Abstract

In intersatellite optical communications it is important to obtain the most efficient performance of acquisition system with respect to acquisition time for a given probability. In this paper a novel approach to the analytical optimization of spatial acquisition is presented as an alternative of the conventional Monte Carlo simulation. First, an analytical expression of estimating mean acquisition time (MAT) is derived as a function of the desired acquisition probability, taking into account the distribution function of satellite position, field of uncertainty (FOU), beam divergence angle and dwell time. Accordingly, the analytical expression of multi-scan, which is always adopted by practical optical terminals to ensure the acquisition success, is also presented. Then, by minimizing the MAT of multi-scan, the optimum ratio of the FOU θUto the pointing error deviation σ is obtained, which is θU/σ=1.3. An example for a practical intersatellite acquisition between a Low Earth Orbit Satellite and a Geostationary Earth Orbit Satellite is given. And the theoretical result calculated by the proposed analytical expression is approximately equal to the result by Monte Carlo simulation. The results can be used in designing acquisition system for the intersatellite optical communications.

© 2011 OSA

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    [CrossRef]
  5. K. Kazaura, K. Omae, T. Suzuki, M. Matsumoto, E. Mutafungwa, T. O. Korhonen, T. Murakami, K. Takahashi, H. Matsumoto, K. Wakamori, and Y. Arimoto, “Enhancing performance of next generation FSO communication systems using soft computing-based predictions,” Opt. Express 14(12), 4958–4968 (2006).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2006 (1)

K. Kazaura, K. Omae, T. Suzuki, M. Matsumoto, E. Mutafungwa, T. O. Korhonen, T. Murakami, K. Takahashi, H. Matsumoto, K. Wakamori, and Y. Arimoto, “Enhancing performance of next generation FSO communication systems using soft computing-based predictions,” Opt. Express 14(12), 4958–4968 (2006).
[CrossRef] [PubMed]

2005 (1)

M. Toyoshima, “Trends in satellite communications and the role of optical free-space communications,” J. Opt. Networking 4(6), 300–311 (2005).
[CrossRef]

2002 (2)

M. Toyoshima, T. Jono, K. Nakagawa, and A. Yamamoto, “Optimum divergence angle of a Gaussian beam wave in the presence of random jitter in free-space laser communication systems,” J. Opt. Soc. Am. A 19(3), 567–571 (2002).
[CrossRef]

T. Tolker-Nielsen and G. Oppenhaeuser, “In orbit test of an operational optical intersatellite link between ARTEMIS and SPOT4, SILEX,” Proc. SPIE 4635, 1–15 (2002).
[CrossRef]

2001 (1)

M. Scheinfeild, N. S. Kopenika, and S. Arnon, “Acquisition time calculation and Influence of vibrations for Micro satellite laser communication in space,” Proc. SPIE 4365, 195–205 (2001).
[CrossRef]

2000 (2)

M. Scheinfeild, N. S. Kopenika, and R. Melamed, “Acquisition system for Microsatelllites laser communication in space,” Proc. SPIE 3932, 166–175 (2000).
[CrossRef]

S. Lee, J. W. Alexander, and M. Jeganathan, “Pointing and tracking subsystem design for optical communications link between the international space station and ground,” Proc. SPIE 3932, 150–157 (2000).
[CrossRef]

1999 (3)

R. W. Kaliski, S. M. Genco, D. Thompson, B. Breshears, T. O’Connor, K. M. Miller, E. W. Taylor, A. D. Sanchez, J. E. Winter, and R. M. Ewart, “Laser communication intersatellite links realized with commercial off-the-shelf technology,” Proc. SPIE 3615, 170–178 (1999).
[CrossRef]

T. Jono, M. toyoda, K. Nakagawa, A. Yamamoto, K. Shiratama, T. Kurii, and Y. Koyama, “Acquisition tracking and pointing system of OICETS for free space laser communications,” Proc. SPIE 3692, 41–50 (1999).
[CrossRef]

J. W. Alexander, S. Lee, and C. Chen, “Pointing and tracking concepts for deep space missions,” Proc. SPIE 3615, 230–249 (1999).
[CrossRef]

1998 (1)

