Performance evaluation of adaptive optics for atmospheric coherent laser communications

Chao Liu; Shanqiu Chen; XinYang Li; Hao Xian

doi:10.1364/OE.22.015554

1. Introduction

Free space laser communication links have some advantages over traditional microwave systems as their high carrier frequencies that allow high modulation bandwidth, enhanced security, and anti-interference [1]. For the long-range and high-speed communication link, e.g. the link between the synchronous satellite and the ground station, the signal light power is so faint that the common non-coherent intensity modulation/ direct detection (IM/DD) scheme nearly cannot be used. The coherent free-space laser communications, with its extremely high sensitivity, has been paid more and more attention and has high potential to be used in practice in the future [2–5]. However, when the coherent laser communications system is used in the atmospheric links, the most significant factor that limits the performance is the effect of the atmospheric turbulence.

It has been demonstrated that the adaptive optics (AO) is a powerful tool that is able to overcome the effect of the atmospheric turbulence, and has been used on numerous areas, such as astronomy observation [6, 7], living retina of human eye imaging [8] and so on. Many researchers have demonstrated that the AO is also a powerful tool to improve the performance of the non-coherent laser communications [9–13]. Some researchers have also pointed out that the AO can be used in the coherent laser communication system to improve its performance [14–16]. However, the detailed results have not been reported up to now. The purpose of this paper is to evaluate the performance improvement of the atmospheric coherent laser communications using the AO system that has different correction orders under different atmospheric turbulence strength. It would be helpful for the AO system design used for the atmospheric coherent laser communications and it is also able to make us understand the functions of the AO to the coherent communications more deeply. In section 2, we focus on the theory analysis about the mixing efficiency and bit-error rate (BER) performance of the coherent detection. Section 3 is devoted to demonstrate the mixing efficiency and the BER improvements when the AO is used. Finally, the conclusions are presented in section 4.

2. The theory

2.1. The mixing efficiency and signal to noise ratio

The idea of the coherent detection scheme is combining the received optical signal coherently with a continuous-wave optical field before it incidents at the photodetector, as shown in Fig. 1. The continuous-wave field is generated locally using a narrow linewidth laser, called the local oscillator (LO). The received optical signal and the LO field can be, respectively, expressed as

E_{S} = A_{S} \exp [- i (ω_{S} t + φ_{S})],

E_{L O} = A_{L O} \exp [- i (ω_{L O} t + φ_{L O})],

where

A_{S}

and

A_{L O}

are the magnitudes,

ω_{S}

and

ω_{L O}

are the angular frequencies,

φ_{S}

and

φ_{L O}

are the phases of the received optical signal and the LO laser, respectively. We assume that both the fields of the optical signal and the LO laser are plane waves, both of their polarization directions are the same, the sizes of the laser beams are the same and both beams coincident with each other well. The optical power incident at the photodetector is given by

P = K \int_{U} {| E_{S} + E_{L O} |}^{2} d U

, where K is a constant of proportionality,

U

is the incident field area on the photodetector. Using Eq. (1) and Eq. (2), giving

P_{} = K \int_{U} A_{S}^{2} + A_{L O}^{2} + 2 A_{S} A_{L O} \cos (Δ ω t + Δ φ) d U,

where

Δ ω = ω_{S} - ω_{L O}

,

Δ φ = φ_{S} - φ_{L O}

. When

Δ ω

equals zero, it is called homodyne detection. Otherwise, it is called heterodyne detection. The photocurrent can be expressed as

I = R P

, where R is the sensitivity of the photodetector . The effective photocurrent of the heterodyne detection is the alternating current (AC) component, which can be expressed as

\begin{array}{l} i_{R F} = 2 R K \int_{U} A_{S} A_{L} \cos (Δ ω t + Δ φ) d U \\ = 2 R K [\cos (Δ ω t) \int_{U} A_{S} A_{L O} \cos (Δ φ) d U - \sin (Δ ω t) \int_{U} A_{S} A_{L O} \sin (Δ φ) d U], \end{array}

and

R = \frac{e η}{h ν},

where

η

is the quantum efficiency of the photodetector, e is the electron charge, h is the Planck constant, and

ν

is the frequency of the carrier wave. The power of the signal photocurrent is

Fig. 1 Schematic illustration of the coherent detection scheme.

Download Full Size | PDF

< i_{R F}^{2} > = \frac{1}{2} {(2 R K)}^{2} {{[\int_{U} A_{S} A_{L O} \cos (Δ φ) d U]}^{2} + {[\int_{U} A_{S} A_{L O} \sin (Δ φ) d U]}^{2}} .

