Abstract

We establish the model of a two-Cassegrain-telescope system that is commonly used in a relay mirror system. With this model, uplink transmission of the relay mirror system is theoretically analyzed. We determined that uplink transmission with turbulence completely corrected is not an optimal mode. We improve power coupling efficiency of the two-Cassegrain-telescope system by optimizing the optical phase at the launching telescope by use of the stochastic parallel gradient descent algorithm. For a 10km vertical uplink transmission, power coupling efficiencies of the system are 63.10%, 87.82%, and 97.80% corresponding to an open-loop mode, a closed-loop mode, and a closed-loop with optimization mode, respectively. For a 30km vertical uplink transmission, power coupling efficiencies of the system are 22.35%, 82.66%, and 91.91%, corresponding to an open-loop mode, a closed-loop mode, and a closed-loop with optimization mode, respectively. The results show that power coupling efficiency of the two-Cassegrain-telescope system is significantly improved.

© 2010 Optical Society of America

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References

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  1. L. D. Welch and D. C. Latham, “Report of the Defense Board Task Force on High Energy Laser Weapon System Applications” (Defense Science Board, 2001), pp. 56–57.
  2. M. Hartman, S. R. Restaino, J. T. Baker, D. M. Payne, and J. W. Bukley, “EAGLE: relay mirror technology development,” Proc. SPIE 4724, 108–115 (2002).
  3. E. A. Duff and D. C. Washburn, “The magic of relay mirrors,” Proc. SPIE 5413, 137–144 (2004).
    [CrossRef]
  4. M. Romano and B. N. Agrawal, “Tracking and pointing of target by a bifocal relay mirror spacecraft using attitude control and fast steering mirrors tilting ,” in AIAA Guidance, Navigation, and Control Conference and Exhibit, AIAA-2002-5030 (AIAA, 2002).
  5. S. L. Johnson, “Beam control of extremely agile relaying laser source for bifocal relay mirror spacecraft,” M.S. thesis (Naval Postgraduate School, 2006), pp. 1–2.
  6. G. E. Glaros, “Broad departmental application of directed energy systems” (Directed Energy Professional Society, 2004), pp. 7–28.
  7. Ren Guo-guang and Huang Ji-jin, “Major progress of U.S. 2005,” Laser Optoelectron. Prog. 43 (6), 5–6 (2006).
  8. S. G. Leonard, “Laser options for national missile defense,” M.S. thesis (Air Command and Staff College, 1998), pp. 75–84.
  9. Wu Huiyun, Wu Wuming, Chen Jinbao, and Xu Xiaojun, “Simulation of effect of 100 kW solid-state laser relay mirror system on 1 km altitude target,” Acta Opt. Sin. 28, 1967–1970 (2008), in Chinese.
    [CrossRef]
  10. St. Louis, “Boeing demonstrates aerospace relay mirror system,” http://www.spacewar.com/reports/ (18 August 2006).
  11. J. Simpson, “Tactical laser relay mirror demonstration anticipated before 2011,” Inside The Air Force 18 (41), 3 (2007).
  12. Ren Guoguang, “Current situation and development trend of high energy laser weapon,” Laser Optoelectron. Prog. 45, 67–69 (2008).
  13. Xu Xiao-jun, Atmospheric Optics and Auto-Adapted Optics Teaching Printed Lecture (National University of Defense Technology, 2007).
  14. J. W. Goodman, Fourier Optics (Roberts & Company, 2005).
  15. Ji Jia-rong, Higher Optics Course (National University of Defense Technology, 2007).
  16. M. A. Vorontsov and V. P. Sivokon, “Stochastic parallel-gradient-descent technique for high-resolution wave-front phase-distortion correction,” J. Opt. Soc. Am. A. 15, 2745–2758(1998).
    [CrossRef]
  17. Zhou Pu, Xu Xiaojun, Liu Zejin, and Chu Xiuxiang, “Improving the power coupling efficiency in relay mirror system using multiple laser array and SPGD algorithm,” Opt. Laser Technol. 42, 186 (2010).
    [CrossRef]

2010

Zhou Pu, Xu Xiaojun, Liu Zejin, and Chu Xiuxiang, “Improving the power coupling efficiency in relay mirror system using multiple laser array and SPGD algorithm,” Opt. Laser Technol. 42, 186 (2010).
[CrossRef]

2008

Ren Guoguang, “Current situation and development trend of high energy laser weapon,” Laser Optoelectron. Prog. 45, 67–69 (2008).

