## A novel approach for simulating the optical misalignment caused by satellite platform vibration in the ground test of satellite optical communication systems |

Optics Express, Vol. 20, Issue 2, pp. 1033-1045 (2012)

http://dx.doi.org/10.1364/OE.20.001033

Acrobat PDF (1239 KB)

### Abstract

Satellite platform vibration causes the misalignment between incident direction of the beacon and optical axis of the satellite optical communication system, which also leads to the instability of the laser link and reduces the precision of the system. So how to simulate the satellite platform vibration is a very important work in the ground test of satellite optical communication systems. In general, a vibration device is used for simulating the satellite platform vibration, but the simulation effect is not ideal because of the limited randomness. An approach is reasonable, which uses a natural random process for simulating the satellite platform vibration. In this paper, we discuss feasibility of the concept that the effect of angle of arrival fluctuation is taken as an effective simulation of satellite platform vibration in the ground test of the satellite optical communication system. Spectrum characteristic of satellite platform vibration is introduced, referring to the model used by the European Space Agency (ESA) in the SILEX program and that given by National Aeronautics and Space Development Agency (NASDA) of Japan. Spectrum characteristic of angle of arrival fluctuation is analyzed based on the measured data from an 11.16km bi-directional free space laser transmission experiment. Spectrum characteristic of these two effects is compared. The results show that spectra of these two effects have similar variation trend with the variation of frequency and feasibility of the concept is proved by the comparison results. At last the procedure of this method is proposed, which uses the power spectra of angle of arrival fluctuation to simulate that of the satellite platform vibration. The new approach is good for the ground test of satellite optical communication systems.

© 2012 OSA

## 1. Introduction

2. R. G. Marshalek, G. S. Mecherle, and P. R. Jordan, “System-level comparison of optical and RF technologies for space-to-Space and space-to-ground communication links,” Proc. SPIE **2699**, 134–145 (1996). [CrossRef]

3. K. Araki, Y. Arimoto, and M. Shikatani, “Performance evaluation of laser communication equipment onboard the ETS-VI satellite,” Proc. SPIE **2699**, 52–59 (1996). [CrossRef]

6. R. Lange, B. Smutny, and B. Wandernoth, “142km, 5.625 Gbps free-space optical link based on homodyne BPSK modulation,” Proc. SPIE **6105**, 61050A, 61050A–9 (2006). [CrossRef]

7. V. A. Skormin and M. A. Tascillo, “Jitter rejection technique in a satellite-based laser communication system,” Opt. Eng. **32**(11), 2764–2769 (1993). [CrossRef]

8. M. Toyoshima and K. Araki, “In-orbit measurements of short term attitude and vibrational environment on the engineering test satellite VI using laser communication equipment,” Opt. Eng. **40**(5), 827–832 (2001). [CrossRef]

9. T. Chiba, “Spot dancing of the laser beam propagated through the turbulent atmosphere,” Appl. Opt. **10**(11), 2456–2461 (1971). [CrossRef] [PubMed]

13. A. Tunick, “Statistical analysis of optical turbulence intensity over a 2.33 km propagation path,” Opt. Express **15**(7), 3619–3628 (2007). [CrossRef] [PubMed]

## 2. Experimental setup

## 3. Data analysis

### 3.1 Computation of spectrum

*X*

_{i},

*Y*

_{i}) of the i-th frame is calculated by the gray centroid algorithm, that is:where

*g*is gray-level value of the pixel with coordinate of (

_{xy}*x*,

*y*).

*X*= (

*X*

_{1},

*X*

_{2}…

*X*

_{n}) and

*Y*= (

*Y*

_{1},

*Y*

_{2}…

*Y*

_{n}). The sequence

*A*= (

*A*

_{1},

*A*

_{2}…

*A*

_{n}) for angle of arrival is obtained from the coordinate sequences by the following formula,where <·> means ensemble average,

*A*is the

_{i}*i-*th element in the sequence of

*A*,

*d*is pixel size of the CMOS,

*f*is focal length of the receiving optical system and

_{L}*M*is enlargement factor of the optical system.

### 3.2 High-frequency spectrum

### 3.3 Contrastive analysis

14. M. E. Wittig, L. van Holtz, and D. E. L. Tunbridge, “In-orbit measurements of microaccelerations of ESA’s communication satellite OLYMPUS,” Proc. SPIE **1218**, 205–214 (1990). [CrossRef]

15. E. M. Arkin, L. P. Chew, D. P. Huttenlocher, K. Kedem, and J. S. B. Mitchell, “An efficiently computable metric for comparing polygonal shapes,” IEEE Trans. Pattern Anal. Mach. Intell. **13**(3), 209–216 (1991). [CrossRef]

15. E. M. Arkin, L. P. Chew, D. P. Huttenlocher, K. Kedem, and J. S. B. Mitchell, “An efficiently computable metric for comparing polygonal shapes,” IEEE Trans. Pattern Anal. Mach. Intell. **13**(3), 209–216 (1991). [CrossRef]

*d*is the distance of two curves, two curves are expressed as

*n*is the total number of elements compared.

