Abstract

A four-element retroreflector was designed for satellite laser ranging and Earth–satellite–Earth laser long-path absorption measurement of the atmosphere. The retroreflector consists of four symmetrically located corner retroreflectors. Each retroreflector element has curved mirrors and tuned dihedral angles to correct velocity aberrations. A genetic algorithm was employed to optimize dihedral angles of each element and the directions of the four elements. The optimized four-element retroreflector has high reflectance with a reasonably broad angular coverage. It is also shown that the genetic algorithm is effective for optimizing optics with many parameters.

© 1998 Optical Society of America

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References

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  1. Advanced Earth Observation Satellite Pamphlet (National Space Development Agency of Japan, Tokyo, 1992).
  2. A. Minato, N. Sugimoto, Y. Sasano, “Optical design of cube corner retroreflectors having curved mirror surfaces,” Appl. Opt. 31, 6015–6020 (1992).
    [CrossRef] [PubMed]
  3. N. Sugimoto, “Retroreflector in Space (RIS) experiment,” in Proceedings of the 17th Laser Rader Conference (National Space Development Agency of Japan, Tokyo, 1994), pp. 181–183.
  4. N Sugimoto, A Minato, I Matsui, Y Sasano, T Itabe, T Aoki, M Takabe, N Hiromoto, H Kunimori, “Plan for the experiment with the retroreflector in space (RIS) on ADEOS,” in Advanced and Next-Generation Satellite, H. Fujisada, M. N. Sweeting, eds., SPIE2583, 217–227 (1995).
  5. N. Sugimoto, A. Minato, “Data reduction method for the laser long-path absorption measurement of atmospheric trace species using the retroreflector in space,” IEICE Trans. Commun. E78-B, 1585–1590 (1995).
  6. N. Sugimoto, A. Minato, “Optical characteristics of the Retroreflector in Space for the Earth Observing Satellite,” Opt. Rev. 3, 62–64 (1996).
    [CrossRef]
  7. J. H. Holland, Adaptation in Natural and Artificial Systems (MIT, Cambridge, Mass., 1992).
  8. D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, Reading, Mass., 1989).

1996 (1)

N. Sugimoto, A. Minato, “Optical characteristics of the Retroreflector in Space for the Earth Observing Satellite,” Opt. Rev. 3, 62–64 (1996).
[CrossRef]

1995 (1)

N. Sugimoto, A. Minato, “Data reduction method for the laser long-path absorption measurement of atmospheric trace species using the retroreflector in space,” IEICE Trans. Commun. E78-B, 1585–1590 (1995).

1992 (1)

Aoki, T

N Sugimoto, A Minato, I Matsui, Y Sasano, T Itabe, T Aoki, M Takabe, N Hiromoto, H Kunimori, “Plan for the experiment with the retroreflector in space (RIS) on ADEOS,” in Advanced and Next-Generation Satellite, H. Fujisada, M. N. Sweeting, eds., SPIE2583, 217–227 (1995).

Goldberg, D. E.

D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, Reading, Mass., 1989).

Hiromoto, N

N Sugimoto, A Minato, I Matsui, Y Sasano, T Itabe, T Aoki, M Takabe, N Hiromoto, H Kunimori, “Plan for the experiment with the retroreflector in space (RIS) on ADEOS,” in Advanced and Next-Generation Satellite, H. Fujisada, M. N. Sweeting, eds., SPIE2583, 217–227 (1995).

Holland, J. H.

J. H. Holland, Adaptation in Natural and Artificial Systems (MIT, Cambridge, Mass., 1992).

Itabe, T

N Sugimoto, A Minato, I Matsui, Y Sasano, T Itabe, T Aoki, M Takabe, N Hiromoto, H Kunimori, “Plan for the experiment with the retroreflector in space (RIS) on ADEOS,” in Advanced and Next-Generation Satellite, H. Fujisada, M. N. Sweeting, eds., SPIE2583, 217–227 (1995).

Kunimori, H

N Sugimoto, A Minato, I Matsui, Y Sasano, T Itabe, T Aoki, M Takabe, N Hiromoto, H Kunimori, “Plan for the experiment with the retroreflector in space (RIS) on ADEOS,” in Advanced and Next-Generation Satellite, H. Fujisada, M. N. Sweeting, eds., SPIE2583, 217–227 (1995).

