can reach values close to one over long atmospheric distances, provided the receiver apertures are smaller than specific intensity speckle structures, while the correlation reduces gradually with larger apertures. This allows transmission capacity to be optimized with adaptive transceiver systems that take into account the degree of correlation.

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Parameter	Unit	Value
Center Wavelength/FWHM, Tx of terminal “ $A$ ”	nm	$1560 / 15$
Center Wavelength/FWHM, Tx of terminal “ $B$ ”	nm	$1555 / 12$
Tx-power in trials $A, B / C, D, E$	mW	$10 mW / 26 mW$
Tx-diameter, $1 / e^{2}$	mm	2.1
Tx-divergence, FWHM	µrad	550
Outer Rx-aperture diameter $D_{o}$	mm	127 or 50
Inner Rx obscuration diameter $D_{i}$ (caused by Tx-collimator)	mm	26
Effective Rx-area 127 mm	$m^{2}$	0.0121
Effective Rx-area 50 mm	$m^{2}$	0.00143
Focal length of Rx-Fresnel-lens	mm	128 mm
Detector diameter (InGaAs-PIN)	mm	1
Amplification stages of detector	$V / μW$	$20 dB : 0.0143 V / μW$
		$30 dB : 0.0451 V / μW$
		$40 dB : 0.143 V / μW$
		$50 dB : 0.451 V / μW$
Sampling rate of Rx-power	$Samples / s$	1000

	$A$	$B$	$D$	$C$	$E$
link distance $L$	750 m	1.5 km	4.3 km	12 km	20 km
Date & Time	17.Feb.2011 12:10–12:38	17.Feb.2011 16:18–16:54	25.Mar.2011 16:30–17:43	9.Mar.2011 18:50–20:05	19.Apr.2011 15:45–16:50
Weather	sunny, clear sky, $\sim 28 ° C$	sunny, clear sky, $\sim 27 ° C$	Partly cloudy, some BGL-variations	Partly cloudy, around sunset	Partly cloudy, strong BGL-variations
mean Rx-power with 127 mm	100 to 116 µW	38 to 47 µW	11.6 to 16 µW	2.0 to 2.8 µW	399 to 467 nW
mean Rx-power with 50 mm	22 to 26 µW	7 to 10 µW	1.4 to 2.4 µW	290 to 490 nW	55 to 102 nW
PSIs with 127 mm Rx aperture	0.29, 0.27	0.37 to 0.40	0.22 to 0.47	0.1 to 0.3	0.2 to 0.6
PSIs with 50 mm Rx aperture	0.60, 0.65	0.72 to 0.91	0.39 to 1.0	0.26 to 0.41	0.24 to 0.76
CCFs with 127 mm Rx aperture	0.19	0.27, 0.31	0.25 to 0.29	0.52 to 0.73	0.48 to 0.56
CCFs with 50 mm Rx aperture	0.13 to 0.24	0.37, 0.38	0.44 to 0.61	0.89 to 0.91	0.76 to 0.89
Cross-correlation peak width (FWHM)	40 to 50 ms	20 to 30 ms	7 to 15 ms	8 to 18 ms	40 to 72 ms
for paths $A$ and $B$ : measured $C_{n}^{2}$ ; for paths $C$ , $E$ , $D$ : average $C_{n}^{2}$ and weighted average $C_{n}^{2}$ for spherical wave below	$0.9 E - 12$ to $1.0 E - 12 m^{- 2 / 3}$	$3.5 E - 13$ to $5.6 E - 13 m^{- 2 / 3}$	$2.7 E - 15 m^{- 2 / 3}$ ; $4.3 E - 16 m^{- 2 / 3}$	$3.3 E - 15 m^{- 2 / 3}$ ; $2.6 E - 16 m^{- 2 / 3}$	$1.4 E - 15 m^{- 2 / 3}$ ; $1.3 E - 16 m^{- 2 / 3}$
Spherical-wave Rytov index $σ_{R, s p}^{2}$	1.42	8.45	0.184	1.59	1.34
$ρ_{I}$ —estimate for spherical waves from IRT in middle of link: $\sqrt{λ \cdot L}$ (limited applicability for long atmospheric paths due to multiple scattering)	34 mm	48 mm	82 mm	136 mm	176 mm

