Abstract

We report a coherent tracking system based on fiber nutation for inter-satellite beaconless laser communication, which uses a piezo-electric ceramic tube (PCT) to drive the end face of single mode fiber (SMF) for nutation, and uses coherent demodulation method to directly calculate the boresight error from the intensity envelope fluctuation of signal light. The method is given theoretically and verified experimentally. Under the condition of fiber nutation frequency is 2000Hz and nutation radius is 1.1um, the experimental verification results in our interested range of signal light power (1nW-10nW) meet our design requirements. The receiving field of view (FOV) of tracking system is more than 300urad, and the closed-loop tracking bandwidth (−3dB) is about 115 Hz. When the boresight error is fixed at 80urad, the real calculation error is less than 10%. The closed-loop performance of tracking system is insensitive to the change of signal light power. Our coherent tracking system is of great significance to the inter-satellite beaconless laser communication.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Corrections

5 November 2019: A typographical correction was made to the author affiliations.

1. Introduction

Vibration noise of satellite platform is the main factor affecting the establishment of inter-satellite laser communication link, which can be decomposed into low-frequency vibration noise with larger amplitude and high-frequency vibration noise with smaller amplitude [1–3]. In order to reduce the impact of vibration noise on the optical communication links, we usually use coarse tracking technology and fine tracking technology based on compound-axis control system to suppress it to an acceptable level. As an important part of inter-satellite laser communication system, fine tracking system (FTS) relies on its high precision and high bandwidth line of sight (LOS) tracking performance to suppress coarse tracking residuals (CTR) and ensure a continuous and stable optical communication link. According to the detection methods of LOS error, the FTS can be divided into two kinds: FTS based on spot position detector (SPD) and FTS without SPD.

The FTS based on SPD uses a high bandwidth SPD to detect coarse tracking residuals, and feeds back to a fast steering mirror (FSM) to achieve the fast tracking of the optical axis of incident light. The technology of FTS based on SPD has been widely verified by in-orbit experiments. The terminal PASTEL loaded on the communication satellite ARTEMIS developed by ESA and the terminal OPALE loaded on the earth observation satellite SPOT4 in the SILEX project use the array CCD camera with region-of-interest to increase the detection frequency of the spot position to 2000Hz, and the control system bandwidth is better than 200Hz [4,5]. The terminal LUCE loaded on the low-orbit optical inter-satellite communication engineering test satellite (OICETS) uses a high-bandwidth quadrant avalanche photodiode (QAPD) as SPD, and the tracking error designed is 1.85urad [6].In addition to the above two schemes, FTS based on position sensitive detector (PSD) has also been proposed with a receiving sensitivity of −38dBm [7]. The FTS based on the SPD has the disadvantages of being sensitive to vibration and temperature. Especially in the non-ideal coaxial optical transmission system, the tracking point on the SPD varies with the change of the azimuth and elevation angle.

The FTS without SPD directly calculates the coarse tracking residual from the incident light, which mainly has two implementation methods: FTS based on the coherent tracking technology of the binary detectors and FTS based on nutation [8]. The former technology was proposed by Dirk Giggenbach et al. from the German Aerospace Research Establishment (DLR) [9], and has been verified by the in-orbit experiments on the TerraSAT-X and NFIRE satellites [10]. The second technology is divided into FTS based on fiber nutation and FTS based on local beam nutation according to the position of the nutation [8]. In 1989, Swanson et al. from the Massachusetts Institute of Technology firstly proposed using the fiber nutation scheme to simplify free-space laser communication systems [11], and the method was verified by NASA’s lunar laser communications demonstration (LLCD) project [12]. In 2014, Ke Deng et al. proposed a scheme using acousto-optic and electro-optic scanning to nutation local-beam [8]. FTS without SPD takes the center of fiber or communication detector as the tracking reference point, the tracking optical axis and communication optical axis coincide completely, so it has the advantages of simple structure and strong adaptability to the change of mechanical structure.

In this paper, we propose a coherent tracking system based on fiber nutation for inter-satellite beaconless laser communication. EDFA is used to perform low-noise amplification of weak light signal, which makes the coherent detection module insensitive to the insertion loss in the optical process and reduce the system's requirement for gain-bandwidth product of photodetector. Considering the requirements of real optical communication terminal parameter settings, we built a complex desktop experiment device and tested the tracking performance of the system. This paper focuses on the tracking function of the system, some principles and parameters related to communication function are not explained in detail.

2. System structure

The structure of the coherent tracking system based on fiber nutation is shown in Fig. 1. The incident light entering the receiving aperture of telescope is circularly polarized and converted to linearly polarized light by a quarter wave plate (QWP). The fast steering mirror (FSM) controls the incident light beam into the FOV of single mode fiber (SMF) and focuses on the focal plane of lens. The system uses a piezoelectric ceramic tube (PCT) to drive the end face of the SMF for nutation, and periodically modulates the intensity of the signal light coupled into the SMF. The SMF in the nutation device is fixed in the center of the two-dimensionally deflected PCT, and its end surface is at the focal plane of the coupling lens. In order to increase the coupling efficiency, the end face of SMF is coated with an anti-reflection film. After modulation, the signal light coupled into the SMF is amplified by EDFA with low noise, and then mixed with the local oscillator in the optical Hybrid. The photodetector (D) converts the mixed light into electrical signal. The boresight error calculation algorithm uses the voltage signal to demodulate the signal intensity envelope fluctuation and boresight error, and the proportional-integral-derivative (PID) controller algorithm controls the FSM based on the boresight error to automatically tracking the boresight of incident light. The two algorithms are executed in the FPGA device.

