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Experimental verification of fiber-coupling efficiency for satellite-to-ground atmospheric laser downlinks

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Abstract

Optical communication is a high-capacity method that can handle considerable satellite data. When common-fiber optical devices such as optical fiber amplifiers based on single mode fibers are used in free-space laser communication systems, the laser beam has to be coupled to a single-mode fiber. Under atmospheric turbulence it would be difficult to make the required fiber coupling efficiency in satellite-to-ground laser propagation paths. A fast-steering mirror that can operate at high frequencies under atmospheric turbulence is fabricated, and its tracking performance is verified in real satellite-to-ground laser communication experiments. The measured fiber coupling loss of 10–19 dB in satellite-to-ground laser communication links under atmospheric turbulence shows good agreement with the predicted fiber coupling efficiency of 17 dB.

©2012 Optical Society of America

1. Introduction

High-resolution, high-precision images and a large information capacity are currently required for earth observation [1]. High-capacity communication over satellite-to-ground communication links is essential. Optical satellite communication systems are very attractive because they offer high-capacity communication and low-mass optical communication terminals [2]. An optical satellite communication system requires high receiving sensitivity, which is needed an erbium-doped fiber amplifier (EDFA) and coherent communication [3,4]. Such systems can realize stable, faster optical communication between optical ground stations and satellites.

In ground-to-satellite optical communication links, laser beams passing through the atmosphere are affected by atmospheric turbulence; therefore, the laser beam must be coupled into the single mode fiber in order to use optical fiber amplifiers based on single mode fibers under atmospheric turbulence and can be also connected to the terrestrial fiber networks. The coherent optical systems will also require to use the single mode fiber coupling in the future. The fiber coupling using a fast-steering mirror (FSM) has been investigated in order to suppress the phase distortions and angle of arrival variations caused by atmospheric turbulence [5,6]. A theoretical description of the fiber coupling efficiency has been developed for free-space optical communication through atmospheric turbulence for horizontal cases [7]. Here we extend this description to fiber coupling for a slanted path. To verify the extended theory, fiber coupling experiments using ground-to-satellite optical downlinks were performed using Optical Inter-orbit Communications Engineering Test Satellite (OICETS) [8]. A FSM designed for fiber coupling in ground-to-satellite optical communication links was implemented for measurements in the fiber coupling tests.

The rest of this paper is organized as follows. Section 2 describes the theory of the fiber coupling efficiency for satellite-to-ground laser links under atmospheric turbulence and presents the prediction results. The configuration of the satellite-to-ground laser communication experiments and the fine tracking system are described in Section 3. The experimental results of the fiber coupling test are also shown and compared with the predicted results.

2. Theory of fiber coupling efficiency for ground-to-satellite laser links

2.1 Fiber coupling efficiency in the presence of atmospheric turbulence

A theory describing the fiber coupling efficiency for horizontal laser communications has been developed [7] and extended to satellite-to-ground laser links. The efficiency for horizontal laser communication links in the presence of atmospheric turbulence is [7]

ηc=8a20101exp[(a2+ARAc)(x12+x22)]×I0(2ARAcx1x2)x1x2dx1dx2,
where

a=DR2πWmλf,
Ac=πρc2,
AR=πDR2/4,
ρc=(1.46Cn2k2L)3/5.

Here DR is the receiver lens diameter, Wm is the mode field radius at the fiber end face, λ is the optical wavelength, f is the focal length of the receiver lens, L is the communication link distance, and k is the wave number of the optical field. The fiber coupling efficiency for a slanted path is obtained by replacing Eq. (5) with Eq. (6) [9]:

ρs=[1.46k21cos(ζ)h0HdzCn2(h)]3/5,
where

H=h0+Lcos(ζ),Cn2(h)=0.00594(v/27)2(105h)10exp(h1000)
+2.7×1016exp(h1500)+Aexp(h100).