Parameter	Unit	Value
Center Wavelength/FWHM, Tx of terminal “ $A$ ”	nm	$1560 / 15$
Center Wavelength/FWHM, Tx of terminal “ $B$ ”	nm	$1555 / 12$
Tx-power in trials $A, B / C, D, E$	mW	$10 mW / 26 mW$
Tx-diameter, $1 / e^{2}$	mm	2.1
Tx-divergence, FWHM	µrad	550
Outer Rx-aperture diameter $D_{o}$	mm	127 or 50
Inner Rx obscuration diameter $D_{i}$ (caused by Tx-collimator)	mm	26
Effective Rx-area 127 mm	$m^{2}$	0.0121
Effective Rx-area 50 mm	$m^{2}$	0.00143
Focal length of Rx-Fresnel-lens	mm	128 mm
Detector diameter (InGaAs-PIN)	mm	1
Amplification stages of detector	$V / μW$	$20 dB : 0.0143 V / μW$
		$30 dB : 0.0451 V / μW$
		$40 dB : 0.143 V / μW$
		$50 dB : 0.451 V / μW$
Sampling rate of Rx-power	$Samples / s$	1000

	$A$	$B$	$D$	$C$	$E$
link distance $L$	750 m	1.5 km	4.3 km	12 km	20 km
Date & Time	17.Feb.2011 12:10–12:38	17.Feb.2011 16:18–16:54	25.Mar.2011 16:30–17:43	9.Mar.2011 18:50–20:05	19.Apr.2011 15:45–16:50
Weather	sunny, clear sky, $\sim 28 ° C$	sunny, clear sky, $\sim 27 ° C$	Partly cloudy, some BGL-variations	Partly cloudy, around sunset	Partly cloudy, strong BGL-variations
mean Rx-power with 127 mm	100 to 116 µW	38 to 47 µW	11.6 to 16 µW	2.0 to 2.8 µW	399 to 467 nW
mean Rx-power with 50 mm	22 to 26 µW	7 to 10 µW	1.4 to 2.4 µW	290 to 490 nW	55 to 102 nW
PSIs with 127 mm Rx aperture	0.29, 0.27	0.37 to 0.40	0.22 to 0.47	0.1 to 0.3	0.2 to 0.6
PSIs with 50 mm Rx aperture	0.60, 0.65	0.72 to 0.91	0.39 to 1.0	0.26 to 0.41	0.24 to 0.76
CCFs with 127 mm Rx aperture	0.19	0.27, 0.31	0.25 to 0.29	0.52 to 0.73	0.48 to 0.56
CCFs with 50 mm Rx aperture	0.13 to 0.24	0.37, 0.38	0.44 to 0.61	0.89 to 0.91	0.76 to 0.89
Cross-correlation peak width (FWHM)	40 to 50 ms	20 to 30 ms	7 to 15 ms	8 to 18 ms	40 to 72 ms
for paths $A$ and $B$ : measured $C_{n}^{2}$ ; for paths $C$ , $E$ , $D$ : average $C_{n}^{2}$ and weighted average $C_{n}^{2}$ for spherical wave below	$0.9 E - 12$ to $1.0 E - 12 m^{- 2 / 3}$	$3.5 E - 13$ to $5.6 E - 13 m^{- 2 / 3}$	$2.7 E - 15 m^{- 2 / 3}$ ; $4.3 E - 16 m^{- 2 / 3}$	$3.3 E - 15 m^{- 2 / 3}$ ; $2.6 E - 16 m^{- 2 / 3}$	$1.4 E - 15 m^{- 2 / 3}$ ; $1.3 E - 16 m^{- 2 / 3}$
Spherical-wave Rytov index $σ_{R, s p}^{2}$	1.42	8.45	0.184	1.59	1.34
$ρ_{I}$ —estimate for spherical waves from IRT in middle of link: $\sqrt{λ \cdot L}$ (limited applicability for long atmospheric paths due to multiple scattering)	34 mm	48 mm	82 mm	136 mm	176 mm

Abstract

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Applied Optics