 

Fig. 1 Structure of the coherent tracking system based on fiber nutation

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3. Principle of fiber-nutation FTS based on coherent detection

3.1 Intensity envelope fluctuation demodulation

The beaconless inter-satellite laser communication system does not have independent beacon beam, the boresight error is directly obtained from the signal light. For a binary phase-shift keying (BPSK) laser communication system, the signal light is expressed as follows

Es(t)=Escos(ωst+φ(t))
whereEsis the signal light amplitude, ωs is the signal light angular frequency,φ(t) is the phase modulation of the signal light.

Fiber nutation causes the intensity envelope fluctuation of the light coupled into SMF, which is physically equivalent to the intensity modulation of the optical signal. The signal light entering the optical Hybrid which has been amplified by EDFA is expressed as follows

As(t)=Ascos(ωst+φ(t))
where As=EsGη(t), η(t) is the coupling efficiency of spatial light to SMF during fiber nutation, G is the gain constant of EDFA.

The local laser electrical field is expressed as follows

El(t)=Elcos(ωlt+φl)
where El is the local oscillator optical amplitude, ωl is the local oscillator optical angular frequency, φl is the local oscillator optical phase.

For a 2x4 90°optical Hybrid, the optical signal intensity at four output ports are expressed as follows [13]

I0=k12|As|2r2+k32|ELO|2t2+2k1k3rt|AsELO|cos[ϕ(t)+(ρτ)π/2(ψπ/4)]
I90=k22|As|2r2+k42|ELO|2t2+2k2k4rt|AsELO|cos[ϕ(t)+(ρτ)(ψπ/4)]
I180=k12|As|2t2+k32|ELO|2r2+2k1k3rt|AsELO|cos[ϕ(t)+(τρ)π/2(ψπ/4)]
I270=k22|As|2t2+k42|ELO|2r2+2k2k4rt|AsELO|cos[ϕ(t)+(τρ)(ψπ/4)]
where r, r, t, t, τ, τ, ρ and ρ are reflection coefficients and transmission coefficients of the polarization beam splitter in optical Hybrid. k1, k2, k3 and k4 are the polarization components parallel to the propagation plane and the perpendicular polarization components. ψ is the phase of local oscillator beam. Ideally, ψ=π/4, τρ=π/2,τρ=π/2, r=r=t=t=1/2 and k1=k2=k3=k4=k.

The photodetectors convert the optical intensity signals I0, I90, I180 and I270 into voltage signals and AC-coupled output. Taking into account that the cutoff frequency of the high pass filter is in the order of MHz, and the DC terms in the Eqs. (4)-(7) is filtered. We obtain the AC terms given by

V0=k12RrL|As|2r2+k1k3RrL|AsELO|cos[ωIFt+φ(t)]
V90=k22RrL|As|2r2+k2k4RrL|AsELO|sin[ωIFt+φ(t)]
V180=k12RrL|As|2t2k1k3RrL|AsELO|cos[ωIFt+φ(t)]
V270=k22RrL|As|2t2k2k4RrL|AsELO|sin[ωIFt+φ(t)]
where R is the responsibility of the photodetectors, rLis the resistance of the trans-impedance, ωIF is the frequency difference between incident signal light and local oscillator.

To improve the receiving sensitivity, the system uses differential signal processing to obtain voltage signals of I and Q paths.

VI(t)=2k1k3RrL|AsELO|cos[ωIFt+φ(t)]
VQ(t)=2k2k4RrL|AsELO|sin[ωIFt+φ(t)]

The signal intensity envelope fluctuation can be demodulated by summing the square of the voltage signals in the I and Q paths as follows.

V(t)=VI2(t)+VQ2(t)=4k4R2rL2Gη(t)|Es|2|ELO|2

The coupling efficiency of spatial light to SMF is defined as [14]

η(t)=PcPin
where Pc is the power of signal light coupled into the SMF, and Pin is the power of incident signal light, satisfying the relationship Pin=|Es|2/2,Eq. (14) can be rewritten as

VI2(t)+VQ2(t)=8k4R2rL2GPc|ELO|2

Usually, the optical power of the local oscillator is stable, so |ELO|2 is a constant. According to the Eq. (16), when the gain constant G of EDFA and the responsibility R of photodetector are constant, the sum of the squares of the voltage signals in the I and Q paths is proportional to the power of the signal light coupled into SMF.

3.2 Principle of fiber nutation

Based on the field-matching theory, when the focus of incident light does not perfectly aligned with SMF, the coupling efficiency decreases. During the process of fiber nutation, the end face of SMF scans the focus at the focal plane with a small amplitude and high frequency. If the focus coincides with the center of fiber nutation, the coupling efficiency is a constant value. Otherwise, the coupling efficiency will change periodically. Figure 2 shows the Cartesian coordinate system established in the plane of the end face of SMF, the origin of which coincides with the center of nutation trail. The X axis of coordinate system and X axis of FSM in the same plane, and the Y axis of coordinate system is parallel to the Y axis of FSM. Driven by two sinusoidal signals with a phase difference of 90°, the two axes of nutation actuator move respectively and control the end face of SMF to scan along a circular trail. Any point (x,y) on the circular trail is expressed as follows.