Structure function for atmospheric turbulence Cn2 is shown in Eq. (8) as the atmospheric turbulence model [10]. Here h0 is the height above the ground, ζ is the zenith angle, and v is the rms windspeed. We extend Eq. (1) to obtain the fiber coupling efficiency for a slanted atmospheric transmission path by adapting Eq. (6) in Eq. (1). We can calculate the fiber coupling efficiency of the ground-to-satellite laser communication for any satellites for swapping Ar and As in Eq. (1),

As=πρs2.

2.2 Predicted fiber coupling efficiency

Figure 1 shows the Cn2(h) profile associated with the Hufnagel–Valley (H–V) model as a function of the altitude calculated using Eq. (9). In the prediction, we assume an optical ground station having A = 1.2 × 10−13 m−2/3 and h0 = 122 m [11].

 figure: Fig. 1

Fig. 1 Cn2 profile associated with the H–V model as a function of the altitude, where A = 1.2 × 10−13 m−2/3 and h0 = 122 m.

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Figure 2 shows the fiber coupling efficiency as a function of A in Eq. (8) under atmospheric turbulence Cn2 with DR = 0.318 m, Wm = 5.2 μm, λ = 0.850 μm, f = 0.1 m, L = 1000 km, and ζ = 58°. The fiber coupling efficiency decreases when the refractive index structure constant increases; the efficiency is degraded to less than half when A change from 10−15 m-2/3 to 10−13 m-2/3.

 figure: Fig. 2

Fig. 2 Fiber coupling efficiency as a function of A for Cn2 and λ = 0.850, 1.060, 1.330, and 1.550 μm, where L = 1000 km, DR = 0.318 m, Wm = 5.2 μm, λ = 0.850 μm, v = 21 m/s, h0 = 122 m and f = 0.1.

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Figure 3 shows the fiber coupling efficiency as a function of the altitude for wavelengths of λ = 0.850, 1.060, 1.330, and 1.550 μm. At lengths greater than 1000 km, the fiber coupling efficiency becomes almost constant because the atmospheric turbulence has a smaller effect at these lengths. As shown in Fig. 1, the atmospheric turbulence resides below the altitude of about 1 km, therefore, the influence of the accumulated effect of the atmospheric turbulence dominates below 1 km.

 figure: Fig. 3

Fig. 3 Fiber coupling efficiency as a function of the communication link distance for λ = 0.850, 1.060, 1.330, and 1.550 μm.;where DR = 0.318 m, Wm = 5.2 μm, f = 0.1 m, A = 1.2 × 10−13 m−2/3, ζ = 58°, v = 21 m/s and h0 = 122 m.

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3. Satellite-to-ground laser link experiments

3.1 Experimental configuration

Laser communication between an optical ground station located at the National Institute of Information and Communications Technology (NICT) and a low earth orbit satellite was experimentally examined. Figure 4 shows the experimental configuration. Commands were initially sent to the satellite from the Tsukuba Space Center of the Japan Aerospace Exploration Agency (JAXA). The laser communication experiments were performed when the satellite was visible from the optical ground station. In these experiments, the downlink angle-of-arrival fluctuation was measured by a quadrant detector (QD), and the FSM was used to compensate for the angle-of-arrival fluctuation.

 figure: Fig. 4

Fig. 4 Experimental setup for laser communication between optical ground station and satellite.