T. H. Carbonneau and D. R. Wisely, “Opportunities and challenges for optical wireless: the competitive advantage of free space telecommunications links in today’s crowded marketplace,” Proc. SPIE 3232, 119–128 (1998).
[CrossRef]

1995 (1)

T. T. Nielsen, “Pointing Acquisition and Tracking System for the free space laser communication system, SILEX,” Proc. SPIE 2381, 194–205 (1995).
[CrossRef]

1994 (1)

G. Baister and P. V. Gatenby, “Pointing, acquisition and tracking for optical space communications,” J. Electron. Commun. Eng. 271–280 (December 1994).
[CrossRef]

1993 (2)

K. M. Iftekharuddin and M. A. Karim, “Acquisition by staring focal plane arrays: pixel geometry effects,” Opt. Eng. 32(11), 2649–2656 (1993).
[CrossRef]

V. A. Skormin, C. R. Herman, M. A. Tascilllo, and J. A. Tasullo, “Mathematical modeling and simulation analysis of pointing, acquisition, and tracking system for laser based Intersatellite communication,” Opt. Eng. 32(11), 2749–2763 (1993).
[CrossRef]

1988 (2)

R. G. Marshalek and G. A. Koepf, “Comparison of optical technologies for intersatellite links in a global telecommunication network,” Opt. Eng. 27, 663–676 (1988).

K. J. Held and J. D. Barry, “Precision pointing and tracking between satellite-born optical systems,” Opt. Eng. 27, 325–333 (1988).

1986 (1)

G. Picchi, G. Prati, and D. Santerini, “Algorithms for Spatial Laser Beacon Acquisition,” IEEE Trans. Aerospace Electron. Syst. AES-22(2), 106–114 (1986).
[CrossRef]

Alexander, J. W.

S. Lee, J. W. Alexander, and M. Jeganathan, “Pointing and tracking subsystem design for optical communications link between the international space station and ground,” Proc. SPIE 3932, 150–157 (2000).
[CrossRef]

J. W. Alexander, S. Lee, and C. Chen, “Pointing and tracking concepts for deep space missions,” Proc. SPIE 3615, 230–249 (1999).
[CrossRef]

Arimoto, Y.

K. Kazaura, K. Omae, T. Suzuki, M. Matsumoto, E. Mutafungwa, T. O. Korhonen, T. Murakami, K. Takahashi, H. Matsumoto, K. Wakamori, and Y. Arimoto, “Enhancing performance of next generation FSO communication systems using soft computing-based predictions,” Opt. Express 14(12), 4958–4968 (2006).
[CrossRef] [PubMed]

Arnon, S.

M. Scheinfeild, N. S. Kopenika, and S. Arnon, “Acquisition time calculation and Influence of vibrations for Micro satellite laser communication in space,” Proc. SPIE 4365, 195–205 (2001).
[CrossRef]

Baister, G.

G. Baister and P. V. Gatenby, “Pointing, acquisition and tracking for optical space communications,” J. Electron. Commun. Eng. 271–280 (December 1994).
[CrossRef]

Barry, J. D.

K. J. Held and J. D. Barry, “Precision pointing and tracking between satellite-born optical systems,” Opt. Eng. 27, 325–333 (1988).

Breshears, B.

R. W. Kaliski, S. M. Genco, D. Thompson, B. Breshears, T. O’Connor, K. M. Miller, E. W. Taylor, A. D. Sanchez, J. E. Winter, and R. M. Ewart, “Laser communication intersatellite links realized with commercial off-the-shelf technology,” Proc. SPIE 3615, 170–178 (1999).
[CrossRef]

Carbonneau, T. H.

T. H. Carbonneau and D. R. Wisely, “Opportunities and challenges for optical wireless: the competitive advantage of free space telecommunications links in today’s crowded marketplace,” Proc. SPIE 3232, 119–128 (1998).
[CrossRef]

Chen, C.

J. W. Alexander, S. Lee, and C. Chen, “Pointing and tracking concepts for deep space missions,” Proc. SPIE 3615, 230–249 (1999).
[CrossRef]

Ewart, R. M.