{x(t)=acos(2πft)y(t)=asin(2πft)
where a is the radius of fiber nutation, and f is the frequency of fiber nutation.

 

Fig. 2 Schematic diagram of fiber nutation scanning spot. The area in the black circle represents the spot at the focal plane, and the black dot represents the geometric center of the spot. The area in the red circle represents the fiber core of SMF, and the green circle represents the nutation trail of the end face of SMF. (x, y) is the position coordinate of fiber core center on the nutation trail. The area in the brown circle is the scanning range in the process of fiber nutation.

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The coupling efficiency ηc of spatial light to SMF can be approximately written as [15]

ηc=PcPin=cexp(ρ2ω02)
where ρ is the static radial offset of the optical beam from the nominal axis of SMF core, ω0 is the mode field radius of SMF, c is the maximum coupling efficiency when ρ=0. IfπDω0/λfl=2.24, the coupling efficiency coefficient c takes the maximum value of 81.45% [15], where D and fl are the lens aperture and focal length.

Coupling efficiency η(t) at the point (x,y) on the circular path is expressed as follows by substituting Eq. (17) into Eq. (18)

η(t)=P1Pin(t)=cexp((acos(2πft)ρx1)2+(asin(2πft)ρy1)2ω02)
where Pin(t), P1 are the incident optical power and optical power coupled to the SMF respectively. (ρx1,ρy1) is the position of the spot center at time t.

For the point (x',y') that is symmetric with (x,y) on the circular track, the coupling efficiency η(t') is expressed as

η(t')=P2Pin(t')=cexp((acos(2πft')ρx2)2+(asin(2πft')ρy2)2ω02)
where T is the nutation cycle, Pin(t') and P2 are the incident optical power and the optical power coupled to the SMF, respectively. (ρx2,ρy2) is the position of the spot center at time t'. From the geometric relationship in Fig. 2, t'=t+T/2=t+1/2f. Substitute Eq. (19) into Eq. (20).

ω02ln(P1Pin(t')P2Pin(t))=2a(ρx1cos(2πft)ρx2cos(2πft'))+2a(ρy1sin(2πft)ρy2sin(2πft'))

Here, we assume that the fiber nutation frequency is fast enough, so it can be considered that the spot position and the incident optical power does not change during the reference time period, and the parameters in Eq. (21) satisfy the following relationships:Pin(t)=Pin(t'), ρx1=ρx2=ρx, ρy1=ρy2=ρy . Equation (21) can be expressed as follows.

ω02ln(P1P2)=2aρx(cos(2πft)cos(2πft'))+2aρy(sin(2πft)sin(2πft'))

Further assuming that fiber nutation rotates counterclockwise and its starting point is on the positive X axis. The moments corresponding to the intersection of nutation trajectory and coordinate axis in each cycle are expressed as nT, nT+T/4, nT+T/2 and nT+3T/4, respectively. The spot position is expressed as follows by substituting the incident optical powers into Eq. (22).

{ρx=ω024aln(P(nT)P(nT+T/2))ρy=ω024aln(P(nT+T/4)P(nT+3T/4))

The boresight error calculated by Eq. (23) can be rewritten as follows in voltage.

{θx=ω024aflln(VI2(nT)+VQ2(nT)VI2(nT+T/2)+VQ2(nT+T/2))θy=ω024aflln(VI2(nT+T/4)+VQ2(nT+T/4)VI2(nT+3T/4)+VQ2(nT+3T/4))
where θx, θy are the components of boresight error on the X and Y axes, respectively.

4. Experiment

4.1 Setup

To verify the performance of our proposed coherent tracking system, we built a desktop experiment system as shown in Fig. 3, which includes four functional modules: signal transmission module, free-space transmission simulation module, coherent detection module and communication and track signal demodulation module. The information about instruments used in the experiment is presented in Table 1. In the signal transmission module, a BER tester (BERT) is used to generate pseudo-random code at 1Gbaud/s, and drive a photoelectric phase modulator (EOSPACE MPZ-LN-10) to generate BPSK signals.

 

Fig. 3 The block diagram of desktop experiment system

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Tables Icon

Table 1. Information about experiment instruments

The free-space transmission simulation module mainly includes two FSMs and a large aperture lens with long focal length. The lens, in combination with the aperture, is to produce an approximate plane wave. The FSM2 is used to generate vibration noise to simulate the vibration of the satellite platform during inter-satellite laser communication. The high frequency vibration noise (f>5Hz) amplitude of the satellite platform is less than 20urad [1]. Here we assume when the coarse tracking system effectively suppresses the large amplitude and low-frequency vibration noise, the residual boresight error (3σ) of the incident light entering the fine tracking field of view (FOV) is less than 20urad. The desktop experimental device does not include a telescope system. To balance its amplification of the boresight error, the vibration noise introduced by the test is multiplied by the magnification (14 times).