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3.2 Fine tracking system

The fine tracking system consists of a beam splitter, the FSM, a single-mode fiber coupler, and a QD sensor. Figures 5 and 6 show a photograph of the FSM and its configuration, respectively [12]; Table 1 lists its specifications. As the resonance frequency is 6.4 kHz and the frequency at the phase of 90° is 6 kHz according to the frequency characteristics based on FSM, it sufficiently meets the required specification of 2 kHz. The inherent hysteresis property in the piezo-element has appeared remarkably with the large stroke; however, it may not cause any particular problem because the hysteresis with the small stroke is lower than that with the large stroke when a closed-loop control system is incorporated. With a resolution of less than 1 μrad achieved, it sufficiently meets the required specification of 10 μrad. The optical signal is received by a 1.5 m telescope and transmitted along the coude path. The sub-aperture of 31.8 cm was used for the proposed fine tracking system. Therefore, this optical system received a part of 1.5m telescope. The beam diameter was 2 cm on the optical bench. The FSM is placed on the coude optical bench. Part of the beam is divided by the beam splitter, and the QD detects the incident angle of the laser beam. The beam is reflected by the FSM. The QD sensor and the FSM are controlled as a closed loop. The FSM is controlled so that the optical signal remains at the center of the QD sensor. The received laser beam is adjusted so that the spot of the laser beam can be coupled into the single-mode fiber.

 figure: Fig. 5

Fig. 5 Photograph of the FSM at experiment.

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 figure: Fig. 6

Fig. 6 Configuration of the fine tracking system from telescope to optical bench.

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Tables Icon

Table 1. FSM specifications [12]

The received power was measured by two photodiodes (PDa and PDb). PDa measured the laser light received by the single-mode fiber, and PDb was used to compare the received power without fiber coupling. The loss of the optical system was measured before the experiments. The coupling loss was determined as the difference between the received power with fiber coupling, PPDa, and the received power without fiber coupling, PPDb. The fiber coupling efficiency can be evaluated experimentally using this setup.

3.3 Experimental results

3.3.1 Comparison of fiber coupling efficiencies in laboratory test and real measurements

We compared the fiber coupling efficiencies in a laboratory test and real measurements using OICETS. The fiber coupling loss ll was determined by comparing the received power coupled into the single-mode fiber and the received power without the fiber coupling, obtained by monitoring PPDb. Similarly, ls is the fiber coupling loss in the real measurements, which was determined by PPDa and PPDb using OICETS. The degraded fiber coupling loss can be compared by using the loss measured in the laboratory tests and the real measurements using the laser source from OICETS.

3.3.2 Measurements of the fiber coupling efficiencies with OICETS

In the experiments, the optical signal was not received by the fiber coupled detector when the FSM was turned-off, which prevented us from determining the fiber coupling efficiency. This was caused by a telescope jitter error due to mechanical telescope tracking errors. If there was no tip/tilt tracking control, no optical signal was coupled into the fiber in the experiment.

Figure 7 shows the experimentally measured fiber coupling loss when the FSM servo was active. During this time, the length between the satellite and ground, L, was 1000 km and v was 88 m/s. This rms wind speed is calculated from the Bufton wind model based on Eq. (23) in Ref [13]. As shown in Fig. 2 in Ref [13], the rms wind speed can exceed 200 m/s when the antenna slew rate is greater than 0.8 deg/sec. The antenna slew rate of 0.35 deg/s corresponds to the rms wind speed of 88 m/s based on the experiment. The measured loss was about 10–19 dB, as shown in Fig. 7. To verify the proposed theoretical calculation by Eq. (9), the fiber coupling loss was estimated by the proposed prediction model. Table 2 gives the parameters of the model. The predicted value was 17 dB, which agrees well with the experimental result. The sub-aperture of 31.8 cm was used for the proposed fine tracking system, which is larger than the atmospheric coherence size, allowing the degradation of the coupling efficiency to reach these values. During the tip/tilt control, the telescope jitter was completely compensated by the fine tracking control within the broadened focused beam spot on the fiber. The image motion (the speckle pattern) caused by atmospheric turbulence broadens the focused beam spot on the fiber. The measured fiber coupling loss corresponds to the degradation due to the speckle pattern. The fiber coupling loss proposed here should be allocated in the link budget design for future satellite-to-ground laser communication links.

 figure: Fig. 7

Fig. 7 Fiber coupling loss level (ηl) as a function of time.

