Experimental verification of coherent tracking system based on fiber nutation

Xueqiang Zhao; Xueqiang Zhao; Xueqiang Zhao; Xia Hou; Xia Hou; Funan Zhu; Tai Li; Jianfeng Sun; Jianfeng Sun; Ren Zhu; Min Gao; Yan Yang; Weibiao Chen; Weibiao Chen

doi:10.1364/OE.27.023996

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

E_{s} (t) = E_{s} \cos (ω_{s} t + φ (t))

where

E_{s}

is the signal light amplitude,

ω_{s}

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

A_{s} (t) = A_{s} \cos (ω_{s} t + φ (t))

where

A_{s} = E_{s} \sqrt{G η (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

E_{l} (t) = E_{l} \cos (ω_{l} t + φ_{l})

where

E_{l}

is the local oscillator optical amplitude,

ω_{l}

is the local oscillator optical angular frequency,

φ_{l}

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]

\begin{array}{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)] \end{array}

\begin{array}{l} 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)] \end{array}

\begin{array}{l} 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)] \end{array}

\begin{array}{l} 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)] \end{array}

where

r_{∥}

,

r_{⊥}

,

t_{∥}

,

t_{⊥}

,

τ_{∥}

,

τ_{⊥}

,

ρ_{∥}

and

ρ_{⊥}

are reflection coefficients and transmission coefficients of the polarization beam splitter in optical Hybrid.

k_{1}

,

k_{2}

,

k_{3}

and

k_{4}

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

,

τ_{∥} - ρ_{∥} = - π / 2

,

τ_{⊥} - ρ_{⊥} = - π / 2

,

r_{∥} = r_{⊥} = t_{∥} = t_{⊥} = 1 / \sqrt{2}

and

k_{1} = k_{2} = k_{3} = k_{4} = k

.

The photodetectors convert the optical intensity signals $I_{0}$ , $I_{90}$ , $I_{180}$ and $I_{270}$ 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

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)]

where

R

is the responsibility of the photodetectors,

r_{L}

is the resistance of the trans-impedance,

ω_{I F}

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.

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)]

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) = 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}

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

η (t) = \frac{P_{c}}{P_{i n}}

where

P_{c}

is the power of signal light coupled into the SMF, and

P_{i n}

is the power of incident signal light, satisfying the relationship

P_{i n} = {| E_{s} |}^{2} / 2

,Eq. (14) can be rewritten as

V_{I}^{2} (t) + V_{Q}^{2} (t) = 8 k^{4} R^{2} r_{L}^{2} G P_{c} {| E_{L O} |}^{2}

Usually, the optical power of the local oscillator is stable, so ${| E_{L O} |}^{2}$ 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.

{\begin{cases} x (t) = a \cos (2 π f t) \\ y (t) = a \sin (2 π f t) \end{cases}

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 $η_{c}$ of spatial light to SMF can be approximately written as [15]

η_{c} = \frac{P_{c}}{P_{i n}} = c \cdot \exp (- \frac{ρ^{2}}{ω_{0}^{2}})

where

ρ

is the static radial offset of the optical beam from the nominal axis of SMF core,

ω_{0}

is the mode field radius of SMF,

c

is the maximum coupling efficiency when

ρ = 0

. If

π D ω_{0} / λ f_{l} = 2.24

, the coupling efficiency coefficient

c

takes the maximum value of 81.45% [15], where

D

and

f_{l}

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) = \frac{P_{1}}{P_{i n} (t)} = c \cdot \exp (- \frac{{(a \cos (2 π f t) - ρ_{x 1})}^{2} + {(a \sin (2 π f t) - ρ_{y 1})}^{2}}{ω_{0}^{2}})

where

P_{i n} (t)

,

P_{1}

are the incident optical power and optical power coupled to the SMF respectively.

(ρ_{x 1}, ρ_{y 1})

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') = \frac{P_{2}}{P_{i n} (t')} = c \cdot \exp (- \frac{{(a \cos (2 π f t') - ρ_{x 2})}^{2} + {(a \sin (2 π f t') - ρ_{y 2})}^{2}}{ω_{0}^{2}})

where

T

is the nutation cycle,

P_{i n} (t')

and

P_{2}

are the incident optical power and the optical power coupled to the SMF, respectively.

