Abstract

Wave-front aberrations due to thermal deformation of elliptical reflectors in periscopic laser communication terminals are studied, and are fitted by Zernike elliptical polynomials. The relationship between pointing error and temperature distribution of elliptical reflectors in intersatellite laser communication systems is researched. The back-fixing method is introduced for fixing the elliptical reflectors, and is proven to reduce pointing error compared to the traditional around-fixing method using a press board. It is shown that the difference between uniform temperature and reference temperature has a much stronger influence than the temperature gradient. For the back-fixing method, the pointing error changes periodically as the uniform temperature changes with a period value of 1.6°C, and the maximum pointing error value is 16.7μrad. The result also tells us that, if the difference between uniform temperature and reference temperature is within 1.0°C, there is no pointing error caused by back-fixed reflectors. We hope this work can contribute to the thermal control of elliptical reflectors in intersatellite laser communication terminals.

© 2010 Optical Society of America

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References

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  1. O. Nilsson, “Fundamental limits and possibilities for future telecommunications,” IEEE Commun. Mag. 39, 504–509(2001).
    [CrossRef]
  2. V. W. S. Chan, “Optical space communications,” IEEE J. Quantum Electron. 6, 959–975 (2002).
    [CrossRef]
  3. G. Robert, G. Marshalek, M. Stephen, and R. Paul, “System-level comparison of optical and RF technologies for space-to-space and space-to-ground communication links circa 2000,” Proc. SPIE 2699, 134–145 (1996).
    [CrossRef]
  4. B. Laurent and G. Planche, “SILEX overview after flight terminals campaign,” Proc. SPIE 2990, 10–22 (1997).
    [CrossRef]
  5. K. Nakagawa and A. Yamamoto, “Engineering model test of LUCE (laser utilizing communications equipment),” Proc. SPIE 2699, 114–120 (1996).
    [CrossRef]
  6. M. Toyoshima, N. Takahashi, T. Jono, T. Yamawaki, K. Nakagawa, and A. Yamamoto, “Mutual alignment errors due to the variation of wave-front aberrations in a free-space laser communication link,” Opt. Express 9, 592–602 (2001).
    [CrossRef] [PubMed]
  7. L. Y. Tan, Y. Q. Yang, J. Ma, and J. J. Yu, “Pointing and tracking errors due to localized deformation in intersatellite laser communication links,” Opt. Express 16, 13372–13380 (2008).
    [CrossRef] [PubMed]
  8. J. Y. Wang and D. E. Silva, “Wave-front interpretation with Zernike polynomials,” Appl. Opt. 19, 1510–1518 (1980).
    [CrossRef] [PubMed]
  9. V. N. Mahajan and G. M. Dai, “Orthonormal polynomials in wavefront analysis: analytical,” J. Opt. Soc. Am. A 24, 2994–3016 (2007).
    [CrossRef]
  10. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
  11. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976).
    [CrossRef]
  12. J. Y. Wang and D. E. Silva, “Wave-front interpretation with Zernike polynomials,” Appl. Opt. 19, 1510–1517 (1980).
    [CrossRef] [PubMed]
  13. N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29, 1174–1180 (1990).
    [CrossRef]
  14. Adaptive Optics in Astronomy, F.Roddier, ed. (Cambridge U. Press, 1999).
    [CrossRef]
  15. Y. W. Song, S. Y. Yu, L. Y. Tan, J. Ma, Q. Q. Han, J. F. Liu, and W. Yang, “The effect of temperature distribution in space on the figure of reflectors,” J. Astronautics 31, 865–874 (2010).
  16. L. Robert, S. Berry, and W. Bernhard, “142km, 5.625Gbps free–space optical link based on homodyne BPSK modulation,” Proc. SPIE 6105, 61050G (2006).
    [CrossRef]

2010 (1)

Y. W. Song, S. Y. Yu, L. Y. Tan, J. Ma, Q. Q. Han, J. F. Liu, and W. Yang, “The effect of temperature distribution in space on the figure of reflectors,” J. Astronautics 31, 865–874 (2010).