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4. Conclusion

In this study, a prediction model of the fiber coupling efficiency for horizontal propagation paths was extended to that for satellite-to-ground laser links through atmospheric turbulence. Efficient fiber coupling could be realized for longer wavelengths in free-space laser communications. It was also shown that the coupling efficiency was degraded by both tracking errors and atmospheric turbulence. The FSM was developed, and the performance of the fine tracking system was verified using real satellite-to-ground laser communication links. The FSM worked effectively to reduce the jitter of telescope. About limitations due to the FSM-system, there is no limitation on the frequency characteristics of the piezo-actuators. However, as can be seen from the result, the larger aperture than speckle patterns degrades the fiber coupling efficiency drastically; therefore, the mirror size against the atmospheric coherence size must be examined and properly chosen if one wants to get much better fiber coupling efficiencies. On the other hand, the received power will be decreased when the mirror size is small. There must be the tradeoff and it contributes to the optical tracking system design. Fiber coupling loss is expected under atmospheric turbulence and depends on system parameters such as atmospheric turbulence, propagation path conditions, laser wavelength, and telescope aperture. About the modeling, we verified the prediction model by using the measured elevation angle. After the confirmation, we can predict the fiber coupling efficiency at any atmospheric conditions and any elevation angles and it is useful to the system design. The fiber coupling loss proposed here should be allocated in the link budget design for future satellite-to-ground laser communication links.

References and links

1. M. Toyoshima, “Trends in satellite communications and the role of optical free-space communications [Invited],” J. Opt. Netw. 4(6), 300–311 (2005). [CrossRef]  

2. V. W. S. Chan, “Optical satellite networks,” J. Lightwave Technol. 21(11), 2811–2827 (2003). [CrossRef]  

3. Y. Koyama, Y. Takayama, and H. Kunimori, “Optical fiber amplifiers for space environments,” Int. Conf. Struct. Surf. 2009(37), 221–225 (2009).

4. J. C. Ricklin and F. M. Davidson, “Atmospheric turbulence effects on a partially coherent Gaussian beam: implications for free-space laser communication,” J. Opt. Soc. Am. A 19(9), 1794–1802 (2002). [CrossRef]   [PubMed]  

5. F. Fidler and O. Wallner, “Application of single-mode fiber-coupled receivers in optical satellite to high-altitude platform communications,” EURASIP J. Wirel. Commun. Netw. 2008, 864031 (2008).

6. M. Toyoshima, “Maximum fiber coupling efficiency and optimum beam size in the presence of random angular jitter for free-space laser systems and their applications,” J. Opt. Soc. Am. A 23(9), 2246–2250 (2006). [CrossRef]   [PubMed]  

7. Y. Dikmelik and F. M. Davidson, “Fiber-coupling efficiency for free-space optical communication through atmospheric turbulence,” Appl. Opt. 44(23), 4946–4952 (2005). [CrossRef]   [PubMed]  

8. T. Jono, Y. Takayama, K. Arai, K. Shiratama, I. Mase, B. Demelenne, M. Toyoshima, and D. Giggenbach, “Overview of the inter-orbit and the orbit-to-ground lasercom demonstration by OICETS,” Proc. SPIE 6457(645702), 1–10 (2007).

9. J. H. Churnside, “Aperture averaging of optical scintillations in the turbulent atmosphere,” Appl. Opt. 30(15), 1982–1994 (1991). [CrossRef]   [PubMed]  

10. L. C. Andrews, R. L. Phillips, and P. T. Yu, “Optical scintillations and fade statistics for a satellite-communication system,” Appl. Opt. 34(33), 7742–7751 (1995). [CrossRef]   [PubMed]  

11. M. Toyoshima, Y. Takayama, H. Kunimori, and T. Jono, “Probability density function of the atmospheric turbulence-induced signal fluctuation in a ground-to-low earth orbit optical communication link,” Proc. 25th LSS, 30–36, (2007).

12. T. Abe, T. Kizaki, H. Kunimori, Y. Takayama, and M. Toyoshima, “The development of two-axes fast steering mirror and high efficiency driver,” Proc. 52nd Space Science and Technology Conference, 487–490, (2008).