For the coherent detection, the LO laser has a relatively high power, in the magnitude of miliwatt, while the received optical signal power is in the magnitude of nanowatt. Therefore, the noise of the receiver is manly determined by the shot noise of the LO laser [17]

< i_{N}^{2} > = 2 e I_{L O} Δ f = 2 e R P_{L O} Δ f = 2 e Δ f R K \int_{U} A_{L O}^{2} d U,

where

Δ f

is the effective noise bandwidth (typically, it is half of the data bit rate B),

P_{L O}

is the power of the LO

P_{L O} = K \int_{U} A_{L O}^{2} d U

. Then the signal to noise ratio (SNR) of heterodyne detection is

S N R_{R F} = \frac{< i_{R F}^{2} >}{< i_{N}^{2} >} = \frac{2 η P_{S}}{h ν B} * \frac{{[\int_{U} A_{S} A_{L O} \cos (Δ φ) d U]}^{2} + {[\int_{U} A_{S} A_{L O} \sin (Δ φ) d U]}^{2}}{\int_{U} A_{S}^{2} d U \int_{U} A_{L O}^{2} d U},

where

P_{S}

is the power of the optical signal

P_{S} = K \int_{U} A_{L O}^{2} d U

.

We define the SNR without atmospheric turbulence

S N R_{0} = \frac{2 η P_{S}}{h ν B},

and define the mixing efficiency of the heterodyne detection

γ_{R F} = \frac{{[\int_{U} A_{S} A_{L O} \cos (Δ φ) d U]}^{2} + {[\int_{U} A_{S} A_{L O} \sin (Δ φ) d U]}^{2}}{\int_{U} A_{S}^{2} d U \int_{U} A_{L O}^{2} d U} .

Then the SNR of heterodyne receiver is

S N R_{R F} = S N R_{0} \cdot γ_{R F} .

For the homodyne detection, the Eq. (4) becomes

i_{Z F} = 2 R K \int_{U} A_{S} A_{L O} \cos (Δ φ) d U .

The power of the photocurrent is

< i_{Z F}^{2} > = {(2 R K)}^{2} {[\int_{U} A_{S} A_{L O} \cos (Δ φ) d U]}^{2}

The corresponding mixing efficiency is

γ_{Z F} = \frac{{[\int_{U} A_{S} A_{L O} \cos (Δ φ) d U]}^{2}}{\int_{U} A_{S}^{2} d U \int_{U} A_{L O}^{2} d U},

and the SNR is

S N R_{Z F} = 2 S N R_{0} \cdot γ_{Z F} .

From Eq. (11) or Eq. (15), it is shown that the mixing efficiency is the ratio of the actual SNR under atmospheric turbulence over the SNR without atmospheric turbulence. From Eq. (10) or Eq. (14), it is shown that the value of the mixing efficiency is determined by the spatial amplitude distribution and the spatial phase distribution difference (SPDD) between the received optical signal and the LO laser. Supposing the amplitude distribution is homogeneous, then the mixing efficiency is only depend on the SPDD between the signal laser and the LO laser. The smaller the SPDD, the larger the mixing efficiency is. The main function of the AO system is to reduce the SPDD for the coherent laser communications. In principle, the SPDD may approach to zero when deploying an ideal AO system, and the mixing efficiency would approach to 1.

2.2. The BER

The BER of the coherent detection is [17]

B E R = \frac{1}{2} e r f c (\frac{Q}{\sqrt{2}}),

where the function erfc is the complementary error function and Q can be expressed as

Q = S N R_{}^{1 / 2}

for the synchronous binary phase shift keying (BPSK) receiver. Usually, the power of the receive optical signal can be expressed as

P_{S} = N_{P} h ν B

, and the SNR₀ can also be written as

S N R_{0} = \frac{2 η P_{S}}{h ν B} = \frac{2 η}{h ν B} N_{P} h ν B = 2 η N_{P},

where

N_{P}

is the number of photons received within a single bit. The BER of the homodyne receiver is

B E R_{Z F} = \frac{1}{2} e r f c (\sqrt{2 η N_{P} γ_{Z F}}) .

Similarly, the BER of the heterodyne receiver is

B E R_{R F} = \frac{1}{2} e r f c (\sqrt{η N_{P} γ_{R F}}) .