2008 (1)

2007 (1)

2006 (1)

L. Robert, S. Berry, and W. Bernhard, “142km, 5.625Gbps free–space optical link based on homodyne BPSK modulation,” Proc. SPIE 6105, 61050G (2006).
[CrossRef]

2002 (1)

V. W. S. Chan, “Optical space communications,” IEEE J. Quantum Electron. 6, 959–975 (2002).
[CrossRef]

2001 (2)

1997 (1)

B. Laurent and G. Planche, “SILEX overview after flight terminals campaign,” Proc. SPIE 2990, 10–22 (1997).
[CrossRef]

1996 (2)

K. Nakagawa and A. Yamamoto, “Engineering model test of LUCE (laser utilizing communications equipment),” Proc. SPIE 2699, 114–120 (1996).
[CrossRef]

G. Robert, G. Marshalek, M. Stephen, and R. Paul, “System-level comparison of optical and RF technologies for space-to-space and space-to-ground communication links circa 2000,” Proc. SPIE 2699, 134–145 (1996).
[CrossRef]

1990 (1)

N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29, 1174–1180 (1990).
[CrossRef]

1980 (2)

1976 (1)

Bernhard, W.

L. Robert, S. Berry, and W. Bernhard, “142km, 5.625Gbps free–space optical link based on homodyne BPSK modulation,” Proc. SPIE 6105, 61050G (2006).
[CrossRef]

Berry, S.

L. Robert, S. Berry, and W. Bernhard, “142km, 5.625Gbps free–space optical link based on homodyne BPSK modulation,” Proc. SPIE 6105, 61050G (2006).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Chan, V. W. S.

V. W. S. Chan, “Optical space communications,” IEEE J. Quantum Electron. 6, 959–975 (2002).
[CrossRef]

Dai, G. M.

Han, Q. Q.

Y. W. Song, S. Y. Yu, L. Y. Tan, J. Ma, Q. Q. Han, J. F. Liu, and W. Yang, “The effect of temperature distribution in space on the figure of reflectors,” J. Astronautics 31, 865–874 (2010).

Jono, T.

Laurent, B.

B. Laurent and G. Planche, “SILEX overview after flight terminals campaign,” Proc. SPIE 2990, 10–22 (1997).
[CrossRef]

Liu, J. F.

Y. W. Song, S. Y. Yu, L. Y. Tan, J. Ma, Q. Q. Han, J. F. Liu, and W. Yang, “The effect of temperature distribution in space on the figure of reflectors,” J. Astronautics 31, 865–874 (2010).

Ma, J.

Y. W. Song, S. Y. Yu, L. Y. Tan, J. Ma, Q. Q. Han, J. F. Liu, and W. Yang, “The effect of temperature distribution in space on the figure of reflectors,” J. Astronautics 31, 865–874 (2010).

L. Y. Tan, Y. Q. Yang, J. Ma, and J. J. Yu, “Pointing and tracking errors due to localized deformation in intersatellite laser communication links,” Opt. Express 16, 13372–13380 (2008).
[CrossRef] [PubMed]

Mahajan, V. N.

Marshalek, G.

G. Robert, G. Marshalek, M. Stephen, and R. Paul, “System-level comparison of optical and RF technologies for space-to-space and space-to-ground communication links circa 2000,” Proc. SPIE 2699, 134–145 (1996).
[CrossRef]

Nakagawa, K.

Nilsson, O.

O. Nilsson, “Fundamental limits and possibilities for future telecommunications,” IEEE Commun. Mag. 39, 504–509(2001).
[CrossRef]

Noll, R. J.

Paul, R.