13. M. Toyoshima, H. Takenaka, and Y. Takayama, “Atmospheric turbulence-induced fading channel model for space-to-ground laser communications links,” Opt. Express 19(17), 15965–15975 (2011). [CrossRef]   [PubMed]  

References

  • View by:

  1. M. Toyoshima, “Trends in satellite communications and the role of optical free-space communications [Invited],” J. Opt. Netw. 4(6), 300–311 (2005).
    [Crossref]
  2. V. W. S. Chan, “Optical satellite networks,” J. Lightwave Technol. 21(11), 2811–2827 (2003).
    [Crossref]
  3. Y. Koyama, Y. Takayama, and H. Kunimori, “Optical fiber amplifiers for space environments,” Int. Conf. Struct. Surf. 2009(37), 221–225 (2009).
  4. J. C. Ricklin and F. M. Davidson, “Atmospheric turbulence effects on a partially coherent Gaussian beam: implications for free-space laser communication,” J. Opt. Soc. Am. A 19(9), 1794–1802 (2002).
    [Crossref] [PubMed]
  5. F. Fidler and O. Wallner, “Application of single-mode fiber-coupled receivers in optical satellite to high-altitude platform communications,” EURASIP J. Wirel. Commun. Netw. 2008, 864031 (2008).
  6. M. Toyoshima, “Maximum fiber coupling efficiency and optimum beam size in the presence of random angular jitter for free-space laser systems and their applications,” J. Opt. Soc. Am. A 23(9), 2246–2250 (2006).
    [Crossref] [PubMed]
  7. Y. Dikmelik and F. M. Davidson, “Fiber-coupling efficiency for free-space optical communication through atmospheric turbulence,” Appl. Opt. 44(23), 4946–4952 (2005).
    [Crossref] [PubMed]
  8. T. Jono, Y. Takayama, K. Arai, K. Shiratama, I. Mase, B. Demelenne, M. Toyoshima, and D. Giggenbach, “Overview of the inter-orbit and the orbit-to-ground lasercom demonstration by OICETS,” Proc. SPIE 6457(645702), 1–10 (2007).
  9. J. H. Churnside, “Aperture averaging of optical scintillations in the turbulent atmosphere,” Appl. Opt. 30(15), 1982–1994 (1991).
    [Crossref] [PubMed]
  10. L. C. Andrews, R. L. Phillips, and P. T. Yu, “Optical scintillations and fade statistics for a satellite-communication system,” Appl. Opt. 34(33), 7742–7751 (1995).
    [Crossref] [PubMed]
  11. M. Toyoshima, Y. Takayama, H. Kunimori, and T. Jono, “Probability density function of the atmospheric turbulence-induced signal fluctuation in a ground-to-low earth orbit optical communication link,” Proc. 25th LSS, 30–36, (2007).
  12. T. Abe, T. Kizaki, H. Kunimori, Y. Takayama, and M. Toyoshima, “The development of two-axes fast steering mirror and high efficiency driver,” Proc. 52nd Space Science and Technology Conference, 487–490, (2008).
  13. M. Toyoshima, H. Takenaka, and Y. Takayama, “Atmospheric turbulence-induced fading channel model for space-to-ground laser communications links,” Opt. Express 19(17), 15965–15975 (2011).
    [Crossref] [PubMed]

2011 (1)

2009 (1)

Y. Koyama, Y. Takayama, and H. Kunimori, “Optical fiber amplifiers for space environments,” Int. Conf. Struct. Surf. 2009(37), 221–225 (2009).

2008 (1)

F. Fidler and O. Wallner, “Application of single-mode fiber-coupled receivers in optical satellite to high-altitude platform communications,” EURASIP J. Wirel. Commun. Netw. 2008, 864031 (2008).

2007 (1)

T. Jono, Y. Takayama, K. Arai, K. Shiratama, I. Mase, B. Demelenne, M. Toyoshima, and D. Giggenbach, “Overview of the inter-orbit and the orbit-to-ground lasercom demonstration by OICETS,” Proc. SPIE 6457(645702), 1–10 (2007).