R. W. Kaliski, S. M. Genco, D. Thompson, B. Breshears, T. O’Connor, K. M. Miller, E. W. Taylor, A. D. Sanchez, J. E. Winter, and R. M. Ewart, “Laser communication intersatellite links realized with commercial off-the-shelf technology,” Proc. SPIE 3615, 170–178 (1999).
[CrossRef]

Gatenby, P. V.

G. Baister and P. V. Gatenby, “Pointing, acquisition and tracking for optical space communications,” J. Electron. Commun. Eng. 271–280 (December 1994).
[CrossRef]

Genco, S. M.

R. W. Kaliski, S. M. Genco, D. Thompson, B. Breshears, T. O’Connor, K. M. Miller, E. W. Taylor, A. D. Sanchez, J. E. Winter, and R. M. Ewart, “Laser communication intersatellite links realized with commercial off-the-shelf technology,” Proc. SPIE 3615, 170–178 (1999).
[CrossRef]

Held, K. J.

K. J. Held and J. D. Barry, “Precision pointing and tracking between satellite-born optical systems,” Opt. Eng. 27, 325–333 (1988).

Herman, C. R.

V. A. Skormin, C. R. Herman, M. A. Tascilllo, and J. A. Tasullo, “Mathematical modeling and simulation analysis of pointing, acquisition, and tracking system for laser based Intersatellite communication,” Opt. Eng. 32(11), 2749–2763 (1993).
[CrossRef]

Iftekharuddin, K. M.

K. M. Iftekharuddin and M. A. Karim, “Acquisition by staring focal plane arrays: pixel geometry effects,” Opt. Eng. 32(11), 2649–2656 (1993).
[CrossRef]

Jeganathan, M.

S. Lee, J. W. Alexander, and M. Jeganathan, “Pointing and tracking subsystem design for optical communications link between the international space station and ground,” Proc. SPIE 3932, 150–157 (2000).
[CrossRef]

Jono, T.

M. Toyoshima, T. Jono, K. Nakagawa, and A. Yamamoto, “Optimum divergence angle of a Gaussian beam wave in the presence of random jitter in free-space laser communication systems,” J. Opt. Soc. Am. A 19(3), 567–571 (2002).
[CrossRef]

T. Jono, M. toyoda, K. Nakagawa, A. Yamamoto, K. Shiratama, T. Kurii, and Y. Koyama, “Acquisition tracking and pointing system of OICETS for free space laser communications,” Proc. SPIE 3692, 41–50 (1999).
[CrossRef]

Kaliski, R. W.

R. W. Kaliski, S. M. Genco, D. Thompson, B. Breshears, T. O’Connor, K. M. Miller, E. W. Taylor, A. D. Sanchez, J. E. Winter, and R. M. Ewart, “Laser communication intersatellite links realized with commercial off-the-shelf technology,” Proc. SPIE 3615, 170–178 (1999).
[CrossRef]

Karim, M. A.

K. M. Iftekharuddin and M. A. Karim, “Acquisition by staring focal plane arrays: pixel geometry effects,” Opt. Eng. 32(11), 2649–2656 (1993).
[CrossRef]

Kazaura, K.

K. Kazaura, K. Omae, T. Suzuki, M. Matsumoto, E. Mutafungwa, T. O. Korhonen, T. Murakami, K. Takahashi, H. Matsumoto, K. Wakamori, and Y. Arimoto, “Enhancing performance of next generation FSO communication systems using soft computing-based predictions,” Opt. Express 14(12), 4958–4968 (2006).
[CrossRef] [PubMed]

Koepf, G. A.

R. G. Marshalek and G. A. Koepf, “Comparison of optical technologies for intersatellite links in a global telecommunication network,” Opt. Eng. 27, 663–676 (1988).

Kopenika, N. S.

M. Scheinfeild, N. S. Kopenika, and S. Arnon, “Acquisition time calculation and Influence of vibrations for Micro satellite laser communication in space,” Proc. SPIE 4365, 195–205 (2001).
[CrossRef]

M. Scheinfeild, N. S. Kopenika, and R. Melamed, “Acquisition system for Microsatelllites laser communication in space,” Proc. SPIE 3932, 166–175 (2000).
[CrossRef]

Korhonen, T. O.

