Abstract

A truncated ellipse Gaussian model to express localized distortion is developed to a transmission-type optical antenna, based on which the effects of localized deformation on pointing and tracking errors are researched. It is shown that localized distortion has the greatest influence on pointing and tracking errors when distortion deepness h0.8λ, which does not depend on other distortion parameters. To reduce the impact of localized deformation on pointing and tracking errors, the machining precision of the objective lens of the transmission-type antenna should be much better than 0.8λ. The requirement of the machining precision for lenses is lower than that for mirrors. The maxima of pointing and tracking errors due to the localized distortion with different radii are given. We hope the results can be used in the design of intersatellite optical communication systems.

© 2009 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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2008 (3)

2007 (6)

Z. Liu, H. Zhao, J. Liu, J. Lin, M. A. Ahmad, and S. Liu, “Generation of hollow Gaussian beams by spatial filtering,” Opt. Lett. 32, 2076-2078 (2007).
[CrossRef] [PubMed]

R. J. Noriega-Manez and J. C. Gutiérrez-Vega, “Rytov theory for Helmholtz-Gauss beams in turbulent atmosphere,” Opt. Express 15, 16328-16341 (2007).
[CrossRef] [PubMed]

G. Baister, T. Dreischer, M. Tüchler, K. Kudielka, and E. Fischer, “OPTEL terminal for deep space telemetry links,” Proc. SPIE 6457, 645706 (2007).
[CrossRef]

N. Perlot, “Turbulence-induced fading probability in coherent optical communication through the atmosphere,” Appl. Opt. 46, 7218-7226 (2007).
[CrossRef] [PubMed]

K. E. Wilson, J. Kovalik, A. Biswas, and W. Roberts, “Development of laser beam transmission strategies for future Ground-to-Space optical communications,” Proc. SPIE 6551, 65510B (2007).
[CrossRef]

Y. Chen, J. Charles, H. Hemmati, and A. Biswas, “Infrared earth tracking for deep-space optical communications: feasibility study based on laboratory emulator,” Proc. SPIE 6457, 64570A (2007).
[CrossRef]

2006 (3)

2005 (2)

2001 (2)

Aharonovich, M.

Ahmad, M. A.

Anguita, J. A.

Arnon, S.

Baister, G.

G. Baister, T. Dreischer, M. Tüchler, K. Kudielka, and E. Fischer, “OPTEL terminal for deep space telemetry links,” Proc. SPIE 6457, 645706 (2007).
[CrossRef]

Biswas, A.

K. E. Wilson, J. Kovalik, A. Biswas, and W. Roberts, “Development of laser beam transmission strategies for future Ground-to-Space optical communications,” Proc. SPIE 6551, 65510B (2007).
[CrossRef]

Y. Chen, J. Charles, H. Hemmati, and A. Biswas, “Infrared earth tracking for deep-space optical communications: feasibility study based on laboratory emulator,” Proc. SPIE 6457, 64570A (2007).
[CrossRef]

A. Biswas, D. Boroson, and B. Edwards, “Mars laser communication demonstration: what it would have been,” Proc. SPIE 6105, 610502 (2006).
[CrossRef]

Boroson, D.

A. Biswas, D. Boroson, and B. Edwards, “Mars laser communication demonstration: what it would have been,” Proc. SPIE 6105, 610502 (2006).
[CrossRef]

Brown, W.

I. Kim, B. Riley, N. M. Wong, M. Mitchell, and W. Brown, “Lessons learned from the STRV-2 satellite-to-ground lasercom experiment,” Proc. SPIE 4272, 1-15 (2001).
[CrossRef]

Charles, J.

Y. Chen, J. Charles, H. Hemmati, and A. Biswas, “Infrared earth tracking for deep-space optical communications: feasibility study based on laboratory emulator,” Proc. SPIE 6457, 64570A (2007).
[CrossRef]

Chen, Y.

Y. Chen, J. Charles, H. Hemmati, and A. Biswas, “Infrared earth tracking for deep-space optical communications: feasibility study based on laboratory emulator,” Proc. SPIE 6457, 64570A (2007).
[CrossRef]

Czichy, R.

B. Smutny, R. Lange, H. Kämpfner, D. Dallmann, G. Mühlnikel, M. Reinhardt, K. Saucke, U. Sterr, B. Wandernoth, and R. Czichy, “In-orbit verification of optical inter-satellite communication links based on homodyne BPSK,” Proc. SPIE 6877, 687702 (2008).
[CrossRef]

Dallmann, D.

B. Smutny, R. Lange, H. Kämpfner, D. Dallmann, G. Mühlnikel, M. Reinhardt, K. Saucke, U. Sterr, B. Wandernoth, and R. Czichy, “In-orbit verification of optical inter-satellite communication links based on homodyne BPSK,” Proc. SPIE 6877, 687702 (2008).
[CrossRef]

Dillon, T.

