Abstract

We analyze mutual alignment errors due to wave-front aberrations. To solve the central obscured problem, we introduce modified Zernike polynomials, which are a set of complete orthogonal polynomials. It is found that different aberrations have different effects on mutual alignment errors. Some aberrations influence only the line of sight, while some aberrations influence both the line of sight and the intensity distributions.

© 2005 Optical Society of America

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References

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  1. A. Mauroschat, “Reliability analysis of a multiple-laser-diode beacon for inter-satellite links,” in Free-Space Laser Communication Technologies III,D. L. Begley, B. D. Seery, eds., Proc. SPIE1417, 513–524 (1991).
    [CrossRef]
  2. M. Renard, P. Dobie, J. Gollier, T. Heinrichs, P. Woszczyk, A. Sobeczko, “Optical telecommunication performance of the qualification model SILEX beacon,” in Free-Space Laser Communication Technologies VII,G. S. Mecherle, ed., Proc. SPIE2381, 289–300 (1995).
    [CrossRef]
  3. F. Cosson, P. Doubrere, 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, B. D. Seery, eds., Proc. SPIE1417, 262–276 (1991).
    [CrossRef]
  4. B. Laurent, G. Planche, “SILEX overview after flight terminals campaign,” in Free-Space Laser Communication Technologies IX,G. S. Mecherle, ed., Proc. SPIE2990, 10–22 (1997).
    [CrossRef]
  5. K. Nakagawa, A. Yamamoto, “Engineering model test of LUCE (laser utilizing communications equipment),” in Free-Space Laser Communication Technologies VIII,G. S. Mecherle, ed., Proc. SPIE2699, 114–120 (1996).
    [CrossRef]
  6. B. M. Levine, E. A. Martinsen, A. Wirth, A. Jankevics, M. Toledo-Quinones, F. Landers, T. L. Bruno, “Horizontal line-of-sight turbulence over near-ground paths and implications for adaptive optics corrections in laser communications,” Appl. Opt. 37, 4553–4560 (1998).
    [CrossRef]
  7. B. R. Strickland, M. J. Lavan, E. Woodbridge, V. Chan, “Effects of fog on the bit-error rate of a free-space laser communication system,” Appl. Opt. 38, 424–431 (1999).
    [CrossRef]
  8. V. N. Mahajan, “Line of sight of an aberrated optical system,” J. Opt. Soc. Am. A 2, 833–836 (1985).
    [CrossRef]
  9. M. Toyoshima, N. Takahashi, T. Jono, T. Yamawaki, K. Nakagawa, A. Yamamoto, “Mutual alignment errors due to the variation of wave-front aberrations in a free-space laser communication link,” Opt. Express 9, 592–602 (2001).
    [CrossRef] [PubMed]
  10. J. Y. Wang, D. E. Silva, “Wave-front interpretation with Zernike polynomials,” Appl. Opt. 19, 1510–1518 (1980).
    [CrossRef] [PubMed]

2001 (1)

1999 (1)

1998 (1)

1985 (1)

1980 (1)

Bruno, T. L.

Chan, V.

Cosson, F.

F. Cosson, P. Doubrere, 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, B. D. Seery, eds., Proc. SPIE1417, 262–276 (1991).
[CrossRef]

Dobie, P.

M. Renard, P. Dobie, J. Gollier, T. Heinrichs, P. Woszczyk, A. Sobeczko, “Optical telecommunication performance of the qualification model SILEX beacon,” in Free-Space Laser Communication Technologies VII,G. S. Mecherle, ed., Proc. SPIE2381, 289–300 (1995).
[CrossRef]

Doubrere, P.

F. Cosson, P. Doubrere, 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, B. D. Seery, eds., Proc. SPIE1417, 262–276 (1991).
[CrossRef]

Gollier, J.

M. Renard, P. Dobie, J. Gollier, T. Heinrichs, P. Woszczyk, A. Sobeczko, “Optical telecommunication performance of the qualification model SILEX beacon,” in Free-Space Laser Communication Technologies VII,G. S. Mecherle, ed., Proc. SPIE2381, 289–300 (1995).
[CrossRef]

Heinrichs, T.

M. Renard, P. Dobie, J. Gollier, T. Heinrichs, P. Woszczyk, A. Sobeczko, “Optical telecommunication performance of the qualification model SILEX beacon,” in Free-Space Laser Communication Technologies VII,G. S. Mecherle, ed., Proc. SPIE2381, 289–300 (1995).
[CrossRef]

Jankevics, A.