K. Kazaura, K. Omae, T. Suzuki, M. Matsumoto, E. Mutafungwa, T. O. Korhonen, T. Murakami, K. Takahashi, H. Matsumoto, K. Wakamori, and Y. Arimoto, “Enhancing performance of next generation FSO communication systems using soft computing-based predictions,” Opt. Express 14(12), 4958–4968 (2006).
[CrossRef] [PubMed]

Koyama, Y.

T. Jono, M. toyoda, K. Nakagawa, A. Yamamoto, K. Shiratama, T. Kurii, and Y. Koyama, “Acquisition tracking and pointing system of OICETS for free space laser communications,” Proc. SPIE 3692, 41–50 (1999).
[CrossRef]

Kurii, T.

T. Jono, M. toyoda, K. Nakagawa, A. Yamamoto, K. Shiratama, T. Kurii, and Y. Koyama, “Acquisition tracking and pointing system of OICETS for free space laser communications,” Proc. SPIE 3692, 41–50 (1999).
[CrossRef]

Lee, S.

S. Lee, J. W. Alexander, and M. Jeganathan, “Pointing and tracking subsystem design for optical communications link between the international space station and ground,” Proc. SPIE 3932, 150–157 (2000).
[CrossRef]

J. W. Alexander, S. Lee, and C. Chen, “Pointing and tracking concepts for deep space missions,” Proc. SPIE 3615, 230–249 (1999).
[CrossRef]

Marshalek, R. G.

R. G. Marshalek and G. A. Koepf, “Comparison of optical technologies for intersatellite links in a global telecommunication network,” Opt. Eng. 27, 663–676 (1988).

Matsumoto, H.

K. Kazaura, K. Omae, T. Suzuki, M. Matsumoto, E. Mutafungwa, T. O. Korhonen, T. Murakami, K. Takahashi, H. Matsumoto, K. Wakamori, and Y. Arimoto, “Enhancing performance of next generation FSO communication systems using soft computing-based predictions,” Opt. Express 14(12), 4958–4968 (2006).
[CrossRef] [PubMed]

Matsumoto, M.

K. Kazaura, K. Omae, T. Suzuki, M. Matsumoto, E. Mutafungwa, T. O. Korhonen, T. Murakami, K. Takahashi, H. Matsumoto, K. Wakamori, and Y. Arimoto, “Enhancing performance of next generation FSO communication systems using soft computing-based predictions,” Opt. Express 14(12), 4958–4968 (2006).
[CrossRef] [PubMed]

Melamed, R.

M. Scheinfeild, N. S. Kopenika, and R. Melamed, “Acquisition system for Microsatelllites laser communication in space,” Proc. SPIE 3932, 166–175 (2000).
[CrossRef]

Miller, K. M.

R. W. Kaliski, S. M. Genco, D. Thompson, B. Breshears, T. O’Connor, K. M. Miller, E. W. Taylor, A. D. Sanchez, J. E. Winter, and R. M. Ewart, “Laser communication intersatellite links realized with commercial off-the-shelf technology,” Proc. SPIE 3615, 170–178 (1999).
[CrossRef]

Murakami, T.

K. Kazaura, K. Omae, T. Suzuki, M. Matsumoto, E. Mutafungwa, T. O. Korhonen, T. Murakami, K. Takahashi, H. Matsumoto, K. Wakamori, and Y. Arimoto, “Enhancing performance of next generation FSO communication systems using soft computing-based predictions,” Opt. Express 14(12), 4958–4968 (2006).
[CrossRef] [PubMed]

Mutafungwa, E.

K. Kazaura, K. Omae, T. Suzuki, M. Matsumoto, E. Mutafungwa, T. O. Korhonen, T. Murakami, K. Takahashi, H. Matsumoto, K. Wakamori, and Y. Arimoto, “Enhancing performance of next generation FSO communication systems using soft computing-based predictions,” Opt. Express 14(12), 4958–4968 (2006).
[CrossRef] [PubMed]

Nakagawa, K.