Wu Huiyun, Wu Wuming, Chen Jinbao, and Xu Xiaojun, “Simulation of effect of 100 kW solid-state laser relay mirror system on 1 km altitude target,” Acta Opt. Sin. 28, 1967–1970 (2008), in Chinese.
[CrossRef]

2007

J. Simpson, “Tactical laser relay mirror demonstration anticipated before 2011,” Inside The Air Force 18 (41), 3 (2007).

2006

Ren Guo-guang and Huang Ji-jin, “Major progress of U.S. 2005,” Laser Optoelectron. Prog. 43 (6), 5–6 (2006).

2004

E. A. Duff and D. C. Washburn, “The magic of relay mirrors,” Proc. SPIE 5413, 137–144 (2004).
[CrossRef]

2002

M. Hartman, S. R. Restaino, J. T. Baker, D. M. Payne, and J. W. Bukley, “EAGLE: relay mirror technology development,” Proc. SPIE 4724, 108–115 (2002).

1998

M. A. Vorontsov and V. P. Sivokon, “Stochastic parallel-gradient-descent technique for high-resolution wave-front phase-distortion correction,” J. Opt. Soc. Am. A. 15, 2745–2758(1998).
[CrossRef]

Agrawal, B. N.

M. Romano and B. N. Agrawal, “Tracking and pointing of target by a bifocal relay mirror spacecraft using attitude control and fast steering mirrors tilting ,” in AIAA Guidance, Navigation, and Control Conference and Exhibit, AIAA-2002-5030 (AIAA, 2002).

Baker, J. T.

M. Hartman, S. R. Restaino, J. T. Baker, D. M. Payne, and J. W. Bukley, “EAGLE: relay mirror technology development,” Proc. SPIE 4724, 108–115 (2002).

Bukley, J. W.

M. Hartman, S. R. Restaino, J. T. Baker, D. M. Payne, and J. W. Bukley, “EAGLE: relay mirror technology development,” Proc. SPIE 4724, 108–115 (2002).

Duff, E. A.

E. A. Duff and D. C. Washburn, “The magic of relay mirrors,” Proc. SPIE 5413, 137–144 (2004).
[CrossRef]

Glaros, G. E.

G. E. Glaros, “Broad departmental application of directed energy systems” (Directed Energy Professional Society, 2004), pp. 7–28.

Goodman, J. W.

J. W. Goodman, Fourier Optics (Roberts & Company, 2005).

Guoguang, Ren

Ren Guoguang, “Current situation and development trend of high energy laser weapon,” Laser Optoelectron. Prog. 45, 67–69 (2008).

Guo-guang, Ren

Ren Guo-guang and Huang Ji-jin, “Major progress of U.S. 2005,” Laser Optoelectron. Prog. 43 (6), 5–6 (2006).

Hartman, M.

M. Hartman, S. R. Restaino, J. T. Baker, D. M. Payne, and J. W. Bukley, “EAGLE: relay mirror technology development,” Proc. SPIE 4724, 108–115 (2002).

Huiyun, Wu

Wu Huiyun, Wu Wuming, Chen Jinbao, and Xu Xiaojun, “Simulation of effect of 100 kW solid-state laser relay mirror system on 1 km altitude target,” Acta Opt. Sin. 28, 1967–1970 (2008), in Chinese.
[CrossRef]

Jia-rong, Ji

Ji Jia-rong, Higher Optics Course (National University of Defense Technology, 2007).

Ji-jin, Huang

Ren Guo-guang and Huang Ji-jin, “Major progress of U.S. 2005,” Laser Optoelectron. Prog. 43 (6), 5–6 (2006).

Jinbao, Chen

Wu Huiyun, Wu Wuming, Chen Jinbao, and Xu Xiaojun, “Simulation of effect of 100 kW solid-state laser relay mirror system on 1 km altitude target,” Acta Opt. Sin. 28, 1967–1970 (2008), in Chinese.
[CrossRef]

Johnson, S. L.

S. L. Johnson, “Beam control of extremely agile relaying laser source for bifocal relay mirror spacecraft,” M.S. thesis (Naval Postgraduate School, 2006), pp. 1–2.

Latham, D. C.

L. D. Welch and D. C. Latham, “Report of the Defense Board Task Force on High Energy Laser Weapon System Applications” (Defense Science Board, 2001), pp. 56–57.

Leonard, S. G.

S. G. Leonard, “Laser options for national missile defense,” M.S. thesis (Air Command and Staff College, 1998), pp. 75–84.

Payne, D. M.

M. Hartman, S. R. Restaino, J. T. Baker, D. M. Payne, and J. W. Bukley, “EAGLE: relay mirror technology development,” Proc. SPIE 4724, 108–115 (2002).