2006 (1)

2005 (2)

2003 (1)

2002 (1)

1995 (1)

1991 (1)

Andrews, L. C.

Arai, K.

T. Jono, Y. Takayama, K. Arai, K. Shiratama, I. Mase, B. Demelenne, M. Toyoshima, and D. Giggenbach, “Overview of the inter-orbit and the orbit-to-ground lasercom demonstration by OICETS,” Proc. SPIE 6457(645702), 1–10 (2007).

Chan, V. W. S.

Churnside, J. H.

Davidson, F. M.

Demelenne, B.

T. Jono, Y. Takayama, K. Arai, K. Shiratama, I. Mase, B. Demelenne, M. Toyoshima, and D. Giggenbach, “Overview of the inter-orbit and the orbit-to-ground lasercom demonstration by OICETS,” Proc. SPIE 6457(645702), 1–10 (2007).

Dikmelik, Y.

Fidler, F.

F. Fidler and O. Wallner, “Application of single-mode fiber-coupled receivers in optical satellite to high-altitude platform communications,” EURASIP J. Wirel. Commun. Netw. 2008, 864031 (2008).

Giggenbach, D.

T. Jono, Y. Takayama, K. Arai, K. Shiratama, I. Mase, B. Demelenne, M. Toyoshima, and D. Giggenbach, “Overview of the inter-orbit and the orbit-to-ground lasercom demonstration by OICETS,” Proc. SPIE 6457(645702), 1–10 (2007).

Jono, T.

T. Jono, Y. Takayama, K. Arai, K. Shiratama, I. Mase, B. Demelenne, M. Toyoshima, and D. Giggenbach, “Overview of the inter-orbit and the orbit-to-ground lasercom demonstration by OICETS,” Proc. SPIE 6457(645702), 1–10 (2007).

Koyama, Y.

Y. Koyama, Y. Takayama, and H. Kunimori, “Optical fiber amplifiers for space environments,” Int. Conf. Struct. Surf. 2009(37), 221–225 (2009).

Kunimori, H.

Y. Koyama, Y. Takayama, and H. Kunimori, “Optical fiber amplifiers for space environments,” Int. Conf. Struct. Surf. 2009(37), 221–225 (2009).

Mase, I.

T. Jono, Y. Takayama, K. Arai, K. Shiratama, I. Mase, B. Demelenne, M. Toyoshima, and D. Giggenbach, “Overview of the inter-orbit and the orbit-to-ground lasercom demonstration by OICETS,” Proc. SPIE 6457(645702), 1–10 (2007).

Phillips, R. L.

Ricklin, J. C.

Shiratama, K.

T. Jono, Y. Takayama, K. Arai, K. Shiratama, I. Mase, B. Demelenne, M. Toyoshima, and D. Giggenbach, “Overview of the inter-orbit and the orbit-to-ground lasercom demonstration by OICETS,” Proc. SPIE 6457(645702), 1–10 (2007).

Takayama, Y.

M. Toyoshima, H. Takenaka, and Y. Takayama, “Atmospheric turbulence-induced fading channel model for space-to-ground laser communications links,” Opt. Express 19(17), 15965–15975 (2011).
[Crossref] [PubMed]

Y. Koyama, Y. Takayama, and H. Kunimori, “Optical fiber amplifiers for space environments,” Int. Conf. Struct. Surf. 2009(37), 221–225 (2009).

T. Jono, Y. Takayama, K. Arai, K. Shiratama, I. Mase, B. Demelenne, M. Toyoshima, and D. Giggenbach, “Overview of the inter-orbit and the orbit-to-ground lasercom demonstration by OICETS,” Proc. SPIE 6457(645702), 1–10 (2007).

Takenaka, H.

Toyoshima, M.

Wallner, O.