The coherent detection module mainly includes a fiber nutation device, an erbium doped fiber amplifier (EDFA) with gain controllable, a 90° optical bridge, and an AC coupled output photodetector. The scanning frequency of fiber nutation is set to 2000Hz, and the nutation radius is 1.1um. To maximize the coupling efficiency coefficient c in Eq. (18), the lens parameters satisfy R=4.65mm, f=42mm. The maximum output voltage range Vpp of the detector is 250mV. When the output voltage is larger than 200mV, the response of the detector is close to the saturation region and exhibits nonlinear characteristics. The input signal power of interest in this experiment ranges from 1nW to 10nW, and the expected detector output voltage range is 60~200mV. Therefore, the EDFA gain is controlled at 18dB.

The communication and track signal demodulation module is the core of the desktop experimental system, mainly to perform specific algorithms to achieve the following functions: (1) calculating the frequency difference between the signal light and the local oscillator light, and controlling the local oscillator laser to lock the frequency difference; (2) automatically setting the EDFA gain to operate the detector in the linear region based on the amplitude of the voltage signal; (3) demodulating the signal intensity envelope fluctuation and calculating the boresight error. The atomic clock provides an accurate reference clock signal for the communication measurement board (FPGA1) and the main control board (FPGA2). FPGA1 samples the voltage signal from the detector at a rate of 2.5Gs/s. FPGA2 drives FSM1 to compensate for the boresight error. Some other necessary parameters are presented in Table 2.

Tables Icon

Table 2. System parameters not mentioned above

4.2 The linearity of intensity envelope fluctuation demodulation

The detector used in the system has a limited linear working area. Excessive input optical power triggers the execution of its automatic gain control function, causing the responsivity to change. In addition, the fixed gain of EDFA is also for small signals, and the excessive input signal causes the gain to drop. Therefore, we input the signal light with different power when the nutation is not turned on, and then use the Eq. (16) to demodulate the signal intensity. Figure 4 shows the relationship between the signal intensity and the power coupled into SMF power. With the input optical power varies from 1nW to 10nW, the curve is approximately linear, and satisfy the linear demodulation requirements for intensity envelope signals.

 

Fig. 4 The calculated signal intensity as a function of the power coupled into SMF

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4.3 The linearity of boresight error calculation

Theoretically, the FOV of fiber nutation device is defined as the corresponding angular range when the coupling efficiency drops to 1/e of the maximum value. We can use the formula FOV=2ω0/f to calculate the FOV of fiber nutation device. For the 1550nm SMF, FOV238urad, where ω0=5μm. Experimentally, we use FSM1 to linearly scan the end face of SMF with an amplitude of 320μrad, and the scanning frequency is 0.01Hz. The boresight error calculated by using Eq. (24) is obtained by the computer from FPGA, Fig. 5(a) shows the calculated X and Y axis boresight error collected by computer, the linear fit curve is obtained by linear fitting the x axis boresight error curve. Figure 5(b) shows the calculated boresight error with the signal power varies from 1nW to 10nW when the boresight error is 80μrad. As a reference, the calculated boresight error of the Y axis also appears in the Fig. 5.

 

Fig. 5 the boresight error calculated by Eq. (24). (a) With FSM1 scanning the end face of SMF. (b) With the signal power change when FSM1 deflected 80urad.

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From Fig. 5(a), our proposed system can accurately calculate the boresight error in the range of ± 150urad. Especially in the theoretical FOV ( ± 119urad), the x axis boresight error curve completely coincides with the linear fit curve. Note that during FSM1 scanning the X axis of fiber nutation device, the Y axis calculated boresight error is not equal to 0urad. The reason is that the calibration error of the system sampling clock for the intensity envelope fluctuation is less than 5%. The existence of this error makes the FSM1 X axis and the fiber nutation X axis no longer in the same plane, so the crosstalk phenomenon in which the motion of the X axis is coupled to the Y axis happens during the scanning process. Figure 5(b) shows that the system can adapt to the power changes from 1nW to 10nW, and the calculation error is less than 10%. When the input optical power is less than 2nW (the system works in a low SNR state), the calculation error increases. The reason is that Eq. (24) is obtained from a noiseless system model, but noise in our system is present.

4.4 The performance of closed loop system

Generally, the control bandwidth (CBW) and tracking residuals are always used to evaluate the tracking performance in the tracking system. The higher the control bandwidth, the stronger the vibration suppression ability. The smaller the residuals, the better the tracking ability of boresight. However, the tracking residuals are difficult to measure in the tracking system without SPD. Considering that the residual boresight error directly affect the coupling efficiency of spatial light to SMF, we use the relative coupling efficiency ηr to evaluate the tracking performance, which is defined as follows

ηr(t)=η(t)ηmax=P(t)/PinPcmax/Pin=P(t)Pcmax
whereP(t),η(t)are the optical power coupled into SMF and coupling efficiency, respectively. Pcmax, ηmax are the maximum optical power coupled into SMF and maximum coupling efficiency, respectively. Pin is the power of incident light. The CBW of the tracking system without SPD is redefined as the corresponding frequency when the relative coupling efficiency is reduced by half.

The performance of our tracking system is tested to verify the performance of our tracking system. We use FSM2 to generate vibration noise with the amplitude of 280μrad and FSM1 to compensate for the boresight error. Figure 6(a) shows the relative coupling efficiency as a function of the vibration frequency in closed loop and open loop, respectively. Figure 6 (b) shows the relative coupling efficiency as a function of the signal power coupled into SMF when the vibration frequency of FSM2 is 70Hz and 30Hz, respectively.

