Abstract

The optical characteristics of a single-element hollow cube-corner retroreflector for a geosynchronous satellite were numerically evaluated for laser ranging and laser long-path absorption measurements of atmospheric species. An optical design with spherical surfaces and tuned dihedral angles was considered to compensate for velocity aberrations. The parameters for the retroreflector were optimized with genetic algorithms for different retroreflector sizes and wavelengths (500 nm and 1, 3, and 10 µm). We found that 20-cm retroreflectors are sufficient for realistic measurements when the laser wavelength is 500 nm or 1 µm. However, a larger retroreflector is necessary to overcome the detector noise level at 3 and 10 µm.

© 2001 Optical Society of America

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References

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  1. A. Minato, N. Sugimoto, Y. Sasano, “Optical design of cube corner retroreflectors having curved mirror surfaces,” Appl. Opt. 31, 6015–6020 (1992).
    [CrossRef] [PubMed]
  2. 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).
  3. N. Sugimoto, A. Minato, “Optical characteristics of the Retroreflector in Space for the Earth Observing Satellite,” Opt. Rev. 3, 62–64 (1996).
    [CrossRef]
  4. N. Sugimoto, N. Koga, I. Matsui, Y. Sasano, A. Minato, K. Ozawa, Y. Saito, A. Nomura, T. Aoki, T. Itabe, H. Kunimori, I. Murata, H. Fukunishi, “Earth–satellite–Earth laser long-path absorption experiment using the Retroreflector in Space (RIS) on the advanced earth observing satellite,” J. Opt. A: Pure Appl. Opt. 1, 201–209 (1999).
    [CrossRef]
  5. S. Riepl, U. Schreiber, W. Schlueter, “WLRS streak camera experiment,” in Laser Radar Ranging and Atmospheric Lidar Techniques, U. Schreiber, C. Werner, eds., Proc. SPIE3218, 19–30 (1997).
    [CrossRef]
  6. T. W. Zagwodzki, J. F. McGarry, J. J. Degnan, T. K. Varghese, “Two-color SLR experiments at the GSFC 1.2-m telescope,” in Laser Radar Ranging and Atmospheric Lidar Techniques, U. Schreiber, C. Werner, eds., Proc. SPIE3218, 113–124 (1997).
    [CrossRef]
  7. A. Minato, N. Sugimoto, “Design of four-element, hollow-cube corner retroreflector for satellites by use of a genetic algorithm,” Appl. Opt. 37, 438–442 (1998).
    [CrossRef]
  8. J. H. Holland, Adaptation in Natural and Artificial Systems (MIT, Cambridge, Mass., 1992).
  9. D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, Reading, Mass., 1989).
  10. N. Sugimoto, A. Minato, K. Ozawa, Y. Saito, A. Nomura, “Theoretical evaluation of Earth-to-satellite laser long-path absorption measurement of atmospheric trace species in the infrared region,” Jpn. J. Appl. Phys. 34, 2329–2334 (1995).
    [CrossRef]
  11. G. Walker, Astronomical Observations: an Optical Perspective (Cambridge University, Cambridge, England, 1987).

1999 (1)

N. Sugimoto, N. Koga, I. Matsui, Y. Sasano, A. Minato, K. Ozawa, Y. Saito, A. Nomura, T. Aoki, T. Itabe, H. Kunimori, I. Murata, H. Fukunishi, “Earth–satellite–Earth laser long-path absorption experiment using the Retroreflector in Space (RIS) on the advanced earth observing satellite,” J. Opt. A: Pure Appl. Opt. 1, 201–209 (1999).
[CrossRef]

1998 (1)

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 (2)

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).

N. Sugimoto, A. Minato, K. Ozawa, Y. Saito, A. Nomura, “Theoretical evaluation of Earth-to-satellite laser long-path absorption measurement of atmospheric trace species in the infrared region,” Jpn. J. Appl. Phys. 34, 2329–2334 (1995).
[CrossRef]

1992 (1)

Aoki, T.

N. Sugimoto, N. Koga, I. Matsui, Y. Sasano, A. Minato, K. Ozawa, Y. Saito, A. Nomura, T. Aoki, T. Itabe, H. Kunimori, I. Murata, H. Fukunishi, “Earth–satellite–Earth laser long-path absorption experiment using the Retroreflector in Space (RIS) on the advanced earth observing satellite,” J. Opt. A: Pure Appl. Opt. 1, 201–209 (1999).
[CrossRef]

Degnan, J. J.