*d*is, the better the similarity is. From Fig. 7(a) , in order to analyze the similarity between the two curves, the blue line needs to be parallel move to superpose the black line. The distance of the two curves can be calculated according to Eq. (3). Here

*f*is frequency. Where

*f*≥ 50Hz,

*d*is 0.6, and where

*f*< 50Hz,

*d*is 37.9.

*f*≥ 50Hz,

*d*is 48.5, and where

*f*<50Hz,

*d*is 1473.1. From Fig. 7(c), where

*f*≥ 50Hz,

*d*is 128.1, and where

*f*< 50Hz,

*d*is 1215.5.

*f*< 1000Hz, the similarity of Fig. 7(a) is the best, and where

*f*≥ 50Hz, the similarities of the three figures are good. But where

*f*< 50Hz, the similarities of Fig. 7(b) and Fig. 7(c) are relatively worse, which is observed from Fig. 7(b) and Fig. 7(c).

*f*< 50Hz, the power spectrum of the satellite platform given by NASDA is slightly higher than the power spectrum of AOA measured by OS2 (T4). But where

*f*> 50Hz, the trend of the power spectra of these is very similar. The order of magnitude of these two power spectra shown in Fig. 7(b) is the same.

*f*< 50Hz, the power spectrum of the satellite platform given by NASDA is slightly higher than the power spectrum of AOA measured by OS2 (T5), too. But where

*f*> 50Hz, the trend of the power spectra of these also is very similar. The order of magnitude of these two power spectra shown in Fig. 7(c) is also the same.

16. W. Du, L. Tan, J. Ma, and Y. Jiang, “Temporal-frequency spectra for optical wave propagating through non-Kolmogorov turbulence,” Opt. Express **18**(6), 5763–5775 (2010). [CrossRef] [PubMed]

16. W. Du, L. Tan, J. Ma, and Y. Jiang, “Temporal-frequency spectra for optical wave propagating through non-Kolmogorov turbulence,” Opt. Express **18**(6), 5763–5775 (2010). [CrossRef] [PubMed]

*L*is the transmission distance of the light wave,

*k*is

*λ*denotes the optical wavelength,

*b*is a constant (

*b*= 0.4832),

*D*is the receiving aperture of optical communication system,

*β*is the angle between the baseline and the AOA observation axis, and

*α*is −11/3, the corresponding variance for a plane wave propagating in non-Kolmogorov atmospheric turbulence [10,16

16. W. Du, L. Tan, J. Ma, and Y. Jiang, “Temporal-frequency spectra for optical wave propagating through non-Kolmogorov turbulence,” Opt. Express **18**(6), 5763–5775 (2010). [CrossRef] [PubMed]

17. D. M. Winker, “Effect of a finite outer scale on the Zernike decomposition of atmospheric optical turbulence,” J. Opt. Soc. Am. A **8**(10), 1568–1574 (1991). [CrossRef]

**18**(6), 5763–5775 (2010). [CrossRef] [PubMed]

*α*is −11/3, the corresponding variance for a spherical wave propagating in non-Kolmogorov atmospheric turbulence [10,16

**18**(6), 5763–5775 (2010). [CrossRef] [PubMed]

17. D. M. Winker, “Effect of a finite outer scale on the Zernike decomposition of atmospheric optical turbulence,” J. Opt. Soc. Am. A **8**(10), 1568–1574 (1991). [CrossRef]

*α*is −11/3, the power spectra for AOA fluctuation obtained by Eq. (4) and Eq. (6) are consistent with the conventional results of Kolmogorov atmospheric turbulence [18]. So the conditions are that

*α*is −11/3,

*β*is 0,

*L*is 11.16km,

*D*is 150mm or 250mm,

*λ*is 800nm and

*v*is 2m/s. According to Eq. (4)-Eq. (7), the temporal power spectra of AOA fluctuation scaled by the corresponding variance are illustrated in Fig. 8 and Fig. 9 . The comparisons between the theoretical values of AOA fluctuation and the power spectra of the satellite platform vibration are shown, with Fig. (8) for a plane wave, Fig. (9) for a spherical wave, respectively.