Pu, Zhou

Zhou Pu, Xu Xiaojun, Liu Zejin, and Chu Xiuxiang, “Improving the power coupling efficiency in relay mirror system using multiple laser array and SPGD algorithm,” Opt. Laser Technol. 42, 186 (2010).
[CrossRef]

Restaino, S. R.

M. Hartman, S. R. Restaino, J. T. Baker, D. M. Payne, and J. W. Bukley, “EAGLE: relay mirror technology development,” Proc. SPIE 4724, 108–115 (2002).

Romano, M.

M. Romano and B. N. Agrawal, “Tracking and pointing of target by a bifocal relay mirror spacecraft using attitude control and fast steering mirrors tilting ,” in AIAA Guidance, Navigation, and Control Conference and Exhibit, AIAA-2002-5030 (AIAA, 2002).

Simpson, J.

J. Simpson, “Tactical laser relay mirror demonstration anticipated before 2011,” Inside The Air Force 18 (41), 3 (2007).

Sivokon, V. P.

M. A. Vorontsov and V. P. Sivokon, “Stochastic parallel-gradient-descent technique for high-resolution wave-front phase-distortion correction,” J. Opt. Soc. Am. A. 15, 2745–2758(1998).
[CrossRef]

Vorontsov, M. A.

M. A. Vorontsov and V. P. Sivokon, “Stochastic parallel-gradient-descent technique for high-resolution wave-front phase-distortion correction,” J. Opt. Soc. Am. A. 15, 2745–2758(1998).
[CrossRef]

Washburn, D. C.

E. A. Duff and D. C. Washburn, “The magic of relay mirrors,” Proc. SPIE 5413, 137–144 (2004).
[CrossRef]

Welch, L. D.

L. D. Welch and D. C. Latham, “Report of the Defense Board Task Force on High Energy Laser Weapon System Applications” (Defense Science Board, 2001), pp. 56–57.

Wuming, Wu

Wu Huiyun, Wu Wuming, Chen Jinbao, and Xu Xiaojun, “Simulation of effect of 100 kW solid-state laser relay mirror system on 1 km altitude target,” Acta Opt. Sin. 28, 1967–1970 (2008), in Chinese.
[CrossRef]

Xiaojun, Xu

Zhou Pu, Xu Xiaojun, Liu Zejin, and Chu Xiuxiang, “Improving the power coupling efficiency in relay mirror system using multiple laser array and SPGD algorithm,” Opt. Laser Technol. 42, 186 (2010).
[CrossRef]

Wu Huiyun, Wu Wuming, Chen Jinbao, and Xu Xiaojun, “Simulation of effect of 100 kW solid-state laser relay mirror system on 1 km altitude target,” Acta Opt. Sin. 28, 1967–1970 (2008), in Chinese.
[CrossRef]

Xiao-jun, Xu

Xu Xiao-jun, Atmospheric Optics and Auto-Adapted Optics Teaching Printed Lecture (National University of Defense Technology, 2007).

Xiuxiang, Chu

Zhou Pu, Xu Xiaojun, Liu Zejin, and Chu Xiuxiang, “Improving the power coupling efficiency in relay mirror system using multiple laser array and SPGD algorithm,” Opt. Laser Technol. 42, 186 (2010).
[CrossRef]

Zejin, Liu

Zhou Pu, Xu Xiaojun, Liu Zejin, and Chu Xiuxiang, “Improving the power coupling efficiency in relay mirror system using multiple laser array and SPGD algorithm,” Opt. Laser Technol. 42, 186 (2010).
[CrossRef]

Acta Opt. Sin.

Wu Huiyun, Wu Wuming, Chen Jinbao, and Xu Xiaojun, “Simulation of effect of 100 kW solid-state laser relay mirror system on 1 km altitude target,” Acta Opt. Sin. 28, 1967–1970 (2008), in Chinese.
[CrossRef]

Inside The Air Force

J. Simpson, “Tactical laser relay mirror demonstration anticipated before 2011,” Inside The Air Force 18 (41), 3 (2007).

J. Opt. Soc. Am. A.

M. A. Vorontsov and V. P. Sivokon, “Stochastic parallel-gradient-descent technique for high-resolution wave-front phase-distortion correction,” J. Opt. Soc. Am. A. 15, 2745–2758(1998).
[CrossRef]

Laser Optoelectron. Prog.

Ren Guoguang, “Current situation and development trend of high energy laser weapon,” Laser Optoelectron. Prog. 45, 67–69 (2008).