Matsui, I

N Sugimoto, A Minato, I Matsui, Y Sasano, T Itabe, T Aoki, M Takabe, N Hiromoto, H Kunimori, “Plan for the experiment with the retroreflector in space (RIS) on ADEOS,” in Advanced and Next-Generation Satellite, H. Fujisada, M. N. Sweeting, eds., SPIE2583, 217–227 (1995).

Minato, A

N Sugimoto, A Minato, I Matsui, Y Sasano, T Itabe, T Aoki, M Takabe, N Hiromoto, H Kunimori, “Plan for the experiment with the retroreflector in space (RIS) on ADEOS,” in Advanced and Next-Generation Satellite, H. Fujisada, M. N. Sweeting, eds., SPIE2583, 217–227 (1995).

Minato, A.

N. Sugimoto, A. Minato, “Optical characteristics of the Retroreflector in Space for the Earth Observing Satellite,” Opt. Rev. 3, 62–64 (1996).
[CrossRef]

N. Sugimoto, A. Minato, “Data reduction method for the laser long-path absorption measurement of atmospheric trace species using the retroreflector in space,” IEICE Trans. Commun. E78-B, 1585–1590 (1995).

A. Minato, N. Sugimoto, Y. Sasano, “Optical design of cube corner retroreflectors having curved mirror surfaces,” Appl. Opt. 31, 6015–6020 (1992).
[CrossRef] [PubMed]

Sasano, Y

N Sugimoto, A Minato, I Matsui, Y Sasano, T Itabe, T Aoki, M Takabe, N Hiromoto, H Kunimori, “Plan for the experiment with the retroreflector in space (RIS) on ADEOS,” in Advanced and Next-Generation Satellite, H. Fujisada, M. N. Sweeting, eds., SPIE2583, 217–227 (1995).

Sasano, Y.

Sugimoto, N

N Sugimoto, A Minato, I Matsui, Y Sasano, T Itabe, T Aoki, M Takabe, N Hiromoto, H Kunimori, “Plan for the experiment with the retroreflector in space (RIS) on ADEOS,” in Advanced and Next-Generation Satellite, H. Fujisada, M. N. Sweeting, eds., SPIE2583, 217–227 (1995).

Sugimoto, N.

N. Sugimoto, A. Minato, “Optical characteristics of the Retroreflector in Space for the Earth Observing Satellite,” Opt. Rev. 3, 62–64 (1996).
[CrossRef]

N. Sugimoto, A. Minato, “Data reduction method for the laser long-path absorption measurement of atmospheric trace species using the retroreflector in space,” IEICE Trans. Commun. E78-B, 1585–1590 (1995).

A. Minato, N. Sugimoto, Y. Sasano, “Optical design of cube corner retroreflectors having curved mirror surfaces,” Appl. Opt. 31, 6015–6020 (1992).
[CrossRef] [PubMed]

N. Sugimoto, “Retroreflector in Space (RIS) experiment,” in Proceedings of the 17th Laser Rader Conference (National Space Development Agency of Japan, Tokyo, 1994), pp. 181–183.

Takabe, M

N Sugimoto, A Minato, I Matsui, Y Sasano, T Itabe, T Aoki, M Takabe, N Hiromoto, H Kunimori, “Plan for the experiment with the retroreflector in space (RIS) on ADEOS,” in Advanced and Next-Generation Satellite, H. Fujisada, M. N. Sweeting, eds., SPIE2583, 217–227 (1995).

Appl. Opt. (1)

IEICE Trans. Commun. (1)

N. Sugimoto, A. Minato, “Data reduction method for the laser long-path absorption measurement of atmospheric trace species using the retroreflector in space,” IEICE Trans. Commun. E78-B, 1585–1590 (1995).

Opt. Rev. (1)

N. Sugimoto, A. Minato, “Optical characteristics of the Retroreflector in Space for the Earth Observing Satellite,” Opt. Rev. 3, 62–64 (1996).
[CrossRef]

Other (5)

J. H. Holland, Adaptation in Natural and Artificial Systems (MIT, Cambridge, Mass., 1992).

D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, Reading, Mass., 1989).