M. Toyoshima, T. Jono, K. Nakagawa, and A. Yamamoto, “Optimum divergence angle of a Gaussian beam wave in the presence of random jitter in free-space laser communication systems,” J. Opt. Soc. Am. A 19(3), 567–571 (2002).
[CrossRef]

T. Jono, M. toyoda, K. Nakagawa, A. Yamamoto, K. Shiratama, T. Kurii, and Y. Koyama, “Acquisition tracking and pointing system of OICETS for free space laser communications,” Proc. SPIE 3692, 41–50 (1999).
[CrossRef]

Nielsen, T. T.

T. T. Nielsen, “Pointing Acquisition and Tracking System for the free space laser communication system, SILEX,” Proc. SPIE 2381, 194–205 (1995).
[CrossRef]

O’Connor, T.

R. W. Kaliski, S. M. Genco, D. Thompson, B. Breshears, T. O’Connor, K. M. Miller, E. W. Taylor, A. D. Sanchez, J. E. Winter, and R. M. Ewart, “Laser communication intersatellite links realized with commercial off-the-shelf technology,” Proc. SPIE 3615, 170–178 (1999).
[CrossRef]

Omae, K.

K. Kazaura, K. Omae, T. Suzuki, M. Matsumoto, E. Mutafungwa, T. O. Korhonen, T. Murakami, K. Takahashi, H. Matsumoto, K. Wakamori, and Y. Arimoto, “Enhancing performance of next generation FSO communication systems using soft computing-based predictions,” Opt. Express 14(12), 4958–4968 (2006).
[CrossRef] [PubMed]

Oppenhaeuser, G.

T. Tolker-Nielsen and G. Oppenhaeuser, “In orbit test of an operational optical intersatellite link between ARTEMIS and SPOT4, SILEX,” Proc. SPIE 4635, 1–15 (2002).
[CrossRef]

Picchi, G.

G. Picchi, G. Prati, and D. Santerini, “Algorithms for Spatial Laser Beacon Acquisition,” IEEE Trans. Aerospace Electron. Syst. AES-22(2), 106–114 (1986).
[CrossRef]

Prati, G.

G. Picchi, G. Prati, and D. Santerini, “Algorithms for Spatial Laser Beacon Acquisition,” IEEE Trans. Aerospace Electron. Syst. AES-22(2), 106–114 (1986).
[CrossRef]

Sanchez, A. D.

R. W. Kaliski, S. M. Genco, D. Thompson, B. Breshears, T. O’Connor, K. M. Miller, E. W. Taylor, A. D. Sanchez, J. E. Winter, and R. M. Ewart, “Laser communication intersatellite links realized with commercial off-the-shelf technology,” Proc. SPIE 3615, 170–178 (1999).
[CrossRef]

Santerini, D.

G. Picchi, G. Prati, and D. Santerini, “Algorithms for Spatial Laser Beacon Acquisition,” IEEE Trans. Aerospace Electron. Syst. AES-22(2), 106–114 (1986).
[CrossRef]

Scheinfeild, M.

M. Scheinfeild, N. S. Kopenika, and S. Arnon, “Acquisition time calculation and Influence of vibrations for Micro satellite laser communication in space,” Proc. SPIE 4365, 195–205 (2001).
[CrossRef]

M. Scheinfeild, N. S. Kopenika, and R. Melamed, “Acquisition system for Microsatelllites laser communication in space,” Proc. SPIE 3932, 166–175 (2000).
[CrossRef]

Shiratama, K.

T. Jono, M. toyoda, K. Nakagawa, A. Yamamoto, K. Shiratama, T. Kurii, and Y. Koyama, “Acquisition tracking and pointing system of OICETS for free space laser communications,” Proc. SPIE 3692, 41–50 (1999).
[CrossRef]

Skormin, V. A.

V. A. Skormin, C. R. Herman, M. A. Tascilllo, and J. A. Tasullo, “Mathematical modeling and simulation analysis of pointing, acquisition, and tracking system for laser based Intersatellite communication,” Opt. Eng. 32(11), 2749–2763 (1993).
[CrossRef]

Suzuki, T.