F. Fidler and O. Wallner, “Application of single-mode fiber-coupled receivers in optical satellite to high-altitude platform communications,” EURASIP J. Wirel. Commun. Netw. 2008, 864031 (2008).

Yu, P. T.

Appl. Opt. (3)

EURASIP J. Wirel. Commun. Netw. (1)

F. Fidler and O. Wallner, “Application of single-mode fiber-coupled receivers in optical satellite to high-altitude platform communications,” EURASIP J. Wirel. Commun. Netw. 2008, 864031 (2008).

Int. Conf. Struct. Surf. (1)

Y. Koyama, Y. Takayama, and H. Kunimori, “Optical fiber amplifiers for space environments,” Int. Conf. Struct. Surf. 2009(37), 221–225 (2009).

J. Lightwave Technol. (1)

J. Opt. Netw. (1)

J. Opt. Soc. Am. A (2)

Opt. Express (1)

Proc. SPIE (1)

T. Jono, Y. Takayama, K. Arai, K. Shiratama, I. Mase, B. Demelenne, M. Toyoshima, and D. Giggenbach, “Overview of the inter-orbit and the orbit-to-ground lasercom demonstration by OICETS,” Proc. SPIE 6457(645702), 1–10 (2007).

Other (2)

M. Toyoshima, Y. Takayama, H. Kunimori, and T. Jono, “Probability density function of the atmospheric turbulence-induced signal fluctuation in a ground-to-low earth orbit optical communication link,” Proc. 25th LSS, 30–36, (2007).

T. Abe, T. Kizaki, H. Kunimori, Y. Takayama, and M. Toyoshima, “The development of two-axes fast steering mirror and high efficiency driver,” Proc. 52nd Space Science and Technology Conference, 487–490, (2008).

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Figures (7)

Fig. 1
Fig. 1 Cn2 profile associated with the H–V model as a function of the altitude, where A = 1.2 × 10−13 m−2/3 and h0 = 122 m.
Fig. 2
Fig. 2 Fiber coupling efficiency as a function of A for Cn2 and λ = 0.850, 1.060, 1.330, and 1.550 μm, where L = 1000 km, DR = 0.318 m, Wm = 5.2 μm, λ = 0.850 μm, v = 21 m/s, h0 = 122 m and f = 0.1.
Fig. 3
Fig. 3 Fiber coupling efficiency as a function of the communication link distance for λ = 0.850, 1.060, 1.330, and 1.550 μm.;where DR = 0.318 m, Wm = 5.2 μm, f = 0.1 m, A = 1.2 × 10−13 m−2/3, ζ = 58°, v = 21 m/s and h0 = 122 m.
Fig. 4
Fig. 4 Experimental setup for laser communication between optical ground station and satellite.
Fig. 5
Fig. 5 Photograph of the FSM at experiment.
Fig. 6
Fig. 6 Configuration of the fine tracking system from telescope to optical bench.
Fig. 7
Fig. 7 Fiber coupling loss level (ηl) as a function of time.

Tables (2)

Tables Icon

Table 1 FSM specifications [12]

Tables Icon

Table 2 Parameters used in Eq. (9)

Equations (9)

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

η c =8 a 2 0 1 0 1 exp[ ( a 2 + A R A c )( x 1 2 + x 2 2 ) ] × I 0 ( 2 A R A c x 1 x 2 ) x 1 x 2 d x 1 d x 2 ,
a= D R 2 π W m λf ,
A c =π ρ c 2 ,
A R =π D R 2 /4,
ρ c = ( 1.46 C n 2 k 2 L ) 3/5 .
ρ s = [ 1.46 k 2 1 cos( ζ ) h 0 H dz C n 2 (h) ] 3/5 ,
H= h 0 +Lcos(ζ), C n 2 (h)=0.00594 ( v/27 ) 2 ( 10 5 h ) 10 exp( h 1000 )
+2.7× 10 16 exp( h 1500 )+Aexp( h 100 ).
A s =π ρ s 2 .

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