*f*< 100Hz, the distance between the blue line and the red line is 781.9, and the distance between the black line and the blue line is 782.03.Where

*f*< 100Hz, the distance between the green line and the red line is 250.04, and the distance between the green line and the black line is 229.8(here the red line or the black line needs to be parallel move to superpose the green line for computing the similarity in the rectangular coordinate system, respectively). In Fig. 9, where

*f*< 100Hz, the distance between the blue line and the sky blue line is 781.9, and the distance between the violet line and the blue line is 782.03.Where

*f*< 100Hz, the distance between the green line and the sky blue line is 250.04, and the distance between the green line and the violet line is 229.8(here the violet line or the sky blue line needs to be parallel move to superpose the green line for computing the similarity in the rectangular coordinate system, respectively). We can get the conclusion that the temporal power spectrum of AOA fluctuation for a plane wave or a spherical wave with a larger receiving aperture of optical communication system is relatively similar to the power spectrum of the satellite platform given by NASDA, which is very consistent with the experimental result (shown in Fig. 7(b) and Fig. 7(c)).

*f*> 100Hz, the temporal power spectra of AOA fluctuation are not well consistent with the power spectra of the satellite platform vibration. We analyze that because the atmospheric turbulence is very complex, and some factors can affect the results, such as turbulence intensity, temperature gradients, moisture. Furthermore, some simplified conditions are specified in the theoretical models in Ref.16

**18**(6), 5763–5775 (2010). [CrossRef] [PubMed]

## 4. Procedure of the new method

_{t}is a smooth time sequence, t = 0, ±1, ±2,…,

## 5 Discussion

## 6. Conclusions

## Acknowledgments

## References and links

1. | M. Toyoshima, W. R. Leeb, and H. Kunimori, “Comparison of microwave and light wave communication systems in space application,” Proc. SPIE |

2. | R. G. Marshalek, G. S. Mecherle, and P. R. Jordan, “System-level comparison of optical and RF technologies for space-to-Space and space-to-ground communication links,” Proc. SPIE |

3. | K. Araki, Y. Arimoto, and M. Shikatani, “Performance evaluation of laser communication equipment onboard the ETS-VI satellite,” Proc. SPIE |

4. | I. I. Kim, B. Riey, and N. M. Wong, “Lessons learned from the STRV-2 satellite-to-ground lasercom experiment,” Proc. SPIE |

5. | T. Tolker-Nielsen and G. Oppenhaeuser, “In orbit test result of an operational optical intersatellite link between ARTEMIS and SPOT4, SILEX,” Proc. SPIE |

6. | R. Lange, B. Smutny, and B. Wandernoth, “142km, 5.625 Gbps free-space optical link based on homodyne BPSK modulation,” Proc. SPIE |

7. | V. A. Skormin and M. A. Tascillo, “Jitter rejection technique in a satellite-based laser communication system,” Opt. Eng. |

8. | M. Toyoshima and K. Araki, “In-orbit measurements of short term attitude and vibrational environment on the engineering test satellite VI using laser communication equipment,” Opt. Eng. |

9. | T. Chiba, “Spot dancing of the laser beam propagated through the turbulent atmosphere,” Appl. Opt. |

10. | L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE Optical Engineering Press, Bellingham, 1998). |

11. | L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE Optical Engineering Press, Bellingham, 2001). |

12. | M. J. Curley, B. H. Peterson, J. C. Wang, S. S. Sarkisov, S. S. Sarkisov II, G. R. Edlin, R. A. Snow, and J. F. Rushing, “Statistical analysis of cloud-cover mitigation of optical turbulence in the boundary layer,” Opt. Express |

13. | A. Tunick, “Statistical analysis of optical turbulence intensity over a 2.33 km propagation path,” Opt. Express |

14. | M. E. Wittig, L. van Holtz, and D. E. L. Tunbridge, “In-orbit measurements of microaccelerations of ESA’s communication satellite OLYMPUS,” Proc. SPIE |

15. | E. M. Arkin, L. P. Chew, D. P. Huttenlocher, K. Kedem, and J. S. B. Mitchell, “An efficiently computable metric for comparing polygonal shapes,” IEEE Trans. Pattern Anal. Mach. Intell. |

16. | W. Du, L. Tan, J. Ma, and Y. Jiang, “Temporal-frequency spectra for optical wave propagating through non-Kolmogorov turbulence,” Opt. Express |

17. | D. M. Winker, “Effect of a finite outer scale on the Zernike decomposition of atmospheric optical turbulence,” J. Opt. Soc. Am. A |

18. | G. Chong, M. Jing, and T. Liying, “Angle-of-arrival fluctuation of light beam propagation in strong turbulence regime,” High Power Laser Particle Beams |

