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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 2 — Jan. 16, 2012
  • pp: 1033–1045
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A novel approach for simulating the optical misalignment caused by satellite platform vibration in the ground test of satellite optical communication systems

Qiang Wang, Liying Tan, Jing Ma, Siyuan Yu, and Yijun Jiang  »View Author Affiliations


Optics Express, Vol. 20, Issue 2, pp. 1033-1045 (2012)
http://dx.doi.org/10.1364/OE.20.001033


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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

Compared with satellite microwave communication, satellite optical communication has many advantages, such as higher data rate, lower probability of intercept, less power consumption, less mass [1

1. M. Toyoshima, W. R. Leeb, and H. Kunimori, “Comparison of microwave and light wave communication systems in space application,” Proc. SPIE 5296, 1–12 (2005).

,2

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]

]. Recently, satellite optical communication has been concerned by many countries and it has turned to be a hot topic in the field of satellite communications [3

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

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]

].

Pointing, Acquisition and Tracking (PAT) technology is one of key technologies in satellite optical communications. In the process of establishing an optical communication link, satellite platform vibration leads to the misalignment between input direction of the beacon and optical axis of receiving system, and then influences the precision of PAT system [7

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]

].

How to simulate the satellite platform vibration is an important technology in the ground test of the satellite optical communication system. In general, to test the performance of PAT system under the condition of vibration, a vibration device is often applied in simulating the satellite platform vibration. The relevant work reported in the reference indicates that satellite vibration has a continuous spectrum [8

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]

]. However, the vibration device used in the test just gives several discrete frequencies, so the simulation of this approach is relatively rough.

When a laser beam propagates though atmosphere, atmosphere turbulence causes phase fluctuation of the beam, which induces the effect of angle of arrival (AOA) fluctuation [9

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

13

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]

]. Because angle of arrival fluctuation is natural, not artificial, and it also has a continuous spectrum. It is necessary to discuss whether spectrum characteristic of these two effects is the same or similar, so in this paper, spectrum characteristic of these two effects is compared. The comparison results give justification to the new approach that angle of arrival fluctuation can be taken as a more effective simulation for the satellite platform vibration in ground test process of PAT system.

2. Experimental setup

As received (input) light, the laser is received by the Cassegrain telescope. After transmitting through the color separator, the laser is divided into two beams by a splitter. One of the two beams is focused on an avalanche photodiode (APD) to perform the communication experiment (not mentioned in this paper). The other beam is focused on a CMOS camera. A computer controls the CMOS camera to record its images at 1900 frames/s.

In Fig. 2, an optical filter is placed before the splitter to mitigate the influence of the background light.

During the experiment, a temperature and humidity recorder is used to record the temperature and humidity of the experiment every 2 minutes.

3. Data analysis

3.1 Computation of spectrum

The effect of angle of arrival fluctuation is investigated with the recorded data. For one experimental data trial, centroid coordinate (Xi, Yi) of the i-th frame is calculated by the gray centroid algorithm, that is:
Xi=Σx,yxgxyΣx,ygxyYi=Σx,yygxyΣx,ygxy
(1)
where gxy is gray-level value of the pixel with coordinate of (x, y).

Centroid coordinates of all frames in one data trial lead to two coordinate sequences of X = (X1, X2Xn) and Y = (Y1, Y2Yn). The sequence A = (A1, A2An) for angle of arrival is obtained from the coordinate sequences by the following formula,
Ai=d(Xi<X>)2+(Yi<Y>)2M×fL
(2)
where <·> means ensemble average, Ai is the i-th element in the sequence of A, d is pixel size of the CMOS, fL is focal length of the receiving optical system and M is enlargement factor of the optical system.

The experiment was performed from April 2009 to August 2009. Partial data set are given in Table 2

Table 2. Experimental data set

table-icon
View This Table
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. Table 2 summarizes the date and climate conditions for an initial data set, consisting of two data trials measured by OS1 (T1 and T2) and four data trials measured by OS2 (T3-T6), respectively.