Jono, T.

Landers, F.

Laurent, B.

B. Laurent, G. Planche, “SILEX overview after flight terminals campaign,” in Free-Space Laser Communication Technologies IX,G. S. Mecherle, ed., Proc. SPIE2990, 10–22 (1997).
[CrossRef]

Lavan, M. J.

Levine, B. M.

Mahajan, V. N.

Martinsen, E. A.

Mauroschat, A.

A. Mauroschat, “Reliability analysis of a multiple-laser-diode beacon for inter-satellite links,” in Free-Space Laser Communication Technologies III,D. L. Begley, B. D. Seery, eds., Proc. SPIE1417, 513–524 (1991).
[CrossRef]

Nakagawa, K.

M. Toyoshima, N. Takahashi, T. Jono, T. Yamawaki, K. Nakagawa, A. Yamamoto, “Mutual alignment errors due to the variation of wave-front aberrations in a free-space laser communication link,” Opt. Express 9, 592–602 (2001).
[CrossRef] [PubMed]

K. Nakagawa, A. Yamamoto, “Engineering model test of LUCE (laser utilizing communications equipment),” in Free-Space Laser Communication Technologies VIII,G. S. Mecherle, ed., Proc. SPIE2699, 114–120 (1996).
[CrossRef]

Perez, E.

F. Cosson, P. Doubrere, 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, B. D. Seery, eds., Proc. SPIE1417, 262–276 (1991).
[CrossRef]

Planche, G.

B. Laurent, G. Planche, “SILEX overview after flight terminals campaign,” in Free-Space Laser Communication Technologies IX,G. S. Mecherle, ed., Proc. SPIE2990, 10–22 (1997).
[CrossRef]

Renard, M.

M. Renard, P. Dobie, J. Gollier, T. Heinrichs, P. Woszczyk, A. Sobeczko, “Optical telecommunication performance of the qualification model SILEX beacon,” in Free-Space Laser Communication Technologies VII,G. S. Mecherle, ed., Proc. SPIE2381, 289–300 (1995).
[CrossRef]

Silva, D. E.

Sobeczko, A.

M. Renard, P. Dobie, J. Gollier, T. Heinrichs, P. Woszczyk, A. Sobeczko, “Optical telecommunication performance of the qualification model SILEX beacon,” in Free-Space Laser Communication Technologies VII,G. S. Mecherle, ed., Proc. SPIE2381, 289–300 (1995).
[CrossRef]

Strickland, B. R.

Takahashi, N.

Toledo-Quinones, M.

Toyoshima, M.

Wang, J. Y.

Wirth, A.

Woodbridge, E.

Woszczyk, P.

M. Renard, P. Dobie, J. Gollier, T. Heinrichs, P. Woszczyk, A. Sobeczko, “Optical telecommunication performance of the qualification model SILEX beacon,” in Free-Space Laser Communication Technologies VII,G. S. Mecherle, ed., Proc. SPIE2381, 289–300 (1995).
[CrossRef]

Yamamoto, A.

M. Toyoshima, N. Takahashi, T. Jono, T. Yamawaki, K. Nakagawa, A. Yamamoto, “Mutual alignment errors due to the variation of wave-front aberrations in a free-space laser communication link,” Opt. Express 9, 592–602 (2001).
[CrossRef] [PubMed]

K. Nakagawa, A. Yamamoto, “Engineering model test of LUCE (laser utilizing communications equipment),” in Free-Space Laser Communication Technologies VIII,G. S. Mecherle, ed., Proc. SPIE2699, 114–120 (1996).
[CrossRef]

Yamawaki, T.

Appl. Opt. (3)

J. Opt. Soc. Am. A (1)

Opt. Express (1)

Other (5)

A. Mauroschat, “Reliability analysis of a multiple-laser-diode beacon for inter-satellite links,” in Free-Space Laser Communication Technologies III,D. L. Begley, B. D. Seery, eds., Proc. SPIE1417, 513–524 (1991).
[CrossRef]

M. Renard, P. Dobie, J. Gollier, T. Heinrichs, P. Woszczyk, A. Sobeczko, “Optical telecommunication performance of the qualification model SILEX beacon,” in Free-Space Laser Communication Technologies VII,G. S. Mecherle, ed., Proc. SPIE2381, 289–300 (1995).
[CrossRef]