 

Fig. 6 Relative coupling efficiency. (a) In closed loop and open loop for different scanning frequency. (b) With different power coupled into SMF in closed loop

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From Fig. 6(a), the relative coupling efficiency decreases with the vibration frequency increases, the control bandwidth of our tracking system is about 115Hz. Figure 6(b) shows that the tracking performance of our system is substantially unchanged when the input power varies from 1nW to 10nW.

5. Conclusion

Our coherent tracking system based on fiber nutation has the advantages of simple structure and high sensitivity. According to theoretical analysis, the premise of signal envelope fluctuation demodulation is that the photodetector and EDFA operate in their linear region. In our interested power range of signal light (1nW-10nW), the receiving FOV of tracking system is more than 300urad, and the closed-loop tracking bandwidth (−3dB) is about 115Hz. Our tracking system realizes the multiplexing of communication and tracking without spot position sensor, which is of great significance for the realization of inter-satellite laser communication without beacon light.

References

1. M. E. Wittig, L. V. Holtz, D. E. L. Tunbridge, and H. C. Vermeulen, “In-orbit measurements of microaccelerations of ESA’s communication satellite OLYMPUS,” Proceedings of SPIE - The International Society for Optical Engineering 1218(1990).

2. 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]  

3. T. J. Schneeberger, “Limits on Line-of-Site Jitter Derived from Image-Resolution Requirements,” Acquisition, Tracking, and Pointing Viii 2221, 704–710 (1994). [CrossRef]  

4. T. T. Nielsen, “Pointing, Acquisition and Tracking System for the Free Space Laser Communication System, Silex,” Free-Space Laser Communication Technologies Vii 2381, 194–205 (1995). [CrossRef]  

5. E. Perez, M. Bailly, and J. Pairot, “Pointing acquisition and tracking system for silex inter satellite optical link,” in 1989 Orlando Symposium, (International Society for Optics and Photonics, 1989), 277–288. [CrossRef]  

6. K. Nakagawa, A. Yamamoto, and Y. Suzuki, “OICETS optical link communications experiment in space,” Semiconductor Lasers Ii 2886, 172–180 (1996). [CrossRef]  

7. R. Zhang, J. Wang, G. Zhao, and J. Lv, “Fiber-based free-space optical coherent receiver with vibration compensation mechanism,” Opt. Express 21(15), 18434–18441 (2013). [CrossRef]   [PubMed]  

8. K. Deng, B.-Z. Wang, G.-H. Zhao, J. Huang, P. Zhang, D.-G. Jiang, and Z.-S. Yao, “Principle and performance analysis of coherent tracking sensor based on local oscillator beam nutation,” Opt. Express 22(19), 23528–23538 (2014). [CrossRef]   [PubMed]  

9. D. Giggenbach, A. Schex, and B. Wandernoth, “Prototype of a coherent tracking and detection receiver with wide band vibration compensation for free-space laser communications,” Free-Space Laser Communication Technologies Viii 2699, 186–191 (1996). [CrossRef]  

10. R. Fields, C. Lunde, R. Wong, J. Wicker, D. Kozlowski, J. Jordan, B. Hansen, G. Muehlnikel, W. Scheel, U. Sterr, R. Kahle, and R. Meyer, “NFIRE-to-TerraSAR-X laser communication results: satellite pointing, disturbances, and other attributes consistent with successful performance,” Sensors and Systems for Space Applications Iii 7330(2009).

11. E. A. SWANSON and R. S. BONDURANT, “Fiber-based receiver for free-space coherent optical communication systems,” in Optical Fiber Communication Conference, (Optical Society of America, 1989), THC5.

12. D. M. Boroson, J. J. Scozzafava, D. V. Murphy, B. S. Robinson, and M. Lincoln, “The lunar laser communications demonstration (LLCD),” in Space Mission Challenges for Information Technology, 2009. SMC-IT 2009. Third IEEE International Conference on, (IEEE, 2009), 23–28. [CrossRef]  

13. R. Garreis, “90-Degrees Optical Hybrid for Coherent Receivers,” Optical Space Communications Ii 1522, 210–219 (1991). [CrossRef]  

14. O. Wallner, P. J. Winzer, and W. R. Leeb, “Alignment tolerances for plane-wave to single-mode fiber coupling and their mitigation by use of pigtailed collimators,” Appl. Opt. 41(4), 637–643 (2002). [CrossRef]   [PubMed]  

15. 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]  