3.2 High-frequency spectrum

Figure 3
Fig. 3 Power spectra of angle of arrival fluctuation for trials T1(a), T2(b), T3(c), T4(d), T5(e) and T6(f).
shows power spectra of angle of arrival fluctuation, which are derived from the Discrete Fourier Transform of data trials T1-T6. The black line is the power spectrum of angle of arrival fluctuation and the blue line represents the power law exponents of high-frequency spectrum, respectively in every subgraph of Fig. 3.

As shown in Fig. 3, power spectra of angle of arrival fluctuation have the characteristic that there is high power in low frequency area and low power in high frequency area. Especially, high-frequency power spectra of angle of arrival fluctuation have the approximate negative exponential power law dependence.

We want to know the scale of the power law exponents of high-frequency spectra, so some experimental data set are used. In Fig. 4
Fig. 4 The Relationship between the power law exponents of high-frequency spectra and variance of AOA (the data are collected by OS1).
and Fig. 5
Fig. 5 The Relationship between the power law exponents of high-frequency spectra and variance of AOA (the data are collected by OS2).
, the power law exponents of high-frequency spectra are not fixed values, and mostly they are greater than −11/3, which is more complicated than the theoretical results reported in Ref. [10

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

]. The theoretical model should be revised according to the specific conditions. Although the power law exponents of high-frequency spectra are not constant, the minimal value of the power law exponents is increasing along with the augmentation of variance of AOA, generally.

3.3 Contrastive analysis

Here, we mainly refer to two important power spectrum models of the satellite platform vibration which are often cited in many references [14

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

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]

] (shown in Fig. 6
Fig. 6 Power spectrum models of the satellite platform vibration.
). In Fig. 6, the blue line is the spectrum model that is used by the European Space Agency (ESA) in the SILEX program, while the green line is given by National Aeronautics and Space Development Agency (NASDA) of Japan.

As shown in Fig. 6, power spectra of the satellite platform vibration have the characteristic that there is high power in low frequency area and low power in high frequency area. Similarly, high-frequency power spectrum has the approximate negative exponential power law dependence, too.

The similarity between the power spectrum of angle of arrival fluctuation and the power spectrum of the satellite platform vibration is analyzed, and it is calculated as [15

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={i=1n[f1(Xi)f2(Xi)]2}1/2
(3)
where d is the distance of two curves, two curves are expressed as f1(X)and f2(X), respectively; n is the total number of elements compared.

If the curvature of one curve is the same or approximately equal as that of the other one, for comparing the similarity of two curves, one curve needs to be parallel move to superpose the other one in the rectangular coordinate system.

From Eq. (3), we see that the less d is, the better the similarity is. From Fig. 7(a)
Fig. 7 Power spectra of angle of arrival fluctuation for trials T1(a), T4(b), and T5(c), in which the black is Power spectra of angle of arrival fluctuation for trials T1,T4,T5, the blue line represents the power spectrum of the satellite platform vibration of ESA and the green line represents the power spectrum of the satellite platform vibration of NASDA.
, 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.

In a similar way, the similarity is analyzed in Fig. 7(b) and Fig. 7(c), and the curves need not to be parallel move. From Fig. 7(b), where f ≥ 50Hz, d is 48.5, and where f <50Hz, dis 1473.1. From Fig. 7(c), where f ≥ 50Hz, d is 128.1, and where f < 50Hz, d is 1215.5.

Based on the results, where 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).

From Fig. 7(a), the power spectrum of angle of arrival fluctuation measured by OS1 (T1) is higher than that of the satellite platform vibration used by ESA. However, the trend of the power spectra of these nearly is the same, and the similarity of the power spectra of these is very high.

In Fig. 7(b), where 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.

In Fig. 7(c), where 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.

In fact, it can be seen in Fig. 7 that spectra of angle of arrival fluctuation are consistent with those of satellite platform vibration. The comparison results confirm the new approach that the effect of angle of arrival fluctuation is taken as an effective simulation of satellite platform vibration in the ground test process of PAT system for a satellite communication optical system.