F. Cosson, P. Doubrere, 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, B. D. Seery, eds., Proc. SPIE1417, 262–276 (1991).
[CrossRef]

B. Laurent, G. Planche, “SILEX overview after flight terminals campaign,” in Free-Space Laser Communication Technologies IX,G. S. Mecherle, ed., Proc. SPIE2990, 10–22 (1997).
[CrossRef]

K. Nakagawa, A. Yamamoto, “Engineering model test of LUCE (laser utilizing communications equipment),” in Free-Space Laser Communication Technologies VIII,G. S. Mecherle, ed., Proc. SPIE2699, 114–120 (1996).
[CrossRef]

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Figures (13)

Fig. 1
Fig. 1

Definition of the coordinate systems.

Fig. 2
Fig. 2

Received intensity distribution without aberrations: (a) x direction and (b) y direction.

Fig. 3
Fig. 3

Effect of the tilt aberration (Z2) on the receiver’s intensity distribution: (a) x direction and (b) y direction.

Fig. 4
Fig. 4

Effect of the defocus aberration (Z4) on the receiver’s intensity distribution: (a) x direction and (b) y direction.

Fig. 5
Fig. 5

Effect of the astigmatism aberration (Z5) on the receiver’s intensity distribution: (a) x direction and (b) y direction.

Fig. 6
Fig. 6

Effect of the coma aberration (Z7) on the receiver’s intensity distribution: (a) x direction and (b) y direction.

Fig. 7
Fig. 7

Effect of the trefoil aberration (Z9) on the receiver’s intensity distribution: (a) x direction and (b) y direction.

Fig. 8
Fig. 8

Transmitted intensity distribution without aberrations: (a) x direction and (b) y direction.

Fig. 9
Fig. 9

Effect of the tilt aberration (Z2) on the transmitted intensity distribution: (a) x direction and (b) y direction.

Fig. 10
Fig. 10

Effect of the defocus aberration (Z4) on the transmitted intensity distribution: (a) x direction and (b) y direction.

Fig. 11
Fig. 11

Effect of the astigmatism aberration (Z5) on the transmitted intensity distribution: (a) x direction and (b) y direction.

Fig. 12
Fig. 12

Effect of the coma aberration (Z7) on the transmitted intensity distribution: (a) x direction and (b) y direction.

Fig. 13
Fig. 13

Effect of the trefoil aberration (Z9) on the transmitted intensity distribution: (a) x direction and (b) y direction.

Equations (9)

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R n m ( r ) = γ n m m Q m m ( r ) + γ n m + 2 m Q m + 2 m ( r ) + + γ n n m Q n m ( r ) ,
γ n n m = [ 2 ( n + 1 ) ] 1 / 2 { β 1 [ R n m ( r ) - j = 0 n - m - 2 γ n m + j m Q m + j m ( r ) ] 2 r d r } 1 / 2 ,
γ n m + j m = 2 ( m + j + 1 ) β 1 R n m ( r ) Q m + j m ( r ) r d r , j = 0 , 2 , 4 n - 2.
U r e ( x , y ) = A j λ f exp [ j k 2 f ( x 2 + y 2 ) ] U 0 ( x 0 , y 0 ) × exp [ - j 2 π λ f ( x x 0 + y y 0 ) ] d x 0 d y 0 ,
U 0 ( x 0 , y 0 ) = B exp [ j k Φ ( x 0 , y 0 ) ] ,
I r e ( x , y ) = A 2 λ 2 f 2 | U 0 ( x 0 , y 0 ) × exp [ - j 2 π λ f ( x x 0 + y y 0 ) ] d x 0 d y 0 | 2 .
X = - - x I f ( x , y ) d x d y - - I f ( x , y ) d x d y , Y = - - y I f ( x , y ) d x d y - - I f ( x , y ) d x d y ,
U 1 ( x 1 , y 1 ) = ( 2 π ω 2 ) 1 / 2 exp [ - x 1 2 + y 1 2 ω 0 2 - j k ( x 1 2 + y 1 2 ) 2 F 0 + j Φ ( x 1 , y 1 ) ] .
I t r ( x , y ) = A 2 λ 2 z 2 | U 1 ( x 1 , y 1 ) × exp [ - j 2 π λ z ( x x 1 + y y 1 ) ] d x 1 d y 1 | 2 .

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