Advanced Earth Observation Satellite Pamphlet (National Space Development Agency of Japan, Tokyo, 1992).

N. Sugimoto, “Retroreflector in Space (RIS) experiment,” in Proceedings of the 17th Laser Rader Conference (National Space Development Agency of Japan, Tokyo, 1994), pp. 181–183.

N Sugimoto, A Minato, I Matsui, Y Sasano, T Itabe, T Aoki, M Takabe, N Hiromoto, H Kunimori, “Plan for the experiment with the retroreflector in space (RIS) on ADEOS,” in Advanced and Next-Generation Satellite, H. Fujisada, M. N. Sweeting, eds., SPIE2583, 217–227 (1995).

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Figures (6)

Fig. 1
Fig. 1

Structure of the four-element retroreflector. Elements are symmetrical with respect to the xy and yz planes.

Fig. 2
Fig. 2

Coverage of the retroreflector. The minimum of optical efficiencies at points A to I was defined as the fitness value in the optimization with the GA.

Fig. 3
Fig. 3

Definition of parameters of an element (element 1 in Fig. 1) of the four-element retroreflector: curvatures of three mirrors, three dihedral angles, and direction of the retroreflector element.

Fig. 4
Fig. 4

Fitness value of the best gene and an average of fitness values of all genes as a function of generation: (a) 15-cm mirror, 532-nm wavelength; (b) 15-cm mirror, 10-μm wavelength; (c) 35-cm mirror, 532-nm wavelength; (d) 35-cm mirror, 10-μm wavelength.

Fig. 5
Fig. 5

Overall efficiencies of the optimized four-element retroreflector with a 15-cm mirror as a function of location of ground station at (a) 532 nm and (b) 10 μm.

Fig. 6
Fig. 6

Efficiency of the element of an optimized retroreflector with a 15-cm mirror at 532 nm.

Tables (1)

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Table 1 Designs of Retroreflectors and Their Optical Efficiencies

Equations (14)

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Δ θ = 2 v   sin   ϕ / c ,
P r = 16 / π 2 P 0 / θ t 2 T 2 η ret A r η sys η ,
δ 1 = B 0 + 2 B 1 + 4 B 2 + 8 B 3 + 16 B 4 + 32 B 5 × 2.4 × 10 - 7 rad ,
δ 2 = B 6 + 2 B 7 + 4 B 8 + 8 B 9 + 16 B 10 + 32 B 11 × 2.4 × 10 - 7 rad ,
δ 3 = B 12 + 2 B 13 + 4 B 14 + 8 B 15 + 16 B 16 + 32 B 17 × 2.4 × 10 - 7 rad ,
1 / r 1 = B 18 + 2 B 19 + 4 B 20 + 8 B 21 + 16 B 22 + 32 B 23 × 2.0 × 10 - 6 1 / m ,
1 / r 2 = B 24 + 2 B 25 + 4 B 26 + 8 B 27 + 16 B 28 + 32 B 29 × 2.0 × 10 - 6 1 / m ,
1 / r 3 = B 30 + 2 B 31 + 4 B 32 + 8 B 33 + 16 B 34 + 32 B 35 × 2.0 × 10 - 6 1 / m ,
e 1 = cos   θ 2 cos   θ 3 ,   - cos   θ 2 sin   θ 3 ,   sin   θ 2 ,
e 2 = sin   θ 1 sin   θ 3 - cos   θ 1 sin   θ 2 cos   θ 3 ,   sin   θ 1 cos   θ 3 + cos   θ 1 sin   θ 2 sin   θ 3 ,   cos   θ 1 cos   θ 2 ,
e 3 = - sin   θ 1 sin   θ 2 cos   θ 3 - cos   θ 1 sin   θ 3 ,   sin   θ 1 sin   θ 2 sin   θ 3 - cos   θ 1 cos   θ 3 ,   sin   θ 1 cos   θ 2 ,
θ 1 = B 36 + 2 B 37 + 4 B 38 + 8 B 39 + 10   deg ,
θ 2 = B 40 + 2 B 41 + 4 B 42 + 8 B 43 deg ,
θ 3 = B 44 + 2 B 45 + 4 B 46 + 8 B 47 deg .

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