K. Kazaura, K. Omae, T. Suzuki, M. Matsumoto, E. Mutafungwa, T. O. Korhonen, T. Murakami, K. Takahashi, H. Matsumoto, K. Wakamori, and Y. Arimoto, “Enhancing performance of next generation FSO communication systems using soft computing-based predictions,” Opt. Express 14(12), 4958–4968 (2006).
[CrossRef] [PubMed]

Takahashi, K.

K. Kazaura, K. Omae, T. Suzuki, M. Matsumoto, E. Mutafungwa, T. O. Korhonen, T. Murakami, K. Takahashi, H. Matsumoto, K. Wakamori, and Y. Arimoto, “Enhancing performance of next generation FSO communication systems using soft computing-based predictions,” Opt. Express 14(12), 4958–4968 (2006).
[CrossRef] [PubMed]

Tascilllo, M. A.

V. A. Skormin, C. R. Herman, M. A. Tascilllo, and J. A. Tasullo, “Mathematical modeling and simulation analysis of pointing, acquisition, and tracking system for laser based Intersatellite communication,” Opt. Eng. 32(11), 2749–2763 (1993).
[CrossRef]

Tasullo, J. A.

V. A. Skormin, C. R. Herman, M. A. Tascilllo, and J. A. Tasullo, “Mathematical modeling and simulation analysis of pointing, acquisition, and tracking system for laser based Intersatellite communication,” Opt. Eng. 32(11), 2749–2763 (1993).
[CrossRef]

Taylor, E. W.

R. W. Kaliski, S. M. Genco, D. Thompson, B. Breshears, T. O’Connor, K. M. Miller, E. W. Taylor, A. D. Sanchez, J. E. Winter, and R. M. Ewart, “Laser communication intersatellite links realized with commercial off-the-shelf technology,” Proc. SPIE 3615, 170–178 (1999).
[CrossRef]

Thompson, D.

R. W. Kaliski, S. M. Genco, D. Thompson, B. Breshears, T. O’Connor, K. M. Miller, E. W. Taylor, A. D. Sanchez, J. E. Winter, and R. M. Ewart, “Laser communication intersatellite links realized with commercial off-the-shelf technology,” Proc. SPIE 3615, 170–178 (1999).
[CrossRef]

Tolker-Nielsen, T.

T. Tolker-Nielsen and G. Oppenhaeuser, “In orbit test of an operational optical intersatellite link between ARTEMIS and SPOT4, SILEX,” Proc. SPIE 4635, 1–15 (2002).
[CrossRef]

toyoda, M.

T. Jono, M. toyoda, K. Nakagawa, A. Yamamoto, K. Shiratama, T. Kurii, and Y. Koyama, “Acquisition tracking and pointing system of OICETS for free space laser communications,” Proc. SPIE 3692, 41–50 (1999).
[CrossRef]

Toyoshima, M.

M. Toyoshima, “Trends in satellite communications and the role of optical free-space communications,” J. Opt. Networking 4(6), 300–311 (2005).
[CrossRef]

M. Toyoshima, T. Jono, K. Nakagawa, and A. Yamamoto, “Optimum divergence angle of a Gaussian beam wave in the presence of random jitter in free-space laser communication systems,” J. Opt. Soc. Am. A 19(3), 567–571 (2002).
[CrossRef]

Wakamori, K.

K. Kazaura, K. Omae, T. Suzuki, M. Matsumoto, E. Mutafungwa, T. O. Korhonen, T. Murakami, K. Takahashi, H. Matsumoto, K. Wakamori, and Y. Arimoto, “Enhancing performance of next generation FSO communication systems using soft computing-based predictions,” Opt. Express 14(12), 4958–4968 (2006).
[CrossRef] [PubMed]

Winter, J. E.

R. W. Kaliski, S. M. Genco, D. Thompson, B. Breshears, T. O’Connor, K. M. Miller, E. W. Taylor, A. D. Sanchez, J. E. Winter, and R. M. Ewart, “Laser communication intersatellite links realized with commercial off-the-shelf technology,” Proc. SPIE 3615, 170–178 (1999).
[CrossRef]

Wisely, D. R.

T. H. Carbonneau and D. R. Wisely, “Opportunities and challenges for optical wireless: the competitive advantage of free space telecommunications links in today’s crowded marketplace,” Proc. SPIE 3232, 119–128 (1998).
[CrossRef]

Yamamoto, A.