References

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  1. M. E. Wittig, L. V. Holtz, D. E. L. Tunbridge, and H. C. Vermeulen, “In-orbit measurements of microaccelerations of ESA’s communication satellite OLYMPUS,” Proceedings of SPIE - The International Society for Optical Engineering 1218(1990).
  2. 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]
  3. T. J. Schneeberger, “Limits on Line-of-Site Jitter Derived from Image-Resolution Requirements,” Acquisition, Tracking, and Pointing Viii 2221, 704–710 (1994).
    [Crossref]
  4. T. T. Nielsen, “Pointing, Acquisition and Tracking System for the Free Space Laser Communication System, Silex,” Free-Space Laser Communication Technologies Vii 2381, 194–205 (1995).
    [Crossref]
  5. E. Perez, M. Bailly, and J. Pairot, “Pointing acquisition and tracking system for silex inter satellite optical link,” in 1989 Orlando Symposium, (International Society for Optics and Photonics, 1989), 277–288.
    [Crossref]
  6. K. Nakagawa, A. Yamamoto, and Y. Suzuki, “OICETS optical link communications experiment in space,” Semiconductor Lasers Ii 2886, 172–180 (1996).
    [Crossref]
  7. R. Zhang, J. Wang, G. Zhao, and J. Lv, “Fiber-based free-space optical coherent receiver with vibration compensation mechanism,” Opt. Express 21(15), 18434–18441 (2013).
    [Crossref] [PubMed]
  8. K. Deng, B.-Z. Wang, G.-H. Zhao, J. Huang, P. Zhang, D.-G. Jiang, and Z.-S. Yao, “Principle and performance analysis of coherent tracking sensor based on local oscillator beam nutation,” Opt. Express 22(19), 23528–23538 (2014).
    [Crossref] [PubMed]
  9. D. Giggenbach, A. Schex, and B. Wandernoth, “Prototype of a coherent tracking and detection receiver with wide band vibration compensation for free-space laser communications,” Free-Space Laser Communication Technologies Viii 2699, 186–191 (1996).
    [Crossref]
  10. R. Fields, C. Lunde, R. Wong, J. Wicker, D. Kozlowski, J. Jordan, B. Hansen, G. Muehlnikel, W. Scheel, U. Sterr, R. Kahle, and R. Meyer, “NFIRE-to-TerraSAR-X laser communication results: satellite pointing, disturbances, and other attributes consistent with successful performance,” Sensors and Systems for Space Applications Iii 7330(2009).
  11. E. A. SWANSON and R. S. BONDURANT, “Fiber-based receiver for free-space coherent optical communication systems,” in Optical Fiber Communication Conference, (Optical Society of America, 1989), THC5.
  12. D. M. Boroson, J. J. Scozzafava, D. V. Murphy, B. S. Robinson, and M. Lincoln, “The lunar laser communications demonstration (LLCD),” in Space Mission Challenges for Information Technology, 2009. SMC-IT 2009. Third IEEE International Conference on, (IEEE, 2009), 23–28.
    [Crossref]
  13. R. Garreis, “90-Degrees Optical Hybrid for Coherent Receivers,” Optical Space Communications Ii 1522, 210–219 (1991).
    [Crossref]
  14. O. Wallner, P. J. Winzer, and W. R. Leeb, “Alignment tolerances for plane-wave to single-mode fiber coupling and their mitigation by use of pigtailed collimators,” Appl. Opt. 41(4), 637–643 (2002).
    [Crossref] [PubMed]
  15. 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]

2014 (1)

2013 (1)

2006 (1)

2002 (1)

2001 (1)

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]

1996 (2)

K. Nakagawa, A. Yamamoto, and Y. Suzuki, “OICETS optical link communications experiment in space,” Semiconductor Lasers Ii 2886, 172–180 (1996).
[Crossref]

D. Giggenbach, A. Schex, and B. Wandernoth, “Prototype of a coherent tracking and detection receiver with wide band vibration compensation for free-space laser communications,” Free-Space Laser Communication Technologies Viii 2699, 186–191 (1996).
[Crossref]

1995 (1)

T. T. Nielsen, “Pointing, Acquisition and Tracking System for the Free Space Laser Communication System, Silex,” Free-Space Laser Communication Technologies Vii 2381, 194–205 (1995).
[Crossref]

1994 (1)

T. J. Schneeberger, “Limits on Line-of-Site Jitter Derived from Image-Resolution Requirements,” Acquisition, Tracking, and Pointing Viii 2221, 704–710 (1994).
[Crossref]

1991 (1)

R. Garreis, “90-Degrees Optical Hybrid for Coherent Receivers,” Optical Space Communications Ii 1522, 210–219 (1991).
[Crossref]

Araki, K.

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]

Bailly, M.

E. Perez, M. Bailly, and J. Pairot, “Pointing acquisition and tracking system for silex inter satellite optical link,” in 1989 Orlando Symposium, (International Society for Optics and Photonics, 1989), 277–288.
[Crossref]

Deng, K.

Garreis, R.

R. Garreis, “90-Degrees Optical Hybrid for Coherent Receivers,” Optical Space Communications Ii 1522, 210–219 (1991).
[Crossref]

Giggenbach, D.

D. Giggenbach, A. Schex, and B. Wandernoth, “Prototype of a coherent tracking and detection receiver with wide band vibration compensation for free-space laser communications,” Free-Space Laser Communication Technologies Viii 2699, 186–191 (1996).
[Crossref]

Huang, J.

Jiang, D.-G.

Leeb, W. R.

Lv, J.

Nakagawa, K.

K. Nakagawa, A. Yamamoto, and Y. Suzuki, “OICETS optical link communications experiment in space,” Semiconductor Lasers Ii 2886, 172–180 (1996).
[Crossref]

Nielsen, T. T.