G. Robert, G. Marshalek, M. Stephen, and R. Paul, “System-level comparison of optical and RF technologies for space-to-space and space-to-ground communication links circa 2000,” Proc. SPIE 2699, 134–145 (1996).
[CrossRef]

Planche, G.

B. Laurent and G. Planche, “SILEX overview after flight terminals campaign,” Proc. SPIE 2990, 10–22 (1997).
[CrossRef]

Robert, G.

G. Robert, G. Marshalek, M. Stephen, and R. Paul, “System-level comparison of optical and RF technologies for space-to-space and space-to-ground communication links circa 2000,” Proc. SPIE 2699, 134–145 (1996).
[CrossRef]

Robert, L.

L. Robert, S. Berry, and W. Bernhard, “142km, 5.625Gbps free–space optical link based on homodyne BPSK modulation,” Proc. SPIE 6105, 61050G (2006).
[CrossRef]

Roddier, N.

N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29, 1174–1180 (1990).
[CrossRef]

Silva, D. E.

Song, Y. W.

Y. W. Song, S. Y. Yu, L. Y. Tan, J. Ma, Q. Q. Han, J. F. Liu, and W. Yang, “The effect of temperature distribution in space on the figure of reflectors,” J. Astronautics 31, 865–874 (2010).

Stephen, M.

G. Robert, G. Marshalek, M. Stephen, and R. Paul, “System-level comparison of optical and RF technologies for space-to-space and space-to-ground communication links circa 2000,” Proc. SPIE 2699, 134–145 (1996).
[CrossRef]

Takahashi, N.

Tan, L. Y.

Y. W. Song, S. Y. Yu, L. Y. Tan, J. Ma, Q. Q. Han, J. F. Liu, and W. Yang, “The effect of temperature distribution in space on the figure of reflectors,” J. Astronautics 31, 865–874 (2010).

L. Y. Tan, Y. Q. Yang, J. Ma, and J. J. Yu, “Pointing and tracking errors due to localized deformation in intersatellite laser communication links,” Opt. Express 16, 13372–13380 (2008).
[CrossRef] [PubMed]

Toyoshima, M.

Wang, J. Y.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Yamamoto, A.

Yamawaki, T.

Yang, W.

Y. W. Song, S. Y. Yu, L. Y. Tan, J. Ma, Q. Q. Han, J. F. Liu, and W. Yang, “The effect of temperature distribution in space on the figure of reflectors,” J. Astronautics 31, 865–874 (2010).

Yang, Y. Q.

Yu, J. J.

Yu, S. Y.

Y. W. Song, S. Y. Yu, L. Y. Tan, J. Ma, Q. Q. Han, J. F. Liu, and W. Yang, “The effect of temperature distribution in space on the figure of reflectors,” J. Astronautics 31, 865–874 (2010).

Appl. Opt. (2)

IEEE Commun. Mag. (1)

O. Nilsson, “Fundamental limits and possibilities for future telecommunications,” IEEE Commun. Mag. 39, 504–509(2001).
[CrossRef]

IEEE J. Quantum Electron. (1)

V. W. S. Chan, “Optical space communications,” IEEE J. Quantum Electron. 6, 959–975 (2002).
[CrossRef]

J. Astronautics (1)

Y. W. Song, S. Y. Yu, L. Y. Tan, J. Ma, Q. Q. Han, J. F. Liu, and W. Yang, “The effect of temperature distribution in space on the figure of reflectors,” J. Astronautics 31, 865–874 (2010).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Eng. (1)

N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29, 1174–1180 (1990).
[CrossRef]

Opt. Express (2)

Proc. SPIE (4)

L. Robert, S. Berry, and W. Bernhard, “142km, 5.625Gbps free–space optical link based on homodyne BPSK modulation,” Proc. SPIE 6105, 61050G (2006).
[CrossRef]

G. Robert, G. Marshalek, M. Stephen, and R. Paul, “System-level comparison of optical and RF technologies for space-to-space and space-to-ground communication links circa 2000,” Proc. SPIE 2699, 134–145 (1996).
[CrossRef]