Dreischer, T.

G. Baister, T. Dreischer, M. Tüchler, K. Kudielka, and E. Fischer, “OPTEL terminal for deep space telemetry links,” Proc. SPIE 6457, 645706 (2007).
[CrossRef]

Edwards, B.

A. Biswas, D. Boroson, and B. Edwards, “Mars laser communication demonstration: what it would have been,” Proc. SPIE 6105, 610502 (2006).
[CrossRef]

Fischer, E.

G. Baister, T. Dreischer, M. Tüchler, K. Kudielka, and E. Fischer, “OPTEL terminal for deep space telemetry links,” Proc. SPIE 6457, 645706 (2007).
[CrossRef]

Gu, T.

Gutiérrez-Vega, J. C.

Haney, M. W.

Hemmati, H.

Y. Chen, J. Charles, H. Hemmati, and A. Biswas, “Infrared earth tracking for deep-space optical communications: feasibility study based on laboratory emulator,” Proc. SPIE 6457, 64570A (2007).
[CrossRef]

Iqbal, M.

Jono, T.

Kämpfner, H.

B. Smutny, R. Lange, H. Kämpfner, D. Dallmann, G. Mühlnikel, M. Reinhardt, K. Saucke, U. Sterr, B. Wandernoth, and R. Czichy, “In-orbit verification of optical inter-satellite communication links based on homodyne BPSK,” Proc. SPIE 6877, 687702 (2008).
[CrossRef]

Kim, I.

I. Kim, B. Riley, N. M. Wong, M. Mitchell, and W. Brown, “Lessons learned from the STRV-2 satellite-to-ground lasercom experiment,” Proc. SPIE 4272, 1-15 (2001).
[CrossRef]

Kovalik, J.

K. E. Wilson, J. Kovalik, A. Biswas, and W. Roberts, “Development of laser beam transmission strategies for future Ground-to-Space optical communications,” Proc. SPIE 6551, 65510B (2007).
[CrossRef]

Kudielka, K.

G. Baister, T. Dreischer, M. Tüchler, K. Kudielka, and E. Fischer, “OPTEL terminal for deep space telemetry links,” Proc. SPIE 6457, 645706 (2007).
[CrossRef]

Lange, R.

B. Smutny, R. Lange, H. Kämpfner, D. Dallmann, G. Mühlnikel, M. Reinhardt, K. Saucke, U. Sterr, B. Wandernoth, and R. Czichy, “In-orbit verification of optical inter-satellite communication links based on homodyne BPSK,” Proc. SPIE 6877, 687702 (2008).
[CrossRef]

Lin, J.

Liu, J.

Liu, L. R.

Liu, S.

Liu, Z.

Ma, J.

McFadden, M. J.

Mitchell, M.

I. Kim, B. Riley, N. M. Wong, M. Mitchell, and W. Brown, “Lessons learned from the STRV-2 satellite-to-ground lasercom experiment,” Proc. SPIE 4272, 1-15 (2001).
[CrossRef]

Mühlnikel, G.

B. Smutny, R. Lange, H. Kämpfner, D. Dallmann, G. Mühlnikel, M. Reinhardt, K. Saucke, U. Sterr, B. Wandernoth, and R. Czichy, “In-orbit verification of optical inter-satellite communication links based on homodyne BPSK,” Proc. SPIE 6877, 687702 (2008).
[CrossRef]

Nair, R.

Nakagawa, K.

Neifeld, M. A.

Noriega-Manez, R. J.

Perlot, N.

Prather, D. W.

Reinhardt, M.

B. Smutny, R. Lange, H. Kämpfner, D. Dallmann, G. Mühlnikel, M. Reinhardt, K. Saucke, U. Sterr, B. Wandernoth, and R. Czichy, “In-orbit verification of optical inter-satellite communication links based on homodyne BPSK,” Proc. SPIE 6877, 687702 (2008).
[CrossRef]

Riley, B.

I. Kim, B. Riley, N. M. Wong, M. Mitchell, and W. Brown, “Lessons learned from the STRV-2 satellite-to-ground lasercom experiment,” Proc. SPIE 4272, 1-15 (2001).
[CrossRef]

Roberts, W.

K. E. Wilson, J. Kovalik, A. Biswas, and W. Roberts, “Development of laser beam transmission strategies for future Ground-to-Space optical communications,” Proc. SPIE 6551, 65510B (2007).
[CrossRef]

Saucke, K.

B. Smutny, R. Lange, H. Kämpfner, D. Dallmann, G. Mühlnikel, M. Reinhardt, K. Saucke, U. Sterr, B. Wandernoth, and R. Czichy, “In-orbit verification of optical inter-satellite communication links based on homodyne BPSK,” Proc. SPIE 6877, 687702 (2008).
[CrossRef]

Smutny, B.