3. The results

For this study we make a number of assumptions about the AO system. As this paper does not investigate the high-bandwidth control, reduce anisoplanatism or reduce the noise of the AO system, we assume that the control bandwidth is unlimited, the noise of the AO and the isoplanatic errors are neglectable. The spatial average phase difference between the received optical signal and the LO laser is zero. That is, our study focuses on the spatial-phase-control effects of the AO system, manifested in the number of aberration modes totally removed, and the effect of the system on the BER. We also assume that the amplitude distributions of the received optical signal and the LO laser are uniform.

The coefficients of the Zernike polynomials of the turbulent wavefront are generated using the method of the Zernike polynomials [18, 19]. The number of the Zernike modes used to generate the turbulent wavefront is 231. In the area of the free-space optical communications, the diameter of the telescope is usually smaller than 1 meter. Therefore, 231 modes are enough for the calculation of the atmospheric turbulence wavefront. After the correction of the AO system with a certain correction order, the Zernike coefficients not bigger than the correction order are all equal to zero. The residual turbulent wavefront error is generated using the residual Zernike coefficients. The grid number of the turbulent wavefront is 120 × 120. When the residual turbulent wavefront is generated, the Eq. (14) or Eq. (10) is used to calculate the mixing efficiency. The Eq. (19) or Eq. (20) is used to calculate the BER. In the area of free-space optical communications, we use the parameter D/r₀ to present the atmospheric turbulence strength. We called it the normalized atmospheric turbulence strength. For a telescope with diameter less than 1 meter, we divide the normalized atmospheric turbulence strength into 3 sections primarily. For the gentle turbulence condition, D/r₀ is around 2. For the moderate turbulence condition, D/r₀ is around 10. For the relative strong turbulence condition, D/r₀ is around 17.

3.1. The mixing efficiency improvement by AO

The mixing efficiency of the homodyne detection over different normalized atmospheric turbulence strength is shown in Fig. 2. Without the correction of AO system, the mixing efficiency reaches 0.74 when D/r₀ equals 0.5, where D is the diameter of the receiver telescope, r₀ is the atmospheric coherent length. When D/r₀ equals 1 or 2, the $γ_{Z F}$ equals 0.40 or 0.05, respectively. When D/r₀ is larger than 2, the mixing efficiency approaches to zero. Generally, the mixing efficiency should be larger than 0.4. Therefore, only when D/r₀ is not larger than 1 can the coherent laser communication system work well without the AO correction.

Fig. 2 The Mixing efficiency of the homodyne detection over different turbulent strength D/r0 with and without adaptive optics correction.

Download Full Size | PDF

When the normalized atmospheric turbulence strength is gentle, e.g. D/r₀ = 2, the mixing efficiency increases significantly from 0.05 to 0.80 for only the tip & tilt correction, and increases to 0.95 for the 9 Zernike modes correction. The improvement reaches 16 or 19 times, respectively. When the normalized atmospheric turbulence strength is moderate, e.g. D/r₀ = 10, only the tip and tilt correction is not enough. It may need to correct 9 or more modes. When the normalized atmospheric turbulence strength is relatively strong, e.g. D/r₀ = 17, the 35 or more Zernike modes should be corrected to improve the mixing efficiency from nearly zero to 0.87.

For the heterodyne detection, the relationship between the mixing efficiency and the normalized atmospheric turbulence strength D/r₀ with and without AO correction is similar to that of the homodyne detection (see Fig. 3).

Fig. 3 The mixing efficiency of the heterodyne detection over different normalized atmospheric turbulence strength D/r₀ with and without adaptive optics correction.

Download Full Size | PDF

3.2. The BER improvement by AO

Before discussion the BER improvement by AO system, we concentrate on the BER degradation due to the atmospheric turbulence without AO correction. The quantum efficiency of the photodetector is assumed to be 1 in this paper. As the BER performances between the heterodyne and the homodyne receivers are similar, as shown in Eq. (19) and Eq. (20), we only discuss the homodyne manner in this paper. In the case of heterodyne receiver, it can be discussed similarly. It is shown in Fig. 4 that, when the BER is smaller than 10⁻⁹ and D/r₀ is smaller than 1, it only needs 22 photons per bit for the communication, which is acceptable. In the case D/r₀ = 2, and 100 photons per bit, the BER reaches 10⁻⁶, which may not be appropriate. In this or more worse turbulent condition, the AO system is needed urgently.

Fig. 4 The effect of the normalized atmospheric turbulence strength on the BER without AO correction.

Download Full Size | PDF

In the gentle turbulence condition (e.g. D/r₀ = 2), the performance of the BER improvement by AO system is shown in Fig. 5. In this case, only the tip & tilt correction or the low order correction can improve the BER significantly.