T. W. Zagwodzki, J. F. McGarry, J. J. Degnan, T. K. Varghese, “Two-color SLR experiments at the GSFC 1.2-m telescope,” in Laser Radar Ranging and Atmospheric Lidar Techniques, U. Schreiber, C. Werner, eds., Proc. SPIE3218, 113–124 (1997).
[CrossRef]

Fukunishi, H.

N. Sugimoto, N. Koga, I. Matsui, Y. Sasano, A. Minato, K. Ozawa, Y. Saito, A. Nomura, T. Aoki, T. Itabe, H. Kunimori, I. Murata, H. Fukunishi, “Earth–satellite–Earth laser long-path absorption experiment using the Retroreflector in Space (RIS) on the advanced earth observing satellite,” J. Opt. A: Pure Appl. Opt. 1, 201–209 (1999).
[CrossRef]

Goldberg, D. E.

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

Holland, J. H.

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

Itabe, T.

N. Sugimoto, N. Koga, I. Matsui, Y. Sasano, A. Minato, K. Ozawa, Y. Saito, A. Nomura, T. Aoki, T. Itabe, H. Kunimori, I. Murata, H. Fukunishi, “Earth–satellite–Earth laser long-path absorption experiment using the Retroreflector in Space (RIS) on the advanced earth observing satellite,” J. Opt. A: Pure Appl. Opt. 1, 201–209 (1999).
[CrossRef]

Koga, N.

N. Sugimoto, N. Koga, I. Matsui, Y. Sasano, A. Minato, K. Ozawa, Y. Saito, A. Nomura, T. Aoki, T. Itabe, H. Kunimori, I. Murata, H. Fukunishi, “Earth–satellite–Earth laser long-path absorption experiment using the Retroreflector in Space (RIS) on the advanced earth observing satellite,” J. Opt. A: Pure Appl. Opt. 1, 201–209 (1999).
[CrossRef]

Kunimori, H.

N. Sugimoto, N. Koga, I. Matsui, Y. Sasano, A. Minato, K. Ozawa, Y. Saito, A. Nomura, T. Aoki, T. Itabe, H. Kunimori, I. Murata, H. Fukunishi, “Earth–satellite–Earth laser long-path absorption experiment using the Retroreflector in Space (RIS) on the advanced earth observing satellite,” J. Opt. A: Pure Appl. Opt. 1, 201–209 (1999).
[CrossRef]

Matsui, I.

N. Sugimoto, N. Koga, I. Matsui, Y. Sasano, A. Minato, K. Ozawa, Y. Saito, A. Nomura, T. Aoki, T. Itabe, H. Kunimori, I. Murata, H. Fukunishi, “Earth–satellite–Earth laser long-path absorption experiment using the Retroreflector in Space (RIS) on the advanced earth observing satellite,” J. Opt. A: Pure Appl. Opt. 1, 201–209 (1999).
[CrossRef]

McGarry, J. F.

T. W. Zagwodzki, J. F. McGarry, J. J. Degnan, T. K. Varghese, “Two-color SLR experiments at the GSFC 1.2-m telescope,” in Laser Radar Ranging and Atmospheric Lidar Techniques, U. Schreiber, C. Werner, eds., Proc. SPIE3218, 113–124 (1997).
[CrossRef]

Minato, A.

N. Sugimoto, N. Koga, I. Matsui, Y. Sasano, A. Minato, K. Ozawa, Y. Saito, A. Nomura, T. Aoki, T. Itabe, H. Kunimori, I. Murata, H. Fukunishi, “Earth–satellite–Earth laser long-path absorption experiment using the Retroreflector in Space (RIS) on the advanced earth observing satellite,” J. Opt. A: Pure Appl. Opt. 1, 201–209 (1999).
[CrossRef]

A. Minato, N. Sugimoto, “Design of four-element, hollow-cube corner retroreflector for satellites by use of a genetic algorithm,” Appl. Opt. 37, 438–442 (1998).
[CrossRef]

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, K. Ozawa, Y. Saito, A. Nomura, “Theoretical evaluation of Earth-to-satellite laser long-path absorption measurement of atmospheric trace species in the infrared region,” Jpn. J. Appl. Phys. 34, 2329–2334 (1995).
[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]

Murata, I.

N. Sugimoto, N. Koga, I. Matsui, Y. Sasano, A. Minato, K. Ozawa, Y. Saito, A. Nomura, T. Aoki, T. Itabe, H. Kunimori, I. Murata, H. Fukunishi, “Earth–satellite–Earth laser long-path absorption experiment using the Retroreflector in Space (RIS) on the advanced earth observing satellite,” J. Opt. A: Pure Appl. Opt. 1, 201–209 (1999).
[CrossRef]

Nomura, A.