We discuss the similarity between the spectra of angle of arrival fluctuation and those of satellite platform vibration theoretically. According to Ref. [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]

], the temporal power spectrum of AOA fluctuation for a plane wave propagating in non-Kolmogorov atmospheric turbulence (W1(α,ω,β)) is expressed as [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]

]
W1(α,ω,β)=7.09Γ(α1)cos(απ2)C˜n2L1+α4k3α44ω0(ωω0)1α2(b2D24)α54×exp[kb2D28L(ωω0)2]{[1cos(2β)]W3α4,3α4[kb2D24L(ωω0)2]+2cos(2β)ωω0(kb2D24L)1/2W1α4,1α4[kb2D24L(ωω0)2]}
(4)
whereαrepresents the spectral power-law exponent, C˜n2is a generalized refractive-index structure parameter with units m3α(whenαis −11/3, C˜n2 = Cn2,Cn2is the conventional refractive-index structure parameter with units m2/3), Γ(x) in the above expression denotes the gamma function, L is the transmission distance of the light wave, k is 2π/λ, and λ denotes the optical wavelength, ω0=v(L/k)1/2, and v denotes the transverse wind velocity; 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 W(z)is Whittaker’s confluent hypergeometric function.

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

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

,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

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]

] is shown as follows:

σ12=2.91LCn2D1/3
(5)

In addition, the temporal power spectrum of AOA fluctuation for a spherical wave propagating in non-Kolmogorov atmospheric turbulence (W2(α,ω,β)) is given by [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]

]

W2(α,ω,β)=2.36Γ(α1)cos(απ2)C˜n2L1+α4k3α44ω0(ωω0)1α2(b2D24)α54×exp[kb2D28L(ωω0)2]{[1cos(2β)]W3α4,3α4[kb2D24L(ωω0)2]+2cos(2β)ωω0(kb2D24L)1/2W1α4,1α4[kb2D24L(ωω0)2]}
(6)

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

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

,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

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]

] is shown as follows:

σ22=0.97LCn2D1/3
(7)

The simulation conditions are based on the parameters of the 11.16km bi-directional FSO near horizontal laser link. Furthermore, when 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

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 18, 891–894 (2006).

]. 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
Fig. 8 Comparison between the theoretical values of the temporal power spectra of AOA fluctuation and the power spectra of the satellite platform vibration. The green line represents the power spectrum of the satellite platform vibration of NASDA, the blue line represents the power spectrum of the satellite platform vibration of ESA, the red line is the temporal power spectrum of AOA fluctuation scaled by the corresponding variance for a plane wave (W1(α,ω,β)/σ12, D = 150mm) and the black line represents the temporal power spectrum of AOA fluctuation scaled by the corresponding variance for a plane wave (W1(α,ω,β)/σ12, D = 250mm).
and Fig. 9
Fig. 9 Comparison between the theoretical values of the temporal power spectra of AOA fluctuation and the power spectra of the satellite platform vibration. The green line represents the power spectrum of the satellite platform vibration of NASDA, the blue line is the power spectrum of the satellite platform vibration of ESA, the sky blue line represents the temporal power spectrum of AOA fluctuation scaled by the corresponding variance for a spherical wave (W2(α,ω,β)/σ22, D = 150mm) and the violet line represents the temporal power spectrum of AOA fluctuation scaled by the corresponding variance for a spherical wave (W2(α,ω,β)/σ22, D = 250mm).
. 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.

We compute the similarity between the temporal power spectrum of AOA fluctuation and the power spectrum of the satellite platform vibration by Eq. (3). In Fig. 8, where 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)).