Fig. 5 The AO corrections under moderate turbulence (D/r0 = 2).

Download Full Size | PDF

For the moderate turbulence condition (e.g. D/r₀ = 10), the performance of the BER improvement by AO system is shown in Fig. 6. In this case, only the tip & tilt correction is not enough. In order to acquire a favorable performance, 9 or more Zernike modes of the turbulent wavefront may need correcting.

Fig. 6 The AO corrections under the middle strength of turbulence (D/r₀ = 10).

Download Full Size | PDF

In the relatively strong turbulence condition (e.g. D/r₀ = 17), the performance of the BER improvement by AO system is shown in Fig. 7. In this case, 35 or more Zernike modes should be corrected to make the performance of the coherent communication to approach to the limit condition, which is the case that all modes of the atmospheric turbulence wavefront have been corrected.

Fig. 7 The AO corrections under relatively strong turbulence (D/r₀ = 17).

Download Full Size | PDF

To help the designer, the relation between the D/r₀ and the corrected Zernike modes have been given in Fig. 8. The number of the photons per bit is, typically, 12. In this case, the BER limit with the correction of an AO system that has infinity correction orders is about 10⁻¹². From Fig. 8, we can easily find the correction order needed for a specific D/r₀ and a given BER.

Fig. 8 The BER performances with and without the AO correction under different normalized atmospheric turbulence strength D/r₀ (the figure is plotted under 12 photons/bit).

Download Full Size | PDF

The BER performance of the coherent laser communications corrected by AO is also affected by the modulation styles and the demodulation manners. For the amplitude shift keying (ASK), frequency shift keying (FSK), phase shift keying (PSK) and the differential phase shift keying (DPSK), the BER performance are illustrated in Fig. 9. The D/r₀ is 10, and the AO system corrects 65 Zernike modes of the turbulence wavefront. The demodulation manners include the synchronous and the asynchronous manners. It is revealed that, the homodyne PSK has the highest sensitivity, the FSK is the following, and the ASK has the lowest sensitivity. It is also depicted that the sensitivity of the synchronous receiver is higher than that of the asynchronous receiver.

Fig. 9 The effect of different modulation and demodulation style on the BER (D/r₀ = 10, 65 modes have been corrected).

Download Full Size | PDF

4. Conclusions

We have shown the performances of the coherent laser communications systems used through the atmospheric turbulence when using the adaptive optics. Without AO correction, the coherent communications can be conducted well when the normalized atmospheric turbulence strength satisfies D/r₀ ≤1. Otherwise, the AO system is needed to overcome the effect of the turbulence. In the gentle turbulent condition, around D/r₀ = 2, only the tip & tilt correction can improve the mixing efficiency or the BER significantly. For the moderate turbulent condition, around D/r₀ = 10, about 9 or more Zernike modes of the turbulent wavefront need correcting to acquire a favorable performance. In the case of a relatively strong turbulent condition, around D/r₀ = 17, 35 or more Zernike modes should be corrected to make the performance of the coherent communications to approach to the limit condition. For different modulation and demodulation manners, the homodyne phase shift keying has the highest sensitivity under the AO correction. In conclusion, we have demonstrated that the AO is a powerful technique to enhance the performances of the coherent laser communication links through the atmospheric turbulence.

Acknowledgments

This work is supported by the National Natural Science Foundation of China (NSFC) (Grant No. 61308082) and the Foundation of Western Light. The authors also gratefully acknowledge the efforts and suggestions of all the referees.

References and links

1. R. K. Tyson and D. E. Canning, “Indirect measurement of a laser communications bit-error-rate reduction with low-order adaptive optics,” Appl. Opt. 42(21), 4239–4243 (2003). [CrossRef] [PubMed]

2. S. Seel, H. Kampfner, F. Heine, D. Dallmann, G. Muhlnikel, M. Gregory, M. Reinhardt, K. Saucke, J. Muckherjee, U. Sterr, B. Wandernoth, R. Meyer, and R. Czichy, “Space to Ground Bidirectional Optical Communication Link at 5.6 Gbps and EDRS Connectivity Outlook,” IEEE (2011).

