Abstract

Binary wavefront control in the focal plane (i.e., binary phase-only filtering) for partial compensation of atmospheric turbulence in fiber-coupled free-space laser communication systems is investigated. Numerical results from wave-optics simulations show that in an air-to-air scenario, the combination of binary phase-only filtering and centroid tracking provides mean fiber coupling efficiency close to that resulting from ideal least-squares adaptive optics, but without the requirement for direct wavefront sensing. This result suggests a simpler and less computationally demanding turbulence mitigation system that is more readily applied to tactical applications.

© 2007 Optical Society of America

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References

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  3. R. K. Tyson, J. S. Tharp, and D. E. Canning, "Measurement of the bit-error rate of an adaptive optics, free-space laser communications system, part 2: multichannel configuration, aberration characterization, and closed-loop results," Opt. Eng. 44, 096003 (2005).
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    [CrossRef]
  16. M. C. Roggemann and B. Welsh, Imaging Through Turbulence (CRC, 1996).
  17. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 1998).
  18. G. R. Osche, Optical Detection Theory for Laser Applications (Wiley-Interscience, 2002).
  19. C. Ruilier, "A study of degraded light coupling into single-mode fibers," Proc. SPIE 3350, 319-329 (1998).
    [CrossRef]

2006

2005

R. K. Tyson, D. E. Canning, and J. S. Tharp, "Measurement of the bit-error rate of an adaptive optics, free-space laser communications system, part 1: tip-tilt configuration, diagnostics, and closed-loop results," Opt. Eng. 44, 096002 (2005).

R. K. Tyson, J. S. Tharp, and D. E. Canning, "Measurement of the bit-error rate of an adaptive optics, free-space laser communications system, part 2: multichannel configuration, aberration characterization, and closed-loop results," Opt. Eng. 44, 096003 (2005).

J. Hines, "Transformational communications air layer," AFRL Technol. Horizons 6, 12 (2005).

2004

J. Horwath, N. Perlot, D. Giggenbach, and R. Jüngling, "Numerical simulations of beam propagation through optical turbulence for high-altitude platform crosslinks," Proc. SPIE 5338, 243-252 (2004).
[CrossRef]

T. A. Rhoadarmer, "Development of a self-referencing interferometer wavefront sensor," Proc. SPIE 5553, 112-126 (2004).
[CrossRef]

2002

1998

1995

J. Khoury, J. Fu, and C. L. Woods, "Phase coding techniques for signal recovery from distortion," Opt. Eng. 34, 840-848 (1995).
[CrossRef]

1994

AFRL Technol. Horizons

J. Hines, "Transformational communications air layer," AFRL Technol. Horizons 6, 12 (2005).

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Eng.

J. Khoury, J. Fu, and C. L. Woods, "Phase coding techniques for signal recovery from distortion," Opt. Eng. 34, 840-848 (1995).
[CrossRef]

R. K. Tyson, D. E. Canning, and J. S. Tharp, "Measurement of the bit-error rate of an adaptive optics, free-space laser communications system, part 1: tip-tilt configuration, diagnostics, and closed-loop results," Opt. Eng. 44, 096002 (2005).

R. K. Tyson, J. S. Tharp, and D. E. Canning, "Measurement of the bit-error rate of an adaptive optics, free-space laser communications system, part 2: multichannel configuration, aberration characterization, and closed-loop results," Opt. Eng. 44, 096003 (2005).

Opt. Express

Opt. Lett.

Proc. SPIE

C. Ruilier, "A study of degraded light coupling into single-mode fibers," Proc. SPIE 3350, 319-329 (1998).
[CrossRef]

T. A. Rhoadarmer, "Development of a self-referencing interferometer wavefront sensor," Proc. SPIE 5553, 112-126 (2004).
[CrossRef]

J. Horwath, N. Perlot, D. Giggenbach, and R. Jüngling, "Numerical simulations of beam propagation through optical turbulence for high-altitude platform crosslinks," Proc. SPIE 5338, 243-252 (2004).
[CrossRef]

Other

M. C. Roggemann and B. Welsh, Imaging Through Turbulence (CRC, 1996).

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 1998).

G. R. Osche, Optical Detection Theory for Laser Applications (Wiley-Interscience, 2002).

R. K. Tyson, Principles of Adaptive Optics, 2nd ed. (Academic, 1998).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

K. Munson, ed., Jane's Unmanned Aerial Vehicles and Targets (Jane's Information Group, 2000).

R. R. Beland, "Propagation through amospheric optical turbulence," in Vol. 2 of The Infrared & Electro-Optical Systems Handbook, F. G. Smith, ed. (SPIE, 1993), pp. 156-232.

