[ieee instruments (icemi) - beijing, china (2009.08.16-2009.08.19)] 2009 9th international...

The Ninth International Conference on Electronic Measurement & Instruments ICEMI’2009

Measurement of Laboratory-simulated Atmospheric Turbulence by PSD

Xiwen Qiang1, 2 Yan Li2 Fei Zong2 Junwei Zhao2 1 Key Laboratory for Physical Electronics and Devices of the Ministry of Education,

Xi'an Jiaotong University, No. 28, West Xianning Road, Xi'an 710049, China 2 Northwest Institute of Nuclear Technology,

No. 28, Pingyu Road, Baqiao District, Xi'an 710024, China Email: qiangxiwen @163.com

Abstract – Atmospheric optical turbulence increases bit error rate and degrades beams quality for wireless laser communication links as laser light propagation in the turbulent atmosphere, and optical turbulence simulation and measurement are important research topics for improving performance of wireless laser communication. An experiment system was built for simulating and measuring optical turbulence for laser propagation experiment. A method based on angle-of-arrival fluctuations of a laser beam through simulated- turbulence is utilized for measuring Fried coherence length (r0) of optical turbulence. Position Sensitive Detectors (PSD) have excellent position resolution and are utilized for measuring centroid fluctuations of laser light flux after propagation through laboratory-simulated turbulence in order to offer turbulence parameters required. An instantaneous value of Fried coherence length can be obtained. The simulated turbulence could be 1000 times stronger than that of real atmosphere and Fried coherence length of simulated turbulence spanned from 1.4 to 12cm. The results show that Fried coherence length of laboratory-simulated atmospheric changes very rapidly with time and varies with temperature and wind velocity of the air along the propagation path. Keywords –Atmospheric turbulence, angle-of-arrival fluctuation, Fried coherence length, Position Sensitive Detectors.

I. INTRODUCTION

In recent decades there have been increasing demands for high data rate wireless laser communication.[1 – 3] This interest stems from the advantages of optical systems over conventional radio frequency systems, such as less mass, power, and volume, along with high power gain and a narrow frequency band. Unfortunately, the performance of optical systems can be significantly degraded by atmospheric optical turbulence. Atmospheric optical turbulence, or refractive index fluctuations in the atmosphere, is induced mostly by small fluctuation of random temperature variety in the atmosphere which is results from heating of air and soil by the radiation of sun. So, we can utilize heated convective air for generating the stronger refractive-index fluctuations and made the turbulence more homogeneous and isotropic in laboratory.

Due to atmospheric media vary randomly in time and

space at various weather conditions in the open air, experiments of wireless laser communication in the open air are difficult and cost expensively. Artificially generated atmospheric turbulence in the laboratory can be controlled at various strength, cost low, and the parameters of turbulence can be measured accurately.

A method based on angle-of-arrival fluctuations of a laser beam through simulated-turbulence is utilized for measuring Fried coherence length of turbulence. The results are analyzed for various air temperature and wind velocity for simulated- turbulence, and the relations between Fried coherence length and air temperature or wind velocity are presented.

II. LABORATORY-SIMULATED TURBULENCE

Laboratory-simulated turbulence artificially have been utilized in laser propagation and imaging experiments from 1970’[4, 5] and nowdays it’s a effective method applied in adaptive optics imaging and wireless laser communications links.[6, 7]

Fig.1 Schematic diagram of turbulence simulation and

measurement

A system for laboratory-simulated turbulence is schematically illustrated in Fig. 1. The system with internal dimensions, 1.5m long, 0.8m wide, and 0.3m high, was assembled on a shock-mounted optical bench. The small electrical heater/blowers were installed on one side of the turbulence generator. The turbulence flows generated by the heater/blowers are parallel to the optical bench surface and perpendicular to the laser propagation direction. The height of center of the flow was 0.15m, about center height of the turbulence generator. The strength of turbulence could be controlled by control temperature and wind velocity of air flows. The temperature of air flows were at range from 25 to 50 Celsius degree and wind velocity about 0.5 to 1.0 m/s, measured by a hot-wire anemometer of model KA32L.