T. T. Nielsen, “Pointing, Acquisition and Tracking System for the Free Space Laser Communication System, Silex,” Free-Space Laser Communication Technologies Vii 2381, 194–205 (1995).
[Crossref]

Pairot, J.

E. Perez, M. Bailly, and J. Pairot, “Pointing acquisition and tracking system for silex inter satellite optical link,” in 1989 Orlando Symposium, (International Society for Optics and Photonics, 1989), 277–288.
[Crossref]

Perez, E.

E. Perez, M. Bailly, and J. Pairot, “Pointing acquisition and tracking system for silex inter satellite optical link,” in 1989 Orlando Symposium, (International Society for Optics and Photonics, 1989), 277–288.
[Crossref]

Schex, A.

D. Giggenbach, A. Schex, and B. Wandernoth, “Prototype of a coherent tracking and detection receiver with wide band vibration compensation for free-space laser communications,” Free-Space Laser Communication Technologies Viii 2699, 186–191 (1996).
[Crossref]

Schneeberger, T. J.

T. J. Schneeberger, “Limits on Line-of-Site Jitter Derived from Image-Resolution Requirements,” Acquisition, Tracking, and Pointing Viii 2221, 704–710 (1994).
[Crossref]

Suzuki, Y.

K. Nakagawa, A. Yamamoto, and Y. Suzuki, “OICETS optical link communications experiment in space,” Semiconductor Lasers Ii 2886, 172–180 (1996).
[Crossref]

Toyoshima, M.

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]

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]

Wallner, O.

Wandernoth, B.

D. Giggenbach, A. Schex, and B. Wandernoth, “Prototype of a coherent tracking and detection receiver with wide band vibration compensation for free-space laser communications,” Free-Space Laser Communication Technologies Viii 2699, 186–191 (1996).
[Crossref]

Wang, B.-Z.

Wang, J.

Winzer, P. J.

Yamamoto, A.

K. Nakagawa, A. Yamamoto, and Y. Suzuki, “OICETS optical link communications experiment in space,” Semiconductor Lasers Ii 2886, 172–180 (1996).
[Crossref]

Yao, Z.-S.

Zhang, P.

Zhang, R.

Zhao, G.

Zhao, G.-H.

Acquisition, Tracking, and Pointing Viii (1)

T. J. Schneeberger, “Limits on Line-of-Site Jitter Derived from Image-Resolution Requirements,” Acquisition, Tracking, and Pointing Viii 2221, 704–710 (1994).
[Crossref]

Appl. Opt. (1)

Free-Space Laser Communication Technologies Vii (1)

T. T. Nielsen, “Pointing, Acquisition and Tracking System for the Free Space Laser Communication System, Silex,” Free-Space Laser Communication Technologies Vii 2381, 194–205 (1995).
[Crossref]

Free-Space Laser Communication Technologies Viii (1)

D. Giggenbach, A. Schex, and B. Wandernoth, “Prototype of a coherent tracking and detection receiver with wide band vibration compensation for free-space laser communications,” Free-Space Laser Communication Technologies Viii 2699, 186–191 (1996).
[Crossref]

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

Opt. Eng. (1)

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]

Opt. Express (2)

Optical Space Communications Ii (1)

R. Garreis, “90-Degrees Optical Hybrid for Coherent Receivers,” Optical Space Communications Ii 1522, 210–219 (1991).
[Crossref]

Semiconductor Lasers Ii (1)

K. Nakagawa, A. Yamamoto, and Y. Suzuki, “OICETS optical link communications experiment in space,” Semiconductor Lasers Ii 2886, 172–180 (1996).
[Crossref]

Other (5)

M. E. Wittig, L. V. Holtz, D. E. L. Tunbridge, and H. C. Vermeulen, “In-orbit measurements of microaccelerations of ESA’s communication satellite OLYMPUS,” Proceedings of SPIE - The International Society for Optical Engineering 1218(1990).

E. Perez, M. Bailly, and J. Pairot, “Pointing acquisition and tracking system for silex inter satellite optical link,” in 1989 Orlando Symposium, (International Society for Optics and Photonics, 1989), 277–288.
[Crossref]

R. Fields, C. Lunde, R. Wong, J. Wicker, D. Kozlowski, J. Jordan, B. Hansen, G. Muehlnikel, W. Scheel, U. Sterr, R. Kahle, and R. Meyer, “NFIRE-to-TerraSAR-X laser communication results: satellite pointing, disturbances, and other attributes consistent with successful performance,” Sensors and Systems for Space Applications Iii 7330(2009).

E. A. SWANSON and R. S. BONDURANT, “Fiber-based receiver for free-space coherent optical communication systems,” in Optical Fiber Communication Conference, (Optical Society of America, 1989), THC5.