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Figures (13)

Fig. 1
Fig. 1

(Color online) Basic pupil plane AO system for compensated space object imaging. Optical and electronic signals are represented by dashed (red) and solid (black) lines, respectively.

Fig. 2
Fig. 2

(Color online) Basic pupil plane AO system for LaserCom using a SMF-coupled detector. Optical and electronic signals are represented by dashed (red) and solid (black) lines, respectively.

Fig. 3
Fig. 3

(Color online) Focal plane AO system for LaserCom using a SMF-coupled detector. Optical and electronic signals are represented by dashed (red) and solid (black) lines, respectively.

Fig. 4
Fig. 4

(Color online) Models of turbulence strength as characterized by the refractive index structure parameter, C n 2 , for altitudes ranging from 8 to 15 km.

Fig. 5
Fig. 5

(Color online) Fried parameter r 0 is plotted as a function of log-amplitude variance in (a). The receiver telescope aperture diameter D is also presented as a point of reference. Analytic results for the open-loop Strehl ratio are shown in (b) for the uncompensated and two-axis tilt removed scenarios. The wavelength is λ = 987   nm and the propagation path is 52.6 km.

Fig. 6
Fig. 6

(Color online) Isoplanatic angle θ 0 is plotted as a function of log-amplitude variance. The diffraction angle λ / D and time-of-flight angle θ v are also plotted as points of reference. The effective wind speed is 389 km / h ( 108 m / s ) , the wavelength is λ = 987   nm , and the propagation path is 52.6   km .

Fig. 7
Fig. 7

(Color online) Example of spot breakup in the focal plane with a π phase shift between the two primary subspots. The wavelength is λ = 987   nm , the receiver aperture diameter is 20 cm, and the propagation path is 52.6 km. The spherical wave log-amplitude variance is σ χ 2 = 0.5 .

Fig. 8
Fig. 8

(Color online) One-dimensional analysis motivating the BPOF wavefront control approach. The uncorrected and corrected fields in the front focal plane are shown in (a) and (d), respectively. Intensity and phase in the rear focal plane are shown in (b) and (c), respectively, for the uncorrected field. Intensity and phase in the rear focal plane are shown in (e) and (f), respectively, for the corrected field.

Fig. 9
Fig. 9

(Color online) Visual description of the BPOF wavefront control process for σ χ 2 = 0.5 . Intensity and phase of the uncompensated focal plane field are shown in (a) and (b), respectively. Intensity and phase within the two regions identified by the segmentation algorithm are presented in (c) and (d), respectively. Intensity and phase of the compensated field are shown in (e) and (f), respectively, where compensation includes application of the BPOF, propagation to the rear focal plane, and centroid tracking. The wavelength is λ = 987   nm , the receiver aperture diameter is 20   cm , and the propagation path is 52.6 km.

Fig. 10
Fig. 10

(Color online) Example focal plane images for the four systems considered and a turbulence strength of σ χ 2 = 0.5 . The uncompensated focal plane image is shown in (a). The results of centroid tracking and ideal LS AO are shown in (b) and (c), respectively. The result of BPOF wavefront control is presented in (d). The wavelength is λ = 987   nm , the receiver aperture diameter is 20 cm, and the propagation path is 52.6 km.

Fig. 11
Fig. 11

(Color online) Mean coupling efficiency is plotted as a function of log-amplitude variance in (a). Mean Strehl ratio is plotted as a function of log-amplitude variance in (b). The wavelength is λ = 987   nm , the receiver aperture diameter is 20 cm, the propagation path is 52.6 km, and the segmentation algorithm threshold is T s e g = 0.4 .

Fig. 12
Fig. 12

(Color online) Mean coupling efficiency as a function of segmentation algorithm threshold, T s e g , for the four turbulence strengths considered. The wavelength is λ = 987   nm , the receiver aperture diameter is 20 cm, and the propagation path is 52.6 km.

Fig. 13
Fig. 13

(Color online) Mean coupling efficiency plotted as a function of SLM phase stroke for the four turbulence strengths considered. The wavelength is λ = 987   nm , the receiver aperture diameter is 20 cm, and the propagation path is 52.6 km.