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_____________________________978-1-4244-3864-8/09/$25.00 ©2009 IEEE


III. MEASURING OF TURBULENCE BY PSD

As described in Fig. 1, a 10 mW He-Ne Laser of uniphase model propagates through a turbulent layer of thickness L = 1.5m. Before propagation through the turbulent layer, the diameter of laser beam was expanded and collimated from 0.65 mm to 10 mm. A pinhole of 0.5 mm diameter was placed before the receiving Position Sensitive Detector, i.e., PSD, to sampling a small portion of the wave-front, and the distance d between pinhole and PSD was 1.0 m. A narrow band filter, centered at 632.8nm and half-width 20 nm, was placed in front of the PSD to filter background light waves out. The signals were digitalized by a 16 bit A/D card and acquired during 50 seconds at a sample rate of 2000 samples/sec. Angles-of-arrival �(i) were obtained by measuring lateral displacements x(i) of the beam after the pinhole and was given as follows,

�(i) = x(i)/d (1) The turbulence parameters retrieval was based on

measurement of angle-of-arrival fluctuations of laser light flux. Angle-of-arrival fluctuations of an optical wave in the plane of the receiver aperture are associated with image dancing in the focal plane of an imaging system. To derive the path average mean-square angle-of-arrival, ��

2, a retrieving technique based on centroid variance calculation is used for a set of data. The variance for angle-of-arrival � is given by[8]

3/50

23/12 1746.0 �� rD �� (2) where D is the aperture size, and � is the wavelength. So, the Fried coherence length should be expressed as

5/65/65/10 18.3 �� kDr (3)

where k = 2�/� . We can see from equation (3) that the Fried coherence

length could be calculated if variance is known for special aperture size and laser wavelength. Here light source is a 10mW He-Ne lasers followed by a beam-expanding telescope. A collimated beam with beam width 10mm propagates through the simulated-turbulence and arrives at PSD, with a lens and narrow-band filter in front of it. The receiver aperture size of lens, D, was 5mm. The PSD signals were digitalized by a 16 bit AT – MIO -16XE – 50 National Instruments board and data sets acquired during 1 minute at a samples rate of 500 samples/sec. Position data were corrected by taking into account the precise calibration curve of the PSD. The variance of centroid fluctuations after laser propagation through turbulence was measured by a PSD. The effective photosensitive area of PSD is 10mm � 10mm, and the resolution is 250nm.

At beginning of each experiment, the measurement background due to residual turbulence and instrumentation noise must be checked. So, let a beam arrive at the PSD after propagation through simulated – turbulence, as shown in Fig. 1, the centroid fluctuations were measured before the turbulence generator turned on. The variance of angle-of-arrival fluctuations was a background noise. After the turbulence generator turned

on, keeping the air temperature and wind velocity fixed at special values, the variance of angle-of-arrival fluctuations was measured and the background noise should be subtracted from the measuring variance.

IV. MEASUREMENTS OF AIR FLOWS AND TURBULENCE

Turbulence parameters are dependent on temperature and wind velocity. So, temperature and wind velocity distribution along beam propagation path and their deviation extent from average values at typical cases were analyzed. The typical measuring results for the Fried coherence length were given.

A. Air temperature wind velocity and distribution

The air temperature and wind velocity were measured along beam propagation path throughout the turbulence generator by a hot-wire anemometer of model KA32L, at the standard height 0.15m.

The air temperature along beam propagation path for the case in which average temperature was 40 is shown in Fig. 2. and the relative deviation of air temperature from average value of air temperature is shown in Fig. 3. From Fig. 2, it shows that the air temperature locate center place of the turbulence generator are higher than that at both sides. From Fig. 3, it shows that the relative deviation from average air temperature are between -6% to 4%.

0 30 60 90 120 15035

36

37

38

39

40

41

42

43

44

45

L/cm

Average air temperature: 400C

Tem

pera

ture

/ 0 C

Fig. 2 The air temperature along beam propagation path

The wind velocity along beam propagation path for the case in which average temperature was 40 is shown in Fig. 4. and the deviation of wind velocity from average value of wind velocity is shown in Fig. 5. From Fig. 4, it shows that the wind velocity locate center place of the turbulence generator are higher than that at both sides. The maximum is 0.59 m/s and minimum is 0.21 m/s. From Fig. 5, it shows that the relative deviation from average value of wind velocity are between -53% to 31%.