19. | R. Wang, |

**OCIS Codes**

(010.1300) Atmospheric and oceanic optics : Atmospheric propagation

(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence

(060.4510) Fiber optics and optical communications : Optical communications

**ToC Category:**

Atmospheric and Oceanic Optics

**History**

Original Manuscript: July 27, 2011

Revised Manuscript: October 29, 2011

Manuscript Accepted: December 15, 2011

Published: January 4, 2012

**Citation**

Qiang Wang, Liying Tan, Jing Ma, Siyuan Yu, and Yijun Jiang, "A novel approach for simulating the optical misalignment caused by satellite platform vibration in the ground test of satellite optical communication systems," Opt. Express **20**, 1033-1045 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-2-1033

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### References

- M. Toyoshima, W. R. Leeb, and H. Kunimori, “Comparison of microwave and light wave communication systems in space application,” Proc. SPIE5296, 1–12 (2005).
- R. G. Marshalek, G. S. Mecherle, and P. R. Jordan, “System-level comparison of optical and RF technologies for space-to-Space and space-to-ground communication links,” Proc. SPIE2699, 134–145 (1996). [CrossRef]
- K. Araki, Y. Arimoto, and M. Shikatani, “Performance evaluation of laser communication equipment onboard the ETS-VI satellite,” Proc. SPIE2699, 52–59 (1996). [CrossRef]
- I. I. Kim, B. Riey, and N. M. Wong, “Lessons learned from the STRV-2 satellite-to-ground lasercom experiment,” Proc. SPIE4272, 1–15 (2001). [CrossRef]
- T. Tolker-Nielsen and G. Oppenhaeuser, “In orbit test result of an operational optical intersatellite link between ARTEMIS and SPOT4, SILEX,” Proc. SPIE4635, 1–15 (2002). [CrossRef]
- R. Lange, B. Smutny, and B. Wandernoth, “142km, 5.625 Gbps free-space optical link based on homodyne BPSK modulation,” Proc. SPIE6105, 61050A, 61050A–9 (2006). [CrossRef]
- V. A. Skormin and M. A. Tascillo, “Jitter rejection technique in a satellite-based laser communication system,” Opt. Eng.32(11), 2764–2769 (1993). [CrossRef]
- M. Toyoshima and K. Araki, “In-orbit measurements of short term attitude and vibrational environment on the engineering test satellite VI using laser communication equipment,” Opt. Eng.40(5), 827–832 (2001). [CrossRef]
- T. Chiba, “Spot dancing of the laser beam propagated through the turbulent atmosphere,” Appl. Opt.10(11), 2456–2461 (1971). [CrossRef] [PubMed]
- L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE Optical Engineering Press, Bellingham, 1998).
- L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE Optical Engineering Press, Bellingham, 2001).
- M. J. Curley, B. H. Peterson, J. C. Wang, S. S. Sarkisov, S. S. Sarkisov, G. R. Edlin, R. A. Snow, and J. F. Rushing, “Statistical analysis of cloud-cover mitigation of optical turbulence in the boundary layer,” Opt. Express14(20), 8929–8946 (2006). [CrossRef] [PubMed]
- A. Tunick, “Statistical analysis of optical turbulence intensity over a 2.33 km propagation path,” Opt. Express15(7), 3619–3628 (2007). [CrossRef] [PubMed]
- M. E. Wittig, L. van Holtz, and D. E. L. Tunbridge, “In-orbit measurements of microaccelerations of ESA’s communication satellite OLYMPUS,” Proc. SPIE1218, 205–214 (1990). [CrossRef]
- E. M. Arkin, L. P. Chew, D. P. Huttenlocher, K. Kedem, and J. S. B. Mitchell, “An efficiently computable metric for comparing polygonal shapes,” IEEE Trans. Pattern Anal. Mach. Intell.13(3), 209–216 (1991). [CrossRef]
- W. Du, L. Tan, J. Ma, and Y. Jiang, “Temporal-frequency spectra for optical wave propagating through non-Kolmogorov turbulence,” Opt. Express18(6), 5763–5775 (2010). [CrossRef] [PubMed]
- D. M. Winker, “Effect of a finite outer scale on the Zernike decomposition of atmospheric optical turbulence,” J. Opt. Soc. Am. A8(10), 1568–1574 (1991). [CrossRef]
- G. Chong, M. Jing, and T. Liying, “Angle-of-arrival fluctuation of light beam propagation in strong turbulence regime,” High Power Laser Particle Beams18, 891–894 (2006).
- R. Wang, Random Process (Xi’an Jiaotong University Press, Xi’an, 2006).

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