(ρ_{x 2}, ρ_{y 2})

is the position of the spot center at time

t'

. From the geometric relationship in Fig. 2,

t' = t + T / 2 = t + 1 / 2 f

. Substitute Eq. (19) into Eq. (20).

\begin{array}{l} ω_{0}^{2} \ln (\frac{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')) \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix}  \end{matrix} \end{matrix} \end{matrix} \end{matrix} \end{matrix} + 2 a (ρ_{y 1} \sin (2 π f t) - ρ_{y 2} \sin (2 π f t')) \end{array}

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: $P_{i n} (t) = P_{i n} (t')$ , $ρ_{x 1} = ρ_{x 2} = ρ_{x}$ , $ρ_{y 1} = ρ_{y 2} = ρ_{y}$ . Equation (21) can be expressed as follows.

ω_{0}^{2} \ln (\frac{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'))

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 $n T$ , $n T + T / 4$ , $n T + T / 2$ and $n T + 3 T / 4$ , respectively. The spot position is expressed as follows by substituting the incident optical powers into Eq. (22).

{\begin{cases} ρ_{x} = \frac{ω_{0}^{2}}{4 a} \ln (\frac{P (n T)}{P (n T + T / 2)}) \\ ρ_{y} = \frac{ω_{0}^{2}}{4 a} \ln (\frac{P (n T + T / 4)}{P (n T + 3 T / 4)}) \end{cases}

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

{\begin{cases} θ_{x} = \frac{ω_{0}^{2}}{4 a f_{l}} \ln (\frac{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} = \frac{ω_{0}^{2}}{4 a f_{l}} \ln (\frac{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)}) \end{cases}

where

θ_{x}

,

θ_{y}

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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Table 1. Information about experiment instruments

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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 $R = 4.65 m m$ , $f = 42 m m$ . 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.

Table 2. System parameters not mentioned above

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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 $F O V = 2 ω_{0} / f$ to calculate the FOV of fiber nutation device. For the 1550nm SMF, $F O V \approx 238 u r a d$ , where $ω_{0} = 5 μ m$ . 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 $η_{r}$ to evaluate the tracking performance, which is defined as follows

η_{r} (t) = \frac{η (t)}{η_{\max}} = \frac{P (t) / P_{i n}}{P_{c \max} / P_{i n}} = \frac{P (t)}{P_{c \max}}

where

P (t)

,

η (t)

are the optical power coupled into SMF and coupling efficiency, respectively.

P_{c \max}

,

η_{\max}

are the maximum optical power coupled into SMF and maximum coupling efficiency, respectively.

P_{i n}

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.

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Instrument	Manufacturer and Model number
BERT	Agilent E8403A
FSM1 FSM2	PI S-330.8SL
FSM Drive2	PI E505
Signal Generator	Tektronix AFG3252C
Atomic Clock	Rock Electronic NAVTF2000
Others	Non-commercial instruments

Frequency locking difference	3MHz ± 10%
Deflection range of FSM	2.5mrad
Filter bandwidth	2nm
Signal light wavelength	1550.50nm
Tuning range of LO wavelength	1550.46nm-1550.57nm

Instrument	Manufacturer and Model number
BERT	Agilent E8403A
FSM1 FSM2	PI S-330.8SL
FSM Drive2	PI E505
Signal Generator	Tektronix AFG3252C
Atomic Clock	Rock Electronic NAVTF2000
Others	Non-commercial instruments

Frequency locking difference	3MHz ± 10%
Deflection range of FSM	2.5mrad
Filter bandwidth	2nm
Signal light wavelength	1550.50nm
Tuning range of LO wavelength	1550.46nm-1550.57nm

Experimental verification of coherent tracking system based on fiber nutation

Abstract

Corrections

1. Introduction

2. System structure

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

3.1 Intensity envelope fluctuation demodulation

3.2 Principle of fiber nutation

4. Experiment

4.1 Setup

4.2 The linearity of intensity envelope fluctuation demodulation

4.3 The linearity of boresight error calculation

4.4 The performance of closed loop system

5. Conclusion

References

Cited By

Figures (6)

Tables (2)

Equations (25)

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