N. Sugimoto, N. Koga, I. Matsui, Y. Sasano, A. Minato, K. Ozawa, Y. Saito, A. Nomura, T. Aoki, T. Itabe, H. Kunimori, I. Murata, H. Fukunishi, “Earth–satellite–Earth laser long-path absorption experiment using the Retroreflector in Space (RIS) on the advanced earth observing satellite,” J. Opt. A: Pure Appl. Opt. 1, 201–209 (1999).
[CrossRef]

N. Sugimoto, A. Minato, K. Ozawa, Y. Saito, A. Nomura, “Theoretical evaluation of Earth-to-satellite laser long-path absorption measurement of atmospheric trace species in the infrared region,” Jpn. J. Appl. Phys. 34, 2329–2334 (1995).
[CrossRef]

Ozawa, K.

N. Sugimoto, N. Koga, I. Matsui, Y. Sasano, A. Minato, K. Ozawa, Y. Saito, A. Nomura, T. Aoki, T. Itabe, H. Kunimori, I. Murata, H. Fukunishi, “Earth–satellite–Earth laser long-path absorption experiment using the Retroreflector in Space (RIS) on the advanced earth observing satellite,” J. Opt. A: Pure Appl. Opt. 1, 201–209 (1999).
[CrossRef]

N. Sugimoto, A. Minato, K. Ozawa, Y. Saito, A. Nomura, “Theoretical evaluation of Earth-to-satellite laser long-path absorption measurement of atmospheric trace species in the infrared region,” Jpn. J. Appl. Phys. 34, 2329–2334 (1995).
[CrossRef]

Riepl, S.

S. Riepl, U. Schreiber, W. Schlueter, “WLRS streak camera experiment,” in Laser Radar Ranging and Atmospheric Lidar Techniques, U. Schreiber, C. Werner, eds., Proc. SPIE3218, 19–30 (1997).
[CrossRef]

Saito, Y.

N. Sugimoto, N. Koga, I. Matsui, Y. Sasano, A. Minato, K. Ozawa, Y. Saito, A. Nomura, T. Aoki, T. Itabe, H. Kunimori, I. Murata, H. Fukunishi, “Earth–satellite–Earth laser long-path absorption experiment using the Retroreflector in Space (RIS) on the advanced earth observing satellite,” J. Opt. A: Pure Appl. Opt. 1, 201–209 (1999).
[CrossRef]

N. Sugimoto, A. Minato, K. Ozawa, Y. Saito, A. Nomura, “Theoretical evaluation of Earth-to-satellite laser long-path absorption measurement of atmospheric trace species in the infrared region,” Jpn. J. Appl. Phys. 34, 2329–2334 (1995).
[CrossRef]

Sasano, Y.

N. Sugimoto, N. Koga, I. Matsui, Y. Sasano, A. Minato, K. Ozawa, Y. Saito, A. Nomura, T. Aoki, T. Itabe, H. Kunimori, I. Murata, H. Fukunishi, “Earth–satellite–Earth laser long-path absorption experiment using the Retroreflector in Space (RIS) on the advanced earth observing satellite,” J. Opt. A: Pure Appl. Opt. 1, 201–209 (1999).
[CrossRef]

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

Schlueter, W.

S. Riepl, U. Schreiber, W. Schlueter, “WLRS streak camera experiment,” in Laser Radar Ranging and Atmospheric Lidar Techniques, U. Schreiber, C. Werner, eds., Proc. SPIE3218, 19–30 (1997).
[CrossRef]

Schreiber, U.

S. Riepl, U. Schreiber, W. Schlueter, “WLRS streak camera experiment,” in Laser Radar Ranging and Atmospheric Lidar Techniques, U. Schreiber, C. Werner, eds., Proc. SPIE3218, 19–30 (1997).
[CrossRef]

Sugimoto, N.

N. Sugimoto, N. Koga, I. Matsui, Y. Sasano, A. Minato, K. Ozawa, Y. Saito, A. Nomura, T. Aoki, T. Itabe, H. Kunimori, I. Murata, H. Fukunishi, “Earth–satellite–Earth laser long-path absorption experiment using the Retroreflector in Space (RIS) on the advanced earth observing satellite,” J. Opt. A: Pure Appl. Opt. 1, 201–209 (1999).
[CrossRef]

A. Minato, N. Sugimoto, “Design of four-element, hollow-cube corner retroreflector for satellites by use of a genetic algorithm,” Appl. Opt. 37, 438–442 (1998).
[CrossRef]

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, K. Ozawa, Y. Saito, A. Nomura, “Theoretical evaluation of Earth-to-satellite laser long-path absorption measurement of atmospheric trace species in the infrared region,” Jpn. J. Appl. Phys. 34, 2329–2334 (1995).
[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]

Varghese, T. K.