3. M. Gregory, F. Heine, H. Kampfner, R. Lange, M. Lutzer, and R. Meyer, “Coherent inter-satellite and satellite-ground laser links,” Proc. SPIE 7923, 792303 (2011). [CrossRef]

4. R. A. Fields, D. A. Kozlowski, H. T. Yura, R. L. Wong, J. M. Wicker, C. T. Lunde, M. Gregory, B. K. Wandernoth, F. F. Heine, and J. J. Luna, “5.625 Gbps bidirectional laser communications measurements between the NFIRE satellite and an optical ground station,” Proc. SPIE 8184, 81840D (2011). [CrossRef]

5. B. Smutny, H. Kaempfner, G. Muehlnikel, U. Sterr, B. Wandernoth, F. Heine, U. Hildebrand, D. Dallmann, M. Reinhardt, A. Freier, R. Lange, K. Boehmer, T. Feldhaus, J. Mueller, A. Weichert, P. Greulich, S. Seel, R. Meyer, and R. Czichy, “5.6 Gbps optical intersatellite communication link,” Proc. SPIE 7199, 719926 (2009). [CrossRef]

6. F. Roddier, Adaptive Optics in Astronomy (Cambridge University Press, 1999).

7. C. Liu, L. Hu, Q. Mu, Z. Cao, and L. Xuan, “Open-loop control of liquid-crystal spatial light modulators for vertical atmospheric turbulence wavefront correction,” Appl. Opt. 50(1), 82–89 (2011). [CrossRef] [PubMed]

8. J. Porter, H. M. Queener, J. E. Lin, K. Thorn, and A. Awwal, Adaptive Optics for Vision Science Principles, Practices, Design, and Applications (Wiley-Interscience, 2006).

9. M. W. Wright, J. Roberts, W. Farr, and K. Wilson, “Improved optical communications performance combining adaptive optics and pulse position modulation,” Opt. Eng. 47, 016003 (2008).

10. Y. Wu, E. Chen, Y. Zhang, H. Ye, M. Li, X. Li, Z. Xiong, J. Chen, Y. Ai, H. Zhao, and Z. Yang, “Simulation and Experiment of Adaptive Optics in 2.5Gbps atmospheric Laser Communication,” Proceeding of the 2011International Conference on Opto-Electronics Engineering and Information Science, 2449–2453 (2011).

11. R. K. Tyson, J. S. Tharp, and D. E. Canning, “Measurement of the bit-error rate of an adaptive optics, free-space laser communications system, part 2: multichannel configuration, aberration characterization, and closed-loop results,” Opt. Eng. 44(9), 096003 (2005). [CrossRef]

12. C. A. Thompson, M. W. Kartz, L. M. Flath, S. C. Wilks, R. A. Young, G. W. Johnson, and A. J. Ruggiero, “Free space optical communications utilizing MEMS adaptive optics correction,” in International Symposium on Optical Science and Technology, (International Society for Optics and Photonics, 2002), 129–138. [CrossRef]

13. T. Weyrauch and M. A. Vorontsov, “Atmospheric compensation with a speckle beacon in strong scintillation conditions: directed energy and laser communication applications,” Appl. Opt. 44(30), 6388–6401 (2005). [CrossRef] [PubMed]

14. M. Gregory, F. Heine, H. Kampfner, R. Lange, M. Lutzer, and R. Meyer, “Commercial optical inter-satellite communication at high data rates,” Opt. Eng. 51(3), 031202 (2012). [CrossRef]

15. Z. Sodnik, J. P. Armengol, R. H. Czichy, and R. Meyer, “Adaptive optics and ESA's optical ground station,” Proc. SPIE 7464, 746406 (2009). [CrossRef]

16. T. Berkefeld, D. Soltau, R. Czichy, E. Fischer, B. Wandernoth, and Z. Sodnik, “Adaptive optics for satellite-to-ground laser communication at the 1m Telescope of the ESA Optical Ground Station, Tenerife, Spain,” Proc. SPIE 7736, 77364C (2010). [CrossRef]

17. G. P. Agrawal, Fiber-Optic Communication Systems (A John Wiley & Sons, Inc., 2002).

18. N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29(10), 1174–1180 (1990). [CrossRef]

19. L. Hu, L. Xuan, Z. Cao, Q. Mu, D. Li, and Y. Liu, “A liquid crystal atmospheric turbulence simulator,” Opt. Express 14(25), 11911–11918 (2006). [CrossRef] [PubMed]

Performance evaluation of adaptive optics for atmospheric coherent laser communications

Abstract

1. Introduction

2. The theory

2.1. The mixing efficiency and signal to noise ratio

2.2. The BER

3. The results

3.1. The mixing efficiency improvement by AO

3.2. The BER improvement by AO

4. Conclusions

Acknowledgments

References and links

Cited By

Figures (9)

Equations (20)

Optics Express