From Fig. 8 and Fig. 9, the temporal power spectrum of AOA fluctuation for a plane wave or a spherical wave has the same characteristic that there is high power in low frequency area and low power in high frequency area. Furthermore, high-frequency power spectrum has the approximate negative exponential power law dependence, too. But the order of magnitude of the temporal power spectrum of AOA fluctuation is lower than that of the power spectrum of the satellite platform vibration, and where 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

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]

. The experimental data show the randomness of AOA fluctuation due to the variation of the atmospheric turbulence, too.

4. Procedure of the new method

We need to use the power spectrum experimental data of angle of arrival fluctuation to simulate the power spectrum of the satellite platform vibration. Because the power spectrum of angle of arrival fluctuation of laser is randomness, here the mathematical processing method is the linear model of smooth time sequence, which is symbolized as ARMA(p,q) [19

19. R. Wang, Random Process (Xi’an Jiaotong University Press, Xi’an, 2006).

]. As an example, the processing procedure of the data trial T3 is illustrated.

The power spectral density of the data trial T3 is described according to the linear model of smooth time sequence,
P(ω)=σa2|A(eiω)B(eiω)|2
(8)
where P(ω)represents the power spectral density of the data trial T3, ω is frequency, A(z) and B(z) are real coefficient polynomial, andσais discrete white noise variance.

A(z) and B(z) can be expressed as follows:
A(z)=1θ1zθ2z2...θqzq
(9)
B(z)=1ϕ1zϕ2z2...ϕqzP
(10)
where θ1,...,θqand ϕ1,…,ϕq are real coefficients.

A smooth time sequence is shown as bellows
Stϕ1St1ϕ2St2...ϕpStp=atθ1at1θ2at2...θqatq
(11)
where St is a smooth time sequence, t = 0, ±1, ±2,…,atis discrete white noise.

According to Eq. (8)-Eq. (10), we obtain a spectral line to simulate the power spectrum of NASDA satellite platform vibration (In fact, we can get many spectral lines by this method, and only one is taken as an example here), illustrated in Fig. 8. From Fig. 8, we see that this simulation spectral line is very similar to the power spectrum of NASDA satellite vibration, so the simulation approach is effective. By Eq. (11), a smooth time sequence (St) is derived from this simulation spectral line by inverse Fourier transform, which is utilized to simulate the satellite vibration equivalently in the time domain, shown in Fig. 9.

Fig. 10 Comparison between the simulation spectral line and the power spectrum of the satellite (NASDA) vibration, in which the black line represents the simulation spectral line and the green line represents the power spectrum of the satellite platform vibration of NASDA.
Fig. 11 Smooth time sequence.

5 Discussion

6. Conclusions

Acknowledgments

The authors are grateful to the National Natural Science Foundation of China (NSFC) for financial support under Projects Nos. 10374023 and 60432040.

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 5296, 1–12 (2005).

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]

4.

I. I. Kim, B. Riey, and N. M. Wong, “Lessons learned from the STRV-2 satellite-to-ground lasercom experiment,” Proc. SPIE 4272, 1–15 (2001). [CrossRef]

5.

T. Tolker-Nielsen and G. Oppenhaeuser, “In orbit test result of an operational optical intersatellite link between ARTEMIS and SPOT4, SILEX,” Proc. SPIE 4635, 1–15 (2002). [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]

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 14(20), 8929–8946 (2006). [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]

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]

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.

G. Chong, M. Jing, and T. Liying, “Angle-of-arrival fluctuation of light beam propagation in strong turbulence regime,” High Power Laser Particle Beams 18, 891–894 (2006).

19.

R. Wang, Random Process (Xi’an Jiaotong University Press, Xi’an, 2006).

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

  1. M. Toyoshima, W. R. Leeb, and H. Kunimori, “Comparison of microwave and light wave communication systems in space application,” Proc. SPIE5296, 1–12 (2005).
  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. SPIE2699, 134–145 (1996). [CrossRef]
  3. K. Araki, Y. Arimoto, and M. Shikatani, “Performance evaluation of laser communication equipment onboard the ETS-VI satellite,” Proc. SPIE2699, 52–59 (1996). [CrossRef]
  4. 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]
  5. 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]
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