T. W. Zagwodzki, J. F. McGarry, J. J. Degnan, T. K. Varghese, “Two-color SLR experiments at the GSFC 1.2-m telescope,” in Laser Radar Ranging and Atmospheric Lidar Techniques, U. Schreiber, C. Werner, eds., Proc. SPIE3218, 113–124 (1997).
[CrossRef]

Walker, G.

G. Walker, Astronomical Observations: an Optical Perspective (Cambridge University, Cambridge, England, 1987).

Zagwodzki, T. W.

T. W. Zagwodzki, J. F. McGarry, J. J. Degnan, T. K. Varghese, “Two-color SLR experiments at the GSFC 1.2-m telescope,” in Laser Radar Ranging and Atmospheric Lidar Techniques, U. Schreiber, C. Werner, eds., Proc. SPIE3218, 113–124 (1997).
[CrossRef]

Appl. Opt. (2)

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).

J. Opt. A: Pure Appl. Opt. (1)

N. Sugimoto, N. Koga, I. Matsui, Y. Sasano, A. Minato, K. Ozawa, Y. Saito, A. Nomura, T. Aoki, T. Itabe, H. Kunimori, I. Murata, H. Fukunishi, “Earth–satellite–Earth laser long-path absorption experiment using the Retroreflector in Space (RIS) on the advanced earth observing satellite,” J. Opt. A: Pure Appl. Opt. 1, 201–209 (1999).
[CrossRef]

Jpn. J. Appl. Phys. (1)

N. Sugimoto, A. Minato, K. Ozawa, Y. Saito, A. Nomura, “Theoretical evaluation of Earth-to-satellite laser long-path absorption measurement of atmospheric trace species in the infrared region,” Jpn. J. Appl. Phys. 34, 2329–2334 (1995).
[CrossRef]

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)

G. Walker, Astronomical Observations: an Optical Perspective (Cambridge University, Cambridge, England, 1987).

S. Riepl, U. Schreiber, W. Schlueter, “WLRS streak camera experiment,” in Laser Radar Ranging and Atmospheric Lidar Techniques, U. Schreiber, C. Werner, eds., Proc. SPIE3218, 19–30 (1997).
[CrossRef]

T. W. Zagwodzki, J. F. McGarry, J. J. Degnan, T. K. Varghese, “Two-color SLR experiments at the GSFC 1.2-m telescope,” in Laser Radar Ranging and Atmospheric Lidar Techniques, U. Schreiber, C. Werner, eds., Proc. SPIE3218, 113–124 (1997).
[CrossRef]

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).

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Figures (4)

Fig. 1
Fig. 1

Concept of measurements taken with a retroreflector on a geosynchronous satellite. Laser long-path absorption measurements and laser ranging with various zenith angles can be performed.

Fig. 2
Fig. 2

Definition of the parameters of a single-element, hollow cube-corner retroreflector for a geosynchronous satellite. Two dihedral angles (δ1 and δ2) and two curvatures (r 1 and r 2) were optimized with the genetic algorithm.

Fig. 3
Fig. 3

Minimum optical efficiencies at five points on the ground, A–E, defined as fitness values.

Fig. 4
Fig. 4

Examples of the optical efficiency distribution of optimized retroreflectors: (a) 20-cm mirror, 500 nm; (b) 20-cm mirror, 1 µm; (c) 50-cm mirror, 3 µm; (d) 50-cm mirror, 10 µm.

Tables (2)

Tables Icon

Table 1 Optimized Parameters and Optical Efficiencies

Tables Icon

Table 2 Parameters Used to Estimate the Received Signals and the Results

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

δ1=B0+2B1+4B2+8B3+16B4+32B5+64B6+128B7×0.66×10-6,
δ2=B8+2B9+4B10+8B11+16B12+32B13+64B14+128B15×0.66×10-6,
1/r1=B16+2B17+4B18+8B19+16B20+32B21+64B22+128B23×0.5×10-6,
1/r2=B24+2B25+4B26+8B27+16B28+32B29+64B30+128B31×0.5×10-6.
Pr=16/π2P0/θt2T2ηretArηsystη,
ρλ=ρλ0λ/λ01.2cos Z0.6,
Nd=Adτ1/2/D*hν,

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