Equations (148)

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1.5   kHz
40 %
( 389 km / h )
9.95   km
C n 2
C n 2
1 × 10 18
3 × 10 17 m 2 / 3
σ χ 2 = 0.01 0.36
σ χ 2 = 0.005 0.15
987   nm
C n 2
σ χ 2 = 1.0
r 0
σ χ 2
r 0
0.2. D / r 0 > 1
σ χ 2 > 0.2
σ χ 2 = 1.0
D / r 0
( σ χ 2 > 0.25 )
θ 0
σ χ 2
λ / D
θ v
θ 0
λ / D
σ χ 2
θ 0
θ v
θ v = 2 v p c ,
v p
v p = 389 km / h
( 108 m / s )
θ v = 0.72 μ rad
θ v
θ 0
σ χ 2 > 0.5
θ 0
θ v
θ v
θ 0
σ χ 2 > 0.5
S = | U ( 0 , 0 ) | 2 | U DL ( 0 , 0 ) | 2 ,
S = | P ( x , y ) U ( x , y ) d A | 2 P ( x , y ) | U ( x , y ) | 2 d A P ( x , y ) 2 d A ,
U ( x , y ) = A ( x , y ) exp { j ϕ ( x , y ) }
P ( x , y )
1 / 0
S = | P ( x , y ) A ( x , y ) e j [ ϕ ( x , y ) + ϕ c ( x , y ) ] d A | 2 P ( x , y ) | U ( x , y ) | 2 d A P ( x , y ) 2 d A ,
ϕ c ( x , y )
ρ = | U ( u , v ) F 01 ( u , v ) d A | 2 | U ( u , v ) | 2 d A | F 01 ( u , v ) | 2 d A ,
U ( u , v )
F 01 ( u , v )
F 01 ( u , v ) e r / ω 0 ,
ω 0
ω 0 opt = 0.71 λ f D ,
U ( u , v ) = exp [ j k ( u 2 + v 2 ) / ( 2 f ) ] λ f × { P ( x , y ) U ( x , y ) } [ u / ( λ f ) , v / ( λ f ) ] ,
( x , y )
( u , v )
{ · } [ · ]
exp [ j k ( u 2 + v 2 ) / ( 2 f ) ]
( N × N )
N 2 f λ d x 2 ,
d x
U ( x , y ) = λ f × { exp [ j k ( ξ 2 + η 2 ) / ( 2 f ) ] U ( ξ , η ) } [ x / ( λ f ) , y / ( λ f ) ] .
d u = d ξ
A ( r ) exp [ r 2 2 ρ 0 2 ] ,
ρ 0 0.37   cm
= 52, 600   m
= 987   nm
l 0 = 1   cm
= 4096 × 4096
= 20
0.29 cm / pixel
263 × 263
4096 × 4096
263 × 263
σ χ 2
T E M 1 , 0
σ χ 2 = 0.5
g ( x ) = exp [ π a 2 ( x + b ) 2 ] exp [ π a 2 ( x b ) 2 ] .
G ( f ) = j 2 | a |   exp [ π f 2 / a 2 ] sin [ 2 π b f ] ,
g c ( x ) = exp [ π a 2 ( x + b ) 2 ] + exp [ π a 2 ( x b ) 2 ] .
G c ( f ) = 2 | a |   exp [ π f 2 / a 2 ] cos [ 2 π b f ] ,
a = ( 3 π ) 1 / 2
b = 5
= 1.22 f λ / D
T s e g
T s e g
σ χ 2
263 × 263
35
263 × 263
512 × 512
512 × 512
263 × 263
263 × 263
512 × 512
512 × 512
263 × 263
263 × 263
512 × 512
512 × 512
( ϕ SLM )
ϕ SLM = π
σ χ 2
σ χ 2
T s e g = 0.4
σ χ 2 = 1.0
1.2   dB
T s e g
T s e g
T s e g
σ χ 2
T s e g
T ^ s e g [ 0.35 , 0.30 , 0.30 , 0.35 ]
σ χ 2 = [ 0.125 , 0.25 , 0.5 , 1.0 ]
T s e g
T s e g = 0.35
ϕ SLM
ϕ SLM
ϕ SLM = 0
ϕ SLM = λ / 2
( D / r 0 )
C n 2
r 0
λ = 987   nm
θ 0
λ / D
θ v
389 km / h
( 108 m / s )
λ = 987   nm
52.6   km
λ = 987   nm
σ χ 2 = 0.5
σ χ 2 = 0.5
λ = 987   nm
20   cm
σ χ 2 = 0.5
λ = 987   nm
λ = 987   nm
T s e g = 0.4
T s e g
λ = 987   nm
λ = 987   nm

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