Ren Guo-guang and Huang Ji-jin, “Major progress of U.S. 2005,” Laser Optoelectron. Prog. 43 (6), 5–6 (2006).

Opt. Laser Technol.

Zhou Pu, Xu Xiaojun, Liu Zejin, and Chu Xiuxiang, “Improving the power coupling efficiency in relay mirror system using multiple laser array and SPGD algorithm,” Opt. Laser Technol. 42, 186 (2010).
[CrossRef]

Proc. SPIE

M. Hartman, S. R. Restaino, J. T. Baker, D. M. Payne, and J. W. Bukley, “EAGLE: relay mirror technology development,” Proc. SPIE 4724, 108–115 (2002).

E. A. Duff and D. C. Washburn, “The magic of relay mirrors,” Proc. SPIE 5413, 137–144 (2004).
[CrossRef]

Other

M. Romano and B. N. Agrawal, “Tracking and pointing of target by a bifocal relay mirror spacecraft using attitude control and fast steering mirrors tilting ,” in AIAA Guidance, Navigation, and Control Conference and Exhibit, AIAA-2002-5030 (AIAA, 2002).

S. L. Johnson, “Beam control of extremely agile relaying laser source for bifocal relay mirror spacecraft,” M.S. thesis (Naval Postgraduate School, 2006), pp. 1–2.

G. E. Glaros, “Broad departmental application of directed energy systems” (Directed Energy Professional Society, 2004), pp. 7–28.

S. G. Leonard, “Laser options for national missile defense,” M.S. thesis (Air Command and Staff College, 1998), pp. 75–84.

St. Louis, “Boeing demonstrates aerospace relay mirror system,” http://www.spacewar.com/reports/ (18 August 2006).

L. D. Welch and D. C. Latham, “Report of the Defense Board Task Force on High Energy Laser Weapon System Applications” (Defense Science Board, 2001), pp. 56–57.

Xu Xiao-jun, Atmospheric Optics and Auto-Adapted Optics Teaching Printed Lecture (National University of Defense Technology, 2007).

J. W. Goodman, Fourier Optics (Roberts & Company, 2005).

Ji Jia-rong, Higher Optics Course (National University of Defense Technology, 2007).

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of the relay mirror system.

Fig. 2
Fig. 2

Schematic diagram of the two-Cassegrain-telescope system.

Fig. 3
Fig. 3

Distribution of the phase screen at the launching telescope.

Fig. 4
Fig. 4

Phase correction of the adaptive optics system under the closed loop with optimization mode.

Fig. 5
Fig. 5

Intensity distribution of the receiving field under the open-loop mode.

Fig. 6
Fig. 6

Intensity distribution of the receiving field under the closed-loop mode.

Fig. 7
Fig. 7

Intensity distribution of the receiving field under the closed loop with optimization mode.

Tables (1)

Tables Icon

Table 1 Power Coupling Efficiencies of the Two-Cassegrain-Telescope System under Different Working Modes

Equations (10)

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U ( x , y ) = e j k z j λ z U 0 ( ε , η ) e j ψ 2 ( ε , η ) e j ψ 3 ( ε , η ) e j k 2 z [ ( x ε ) 2 + ( y η ) 2 ] d ε d η ,
U 0 ( ε , η ) = { 1 d 1 2 ε 2 + η 2 d 2 2 0 otherwise ,
ψ 3 ( ε , η ) = { ψ 2 ( ε , η ) closed loop 0 open loop ,
η = S I ( x , y ) d s S 0 I 0 ( ε , η ) d s 0 ,
U ( r ) = 2 π e j k z e j k 2 z r 2 j λ z 0 U 0 ( R ) e j k 2 z R 2 J 0 ( k R r 2 z ) R d R ,
U ( r ) = 2 π e j k z e j k 2 z r 2 j λ z 0 U 0 ( R ) e j ψ 1 ( R ) e j k 2 z R 2 J 0 ( k R r 2 z ) R d R .
η = d 3 / 2 d 4 / 2 I ( r ) d s S 0 I 0 ( R ) d s 0 ,
ψ 3 ( ε , η ) = { 0 open loop ψ 2 ( ε , η ) closed loop ψ m ( ε , η ) ψ 2 ( ε , η ) closed loop with optimization .
C n 2 ( h ) = 8.2 × 10 56 V ( h ) 2 h 10 exp ( h / 1000 ) + 2.7 × 10 16 exp ( h / 1500 ) + C 0 exp ( h / 100 ) ,
V ( h ) = 5 + 30 exp { [ ( h 9400 ) / 4800 ] 2 } ,

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