B. Smutny, R. Lange, H. Kämpfner, D. Dallmann, G. Mühlnikel, M. Reinhardt, K. Saucke, U. Sterr, B. Wandernoth, and R. Czichy, “In-orbit verification of optical inter-satellite communication links based on homodyne BPSK,” Proc. SPIE 6877, 687702 (2008).
[CrossRef]

Sterr, U.

B. Smutny, R. Lange, H. Kämpfner, D. Dallmann, G. Mühlnikel, M. Reinhardt, K. Saucke, U. Sterr, B. Wandernoth, and R. Czichy, “In-orbit verification of optical inter-satellite communication links based on homodyne BPSK,” Proc. SPIE 6877, 687702 (2008).
[CrossRef]

Sun, J. F.

Takahashi, N.

Tan, L.

Toyoshima, M.

Tüchler, M.

G. Baister, T. Dreischer, M. Tüchler, K. Kudielka, and E. Fischer, “OPTEL terminal for deep space telemetry links,” Proc. SPIE 6457, 645706 (2007).
[CrossRef]

Vasic, B. V.

Wan, L. Y.

Wandernoth, B.

B. Smutny, R. Lange, H. Kämpfner, D. Dallmann, G. Mühlnikel, M. Reinhardt, K. Saucke, U. Sterr, B. Wandernoth, and R. Czichy, “In-orbit verification of optical inter-satellite communication links based on homodyne BPSK,” Proc. SPIE 6877, 687702 (2008).
[CrossRef]

Wilson, K. E.

K. E. Wilson, J. Kovalik, A. Biswas, and W. Roberts, “Development of laser beam transmission strategies for future Ground-to-Space optical communications,” Proc. SPIE 6551, 65510B (2007).
[CrossRef]

Wong, N. M.

I. Kim, B. Riley, N. M. Wong, M. Mitchell, and W. Brown, “Lessons learned from the STRV-2 satellite-to-ground lasercom experiment,” Proc. SPIE 4272, 1-15 (2001).
[CrossRef]

Yamamoto, A.

Yamawaki, T.

Yang, Y.

Yu, J.

Yun, M. J.

Zhao, H.

Appl. Opt. (4)

J. Opt. Soc. Am. A (2)

Opt. Express (3)

Opt. Lett. (1)

Proc. SPIE (6)

B. Smutny, R. Lange, H. Kämpfner, D. Dallmann, G. Mühlnikel, M. Reinhardt, K. Saucke, U. Sterr, B. Wandernoth, and R. Czichy, “In-orbit verification of optical inter-satellite communication links based on homodyne BPSK,” Proc. SPIE 6877, 687702 (2008).
[CrossRef]

G. Baister, T. Dreischer, M. Tüchler, K. Kudielka, and E. Fischer, “OPTEL terminal for deep space telemetry links,” Proc. SPIE 6457, 645706 (2007).
[CrossRef]

I. Kim, B. Riley, N. M. Wong, M. Mitchell, and W. Brown, “Lessons learned from the STRV-2 satellite-to-ground lasercom experiment,” Proc. SPIE 4272, 1-15 (2001).
[CrossRef]

K. E. Wilson, J. Kovalik, A. Biswas, and W. Roberts, “Development of laser beam transmission strategies for future Ground-to-Space optical communications,” Proc. SPIE 6551, 65510B (2007).
[CrossRef]

Y. Chen, J. Charles, H. Hemmati, and A. Biswas, “Infrared earth tracking for deep-space optical communications: feasibility study based on laboratory emulator,” Proc. SPIE 6457, 64570A (2007).
[CrossRef]

A. Biswas, D. Boroson, and B. Edwards, “Mars laser communication demonstration: what it would have been,” Proc. SPIE 6105, 610502 (2006).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Truncated ellipse Gaussian model for localized deformation.

Fig. 2
Fig. 2

Formation of an ellipse Gaussian model.

Fig. 3
Fig. 3

Definition of the pointing error.

Fig. 4
Fig. 4

Definition of the tracking error.

Fig. 5
Fig. 5

(a) Pointing and (b) tracking errors versus deepness h for different parameters of a, b and d. Here α = 1.5 , a = 2 b .

Fig. 6
Fig. 6

(a) Pointing and (b) tracking errors versus the radius a and b for different deepness h. Here α = 1.5 , d = 0.2 D , and a = 2 b .

Fig. 7
Fig. 7

(a) Pointing and (b) tracking errors versus distance d for h = 0.8 λ against radii. Here α = 1.5 , a = b .

Fig. 8
Fig. 8

Pointing error versus deepness h, radii a and b, and distance d for different truncation ratio α. Here (a)  a = 2 b = 0.2 D , d = 0.2 D , (b)  h = 0.5 λ , d = 0.2 D , and a = 2 b , and (c)  h = 0.5 λ , and a = 2 b = 0.2 D .

Equations (17)

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

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