D. M. Boroson, J. J. Scozzafava, D. V. Murphy, B. S. Robinson, and M. Lincoln, “The lunar laser communications demonstration (LLCD),” in Space Mission Challenges for Information Technology, 2009. SMC-IT 2009. Third IEEE International Conference on, (IEEE, 2009), 23–28.
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 Structure of the coherent tracking system based on fiber nutation
Fig. 2
Fig. 2 Schematic diagram of fiber nutation scanning spot. The area in the black circle represents the spot at the focal plane, and the black dot represents the geometric center of the spot. The area in the red circle represents the fiber core of SMF, and the green circle represents the nutation trail of the end face of SMF. (x, y) is the position coordinate of fiber core center on the nutation trail. The area in the brown circle is the scanning range in the process of fiber nutation.
Fig. 3
Fig. 3 The block diagram of desktop experiment system
Fig. 4
Fig. 4 The calculated signal intensity as a function of the power coupled into SMF
Fig. 5
Fig. 5 the boresight error calculated by Eq. (24). (a) With FSM1 scanning the end face of SMF. (b) With the signal power change when FSM1 deflected 80urad.
Fig. 6
Fig. 6 Relative coupling efficiency. (a) In closed loop and open loop for different scanning frequency. (b) With different power coupled into SMF in closed loop

Tables (2)

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Table 1 Information about experiment instruments

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Table 2 System parameters not mentioned above

Equations (25)

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E s ( t ) = E s cos ( ω s t + φ ( t ) )
A s ( t ) = A s cos ( ω s t + φ ( t ) )
E l ( t ) = E l cos ( ω l t + φ l )
I 0 = k 1 2 | A s | 2 r 2 + k 3 2 | E L O | 2 t 2 + 2 k 1 k 3 r t | A s E L O | cos [ ϕ ( t ) + ( ρ τ ) π / 2 ( ψ π / 4 ) ]
I 90 = k 2 2 | A s | 2 r 2 + k 4 2 | E L O | 2 t 2 + 2 k 2 k 4 r t | A s E L O | cos [ ϕ ( t ) + ( ρ τ ) ( ψ π / 4 ) ]
I 180 = k 1 2 | A s | 2 t 2 + k 3 2 | E L O | 2 r 2 + 2 k 1 k 3 r t | A s E L O | cos [ ϕ ( t ) + ( τ ρ ) π / 2 ( ψ π / 4 ) ]
I 270 = k 2 2 | A s | 2 t 2 + k 4 2 | E L O | 2 r 2 + 2 k 2 k 4 r t | A s E L O | cos [ ϕ ( t ) + ( τ ρ ) ( ψ π / 4 ) ]
V 0 = k 1 2 R r L | A s | 2 r 2 + k 1 k 3 R r L | A s E L O | cos [ ω I F t + φ ( t ) ]
V 90 = k 2 2 R r L | A s | 2 r 2 + k 2 k 4 R r L | A s E L O | sin [ ω I F t + φ ( t ) ]
V 180 = k 1 2 R r L | A s | 2 t 2 k 1 k 3 R r L | A s E L O | cos [ ω I F t + φ ( t ) ]
V 270 = k 2 2 R r L | A s | 2 t 2 k 2 k 4 R r L | A s E L O | sin [ ω I F t + φ ( t ) ]
V I ( t ) = 2 k 1 k 3 R r L | A s E L O | cos [ ω I F t + φ ( t ) ]
V Q ( t ) = 2 k 2 k 4 R r L | A s E L O | sin [ ω I F t + φ ( t ) ]
V ( t ) = V I 2 ( t ) + V Q 2 ( t ) = 4 k 4 R 2 r L 2 G η ( t ) | E s | 2 | E L O | 2
η ( t ) = P c P i n
V I 2 ( t ) + V Q 2 ( t ) = 8 k 4 R 2 r L 2 G P c | E L O | 2
{ x ( t ) = a cos ( 2 π f t ) y ( t ) = a sin ( 2 π f t )
η c = P c P i n = c exp ( ρ 2 ω 0 2 )
η ( t ) = P 1 P i n ( t ) = c exp ( ( a cos ( 2 π f t ) ρ x 1 ) 2 + ( a sin ( 2 π f t ) ρ y 1 ) 2 ω 0 2 )
η ( t ' ) = P 2 P i n ( t ' ) = c exp ( ( a cos ( 2 π f t ' ) ρ x 2 ) 2 + ( a sin ( 2 π f t ' ) ρ y 2 ) 2 ω 0 2 )
ω 0 2 ln ( P 1 P i n ( t ' ) P 2 P i n ( t ) ) = 2 a ( ρ x 1 cos ( 2 π f t ) ρ x 2 cos ( 2 π f t ' ) ) + 2 a ( ρ y 1 sin ( 2 π f t ) ρ y 2 sin ( 2 π f t ' ) )
ω 0 2 ln ( P 1 P 2 ) = 2 a ρ x ( cos ( 2 π f t ) cos ( 2 π f t ' ) ) + 2 a ρ y ( sin ( 2 π f t ) sin ( 2 π f t ' ) )
{ ρ x = ω 0 2 4 a ln ( P ( n T ) P ( n T + T / 2 ) ) ρ y = ω 0 2 4 a ln ( P ( n T + T / 4 ) P ( n T + 3 T / 4 ) )
{ θ x = ω 0 2 4 a f l ln ( V I 2 ( n T ) + V Q 2 ( n T ) V I 2 ( n T + T / 2 ) + V Q 2 ( n T + T / 2 ) ) θ y = ω 0 2 4 a f l ln ( V I 2 ( n T + T / 4 ) + V Q 2 ( n T + T / 4 ) V I 2 ( n T + 3 T / 4 ) + V Q 2 ( n T + 3 T / 4 ) )
η r ( t ) = η ( t ) η max = P ( t ) / P i n P c max / P i n = P ( t ) P c max

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