Abstract

Instead of Zernike polynomials, ellipse Gaussian model is proposed to represent localized wave-front deformation in researching pointing and tracking errors in inter-satellite laser communication links, which can simplify the calculation. It is shown that both pointing and tracking errors depend on the center deepness h, the radiuses a and b, and the distance d of the Gaussian distortion and change regularly as they increase. The maximum peak values of pointing and tracking errors always appear around h=0.2λ. The influence of localized deformation is up to 0.7µrad for pointing error, and 0.5µrad for tracking error. To reduce the impact of localized deformation on pointing and tracking errors, the machining precision of optical devices, which should be more greater than 0.2λ, is proposed. The principle of choosing the optical devices with localized deformation is presented, and the method that adjusts the pointing direction to compensate pointing and tracking errors is given. We hope the results can be used in the design of inter-satellite lasercom systems.

© 2008 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2007 (2)

2005 (1)

2001 (1)

1999 (2)

1981 (1)

1980 (2)

Ahmad, M. A.

Arnon, Shlomi

Chan, Victor

Gutirrez-Vega, Julio C.

Jono, T.

Lavan, Michael J.

Lin, J.

Liu, J.

Liu, L. R.

Liu, S.

Liu, Z.

Lowrey, W. H.

Mahajan, V. N.

Nakagawa, K.

Noriega-Manez, Rodrigo J.

Silva, D. E.

Strickland, Brian R.

Sun, J. F.

Swantner, W. H.

Takahashi, N.

Toyoshima, M.

Wan, L. Y.

Wang, J. Y.

Woodbridge, Eric

Yamamoto, A.

Yamawaki, T.

Yun, M. J.

Zhao, H.

Appl. Opt. (5)

J. Opt. Soc. Am. (1)

Opt. Express (2)

Opt. Lett. (1)

Other (8)

F. Cosson, P. Doubrere, and E. Perez, "Simulation model and on-ground performances validation of the PAT system for SILEX program, in Free-Space Laser Communication Technologies III, D. L. Begley and B. D. Seery, eds.," Proc. SPIE 1417, 262-276 (1991).
[CrossRef]

B. Laurent and G. Planche, "SILEX overview after flight terminals campaign, in Free-Space Laser Communication Technologies IX, G. S. Mecherle, ed.," Proc. SPIE 2990, 10-22 (1997).
[CrossRef]

A. Mauroschat, "Reliability analysis of a multiple-laser-diode beacon for inter-satellite links, in Free-Space Laser Communication Technologies III, D. L. Begley and B. D. Seery, eds.," Proc. SPIE 1417, 513-524 (1991).
[CrossRef]

M. Renard, P. Dobie, J. Gollier, T. Heinrichs, P. Woszczyk, and A. Sobeczko, "Optical telecommunication performance of the qualification model SILEX beacon, in Free-Space Laser Communication Technologies VII, G. S. Mecherle, ed.," Proc. SPIE 2381, 289-300 (1995).
[CrossRef]

K. Nakagawa and A. Yamamoto, "Engineering model test of LUCE (laser utilizing communications equipment), in Free-Space Laser Communication Technologies VIII, G. S. Mecherle, ed.," Proc. SPIE 2699, 114-120 (1996).
[CrossRef]

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

J. W. Goodman, Introduction to Fourier Optics, Second Edition, (New York, McGraw-Hill, 1996).

M. Katzman, Ed., Laser Satellite Communications, (Englewood Cliffs, N.J., Prentice-Hall, 1987).

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Figures (8)

Fig. 1.
Fig. 1.

Ellipse Gaussian model for the localized distortion.

Fig. 2.
Fig. 2.

Formation of Gaussian localized wave-front deformation.

Fig. 3.
Fig. 3.

Definition of the coordinate systems of inter-satellite lasercom links.

Fig. 4.
Fig. 4.

Localized wave-front deformation expressed by Zernike polynomials with different terms N.

Fig. 5.
Fig. 5.

Zernike expressing results for different values of a/D.

Fig. 6.
Fig. 6.

Dependence of pointing and tracking errors on the center deepness A, the radius a and b, and the distance d of the localized distortion.

Fig. 7.
Fig. 7.

Pointing and tracking errors changes with h and rms.

Fig. 8.
Fig. 8.

Comparison of pointing and tracking errors due to wave-front deformation described by ellipse Gaussian function and Zernike polynomials.

Equations (18)

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l ( x , y ) = A exp { [ ( x x 0 ) 2 a 2 + ( y y 0 ) 2 b 2 ] } A e ,
d = x 0 2 + y 0 2 .
Φ ( x , y ) = Φ 1 ( x , y ) + Φ 2 ( x , y )
= ψ exp { [ ( x x 0 ) 2 a 2 + ( y y 0 ) 2 b 2 ] } ψ e ,
E ( x , y ) = H ( x , y ) exp [ j Φ ( x , y ) ] ,
rms = S Φ 1 2 ( x , y ) dxdy S dxdy = 4 A π λ e 2 1 2 e 2 = 4 h π λ e + 1 2 ( e 1 ) ,
E 0 ( x 0 , y 0 ) = C M 1 ( x 0 , y 0 ) exp [ x 0 2 + y 0 2 2 ω 0 2 j x 0 2 + y 0 2 2 F 0 + j Φ ( x 0 , y 0 ) ] ,
M ( x 0 , y 0 ) = { 1 , if R 2 x 0 2 + y 0 2 R 1 0 , otherwise ,
I re ( x , y ) = C 2 λ 2 z f 2 E 0 ( x 0 , y 0 ) exp [ j k z f ( x x 0 + y y 0 ) ] d x 0 d y 0 2 ,
θ P = θ Px 2 + θ Py 2 = x max 2 + y max 2 z f .
I f ( x 1 , y 1 ) = B λ 2 f 2 M 2 ( x , y ) exp [ j Φ ( x , y ) ] exp [ j k f ( x x 1 + y y 1 ) ] d x d y 2 ,
M 2 ( x , y ) = { 1 , if r 2 x 2 + y 2 r 1 0 , otherwise ,
θ T = θ Tx 2 + θ Ty 2 = X 2 + Y 2 f ,
X = x I f ( x , y ) dxdy I f ( x , y ) dxdy , Y = y I f ( x , y ) dxdy I f ( x , y ) dxdy .
U ( u ) = D 2 D 2 H ( x ) exp [ j Φ ( x ) ] exp ( j k F x u ) d x ,
U ( u ) = D 2 D 2 H ( x ) exp ( j k F x u ) d x x 0 a x 0 + a H ( x ) exp ( j k F x u ) d x
+ exp ( j ψ e ) x 0 a x 0 + a H ( x ) exp ( j Φ 1 ) exp ( j k F x u ) d x .
h ( u ) = exp ( j ψ e ) x 0 a x 0 + a H ( x ) exp ( j Φ 1 ) exp ( j k F x u ) d x .

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