B. Laurent and G. Planche, “SILEX overview after flight terminals campaign,” Proc. SPIE 2990, 10–22 (1997).
[CrossRef]

K. Nakagawa and A. Yamamoto, “Engineering model test of LUCE (laser utilizing communications equipment),” Proc. SPIE 2699, 114–120 (1996).
[CrossRef]

Other (2)

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Adaptive Optics in Astronomy, F.Roddier, ed. (Cambridge U. Press, 1999).
[CrossRef]

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Figures (12)

Fig. 1
Fig. 1

Transmitting optical path of periscopic LCT.

Fig. 2
Fig. 2

Structural composition of gimbals in a periscopic LCT. 1, azimuth axis; 2, transition of azimuth axis; 3, reflector of azimuth axis; 4, elevation axis; 5, transition of elevation axis; 6, reflector of elevation axis.

Fig. 3
Fig. 3

Assembly of the two fixing methods: (a) around-fixing and (b) back-fixing. 1, reflector; 2, connector of one axis; 3, press board; 4, blank.

Fig. 4
Fig. 4

Boundary conditions of around-fixing method: (a) contact setting; (b) fixing points setting.

Fig. 5
Fig. 5

Boundary conditions of back-fixing method: (a) contact setting; (b) fixing points setting.

Fig. 6
Fig. 6

Root-mean-square value variation with (a) temperature gradient and (b) uniform temperature.

Fig. 7
Fig. 7

Pointing error variation with temperature gradient.

Fig. 8
Fig. 8

Intensity distribution through the around-fixed reflector without a temperature gradient and with a temperature gradient of 14 ° C / m .

Fig. 9
Fig. 9

Pointing error variation with uniform temperature.

Fig. 10
Fig. 10

Intensity through the around-fixed reflector with different uniform temperatures: (a) t d = 0 , (b) t d = 0.6 ° C , (c) t d = 0.7 ° C , (d) t d = 1.0 ° C , (e) t d = 1.1 ° C , (f) t d = 2.5 ° C , and (g) t d = 4.0 ° C .

Fig. 11
Fig. 11

Intensity distribution through back-fixed reflector with different uniform temperatures (a) t d = 0 , (b) t d = 0.9 ° C , (c) t d = 1.1 ° C , (d) t d = 1.7 ° C , (e) t d = 1.8 ° C , (f) t d = 1.9 ° C , (g) t d = 2.6 ° C , and (h) t d = 2.7 ° C .

Fig. 12
Fig. 12

Peak intensity degradation variation with (a) temperature gradient and (b) uniform temperature.

Tables (1)

Tables Icon

Table 1 Thermodynamic Properties of SiC

Equations (11)

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u i + 1 1 2 ν · e i + ρ μ · f i 2 ( 1 + ν ) 1 2 ν · α · θ i = ρ μ · u ¨ i ,
rms = i = 1 N ( u i ) 2 N 1 ,
G 1 = Z 1 = 1 ,
G j + 1 = k = 1 j c j + 1 F k + Z j + 1 ,
F j + 1 = G j + 1 G j + 1 = G j + 1 ( 1 A s G j + 1 2 d x d y ) 1 / 2 ,
c j + 1 , k = 1 A S Z j + 1 F k d x d y
Φ ( u , v ) = i = 1 a i F i ( u , v ) ,
I ( X , Y ) = A 2 λ 2 z 2 | M ( u , v ) exp [ u 2 + v 2 ω 0 2 j k u 2 + v 2 2 F 0 + j Φ ( u , v ) ] exp [ j k z ( X u + Y v ) ] d u d v | 2 ,
M ( u , v ) = { 1 0 u 2 a 2 + v 2 b 2 1 0 else ,
θ p = X 0 2 + Y 0 2 / z ,
p = 10 lg I 1 I 0 ,

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