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[CrossRef]

IEEE Trans. Aerospace Electron. Syst. (1)

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M. Toyoshima, T. Jono, K. Nakagawa, and A. Yamamoto, “Optimum divergence angle of a Gaussian beam wave in the presence of random jitter in free-space laser communication systems,” J. Opt. Soc. Am. A 19(3), 567–571 (2002).
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Opt. Eng. (4)

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Opt. Express (1)

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Proc. SPIE (9)

J. W. Alexander, S. Lee, and C. Chen, “Pointing and tracking concepts for deep space missions,” Proc. SPIE 3615, 230–249 (1999).
[CrossRef]

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[CrossRef]

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Other (2)

C. Hindman, and L. Toberton, “Beaconless satellite laser acquisition – modeling and feasibility,” MILCOM 2004 – IEEE Military Communications Conference, Montery, CA 2004. pp. 41–47.

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Figures (7)

Fig. 1
Fig. 1

Illustration of spatial acquisition

Fig. 2
Fig. 2

Position of satellite with Gaussian distribution 400 points in the relative field of uncertainty area; probability of acquisition as a function of the ratio of half-width of uncertainty area to the deviation of satellite position

Fig. 3
Fig. 3

Sketch of spiral scan in the field of uncertainty area

Fig. 4
Fig. 4

Single-scan MAT Vs. the FOU for various deviation of satellite position

Fig. 5
Fig. 5

Multi-scan MAT Vs. FOU and deviation of satellite position with Δ t = 0.1 s and I θ = 0.6 m r a d

Fig. 6
Fig. 6

Multi-scan MAT Vs. deviation of satellite position at different level of FOU with Δ t = 0.1 s and I θ = 0.6 m r a d

Fig. 7
Fig. 7

Comparison of simulation and theoretical MAT of multi-scan Vs. the ratio of FOU to deviation of satellite position

Equations (21)

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f ( θ v , h ) = 1 2 π σ v , h exp ( θ v , h 2 2 σ v , h 2 )
f ( θ ) = θ σ 2 exp ( θ 2 2 σ 2 )
P a c q = 0 θ U f ( θ ) d θ = 1 exp ( θ U 2 2 σ 2 )
r s = I θ 2 π θ s
T ( r s ) π r s 2 I θ 2 Δ t
Δ t = T R + 2 l c
T U = π θ U 2 I θ 2 Δ t
E T S = 0 θ U T ( θ r ) f ( θ r ) d θ r
E T S = 2 π σ 2 I θ 2 [ 1 ( θ U 2 2 σ 2 + 1 ) exp ( θ U 2 2 σ 2 ) ] Δ t
θ U = 2 σ 2 ln ( 1 P S )
M = A 1 + A 1 ¯ A 2 + ... + A 1 ¯ A 2 ¯ ... A i 1 ¯ A i + ...
P M = P ( A 1 ) + P ( A 1 ¯ A 2 ) + ... + P ( A 1 ¯ A 2 ¯ ... A i 1 ¯ A i ) + ...
P M = i = 1 n P S ( 1 P S ) i 1
E T M = E T ( A 1 ) + E T ( A 1 ¯ A 2 ) + ... + E T ( A 1 ¯ A 2 ¯ ... A i 1 ¯ A i ) + ...
E T M = E T S P S + ( T U + E T S ) ( 1 P S ) P S + ... + [ ( i 1 ) T U + E T S ] ( 1 P S ) i 1 P S + ...
E T M = E T S + ( 1 P S P S ) T U
E T M = 2 π σ 2 I θ 2 [ 1 ( θ U 2 2 σ 2 + 1 ) exp ( θ U 2 2 σ 2 ) + exp ( θ U 2 2 σ 2 ) 1 exp ( θ U 2 2 σ 2 ) θ U 2 2 σ 2 ] Δ t
E T M ( θ U ) θ U = 0
E T M ( θ U ) θ U = E T M ( ε ) ε d ε d θ U = 0
E T M ( ε ) ε = 0
θ U = 1.3 σ

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