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0 30 60 90 120 150-10

-8

-6

-4

-2

0

2

4

6

8

10

L/cm

Average air temperature: 400C

T/T

(%)

Fig. 3 The relative deviation of the air temperature from

average values along beam propagation path

From Fig. 2 to Fig. 5, it shows that the air temperature uniformity along beam propagation path is better than that of the wind velocity. These uniformity will result in uniformity of turbulence along beam propagation path within the turbulence generator. A conclusion deduced at latter was that the air temperature was a more primary factor, compared with wind velocity. So, these uniformity, especially the uniformity of air temperature, should be restrained by some means and techniques in the future.

0 30 60 90 120 1500.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

The average air temperature: 400CThe average wind velocity: 0.39m/s

/m

.s-1

L/cm Fig. 4 The wind velocity along beam propagation path

0 30 60 90 120 150-60

-50

-40

-30

-20

-10

0

10

20

30

40

/

(%)

L/cm

The average air temperature: 400CThe average wind velocity: 0.39m/s

Fig. 5 The relative deviation of the wind temperature

from average values along beam propagation path

B. The Fried coherence length

Because the uniformity of the air temperature and wind velocity along propagation path, the simulated turbulence was not equal at different position within the turbulence generator. The Fried coherence length describes integral effect of turbulence along propagation path and should be given as follows,

5/3

0

220 )(423.0

�

��

��

L

n dllCkr (4)

where Cn2 is the refractive index structure constant at

a special position along propagation path. So, r0 is a appropriate parameter for measuring in this experiment.

The Fried coherence length measured for various air temperature at wind velocity = 0.7m/s are shown in Fig.6. And the Fried coherence length measured for various wind velocity at air temperature 40 are shown in Fig.7.

20 25 30 35 40 45 50 55

2

4

6

8

10

12 =0.7m/s

r 0/mm

Temperature/oC Fig. 6 The Fried coherence length measured for various

air temperature (wind velocity = 0.7m/s)

0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.11.8

1.9

2.0

2.1

2.2

2.3

2.4

2.5 Temperature=40oC

r 0/mm

/m.s-1

Fig. 7 The Fried coherence length measured for various

wind velocity (Air Temperature = 40 )

From Fig. 6, it shows that the Fried coherence length of simulated turbulence could vary from 1.4cm to 12cm which span the values of weaker turbulence to the strongest turbulence in the real atmosphere. For the case 1.4cm r0, the average refractive index structure constant, Cn

2, is about 2.0�10-11m-2/3, which is 1000 times stronger than the typical values in the real atmosphere. The typical values of r0 for whole atmosphere are about 5cm to 12cm at visible wavelength. So, the designed turbulence generator could simulate the turbulence along the whole atmosphere. Besides, increasing the air temperature

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could change Fried coherence length remarkably, especially from 25 to 35 .

From Fig.7, it shows that wind velocity do not influence the Fried coherence length remarkably. So, the turbulence in laboratory could be simulated by the means of changing air temperature of air flows at some special wind velocity.

V. UNCERTAINTY OF MEASUREMENT OF THE FRIED COHERENCE LENGTH

Based on theoretical analysis and processing of experiments data, the combined standard uncertainty and type A evaluation of uncertainty of measurement of the Fried coherence length (r0) were analyzed and given respectively. The unstable characteristics of simulated-turbulence induced by unstable air temperature and wind velocity were considered.

A. Theoretical analysis of uncertainty of measurement of r0

The Fried coherence length (r0) is a function of L and the variance of angle-of arrival fluctuations, <�2>. The combined standard uncertainty of r0 is given as follows,

2

2

2222

222

20

0

22

0

00

0

)(107)(

51

)(1)(1)(

��

��

��

��

��

�

��

��

��

��

��

��

��

�

��

��

��

��

uLLu

ur

rLu

Lr

rrruC

( 5 )

The distance L is a geometrical quantity and could has a very small uncertainty of measurement,

%33.05.1105.0)( 3

��

��

LLu (6)

Hereinafter, let’s consider uncertainty of measurement of the variance of angle-of arrival fluctuations. For a measurement of N times samples, the variance of angle-of arrival fluctuations, <�2>, is as follows,

� ��

��

��

��N

i

N

ixix

Nddxix

N 1

202

1

202 )(1)(1� (7)

where x0 is average of centroid of laser beam for N times measuring. <�2> is a function of x(i) d and x0 and their partial derivatives are given as follows, respectively,

� �

� � 02

1)(12)(2)(

002

10

12

102

2

��

��

!"

��

��

xxd

xN

ixNd

xixNdix

N

i

N

i

N

i

�

(8)

� � 0)(2

102

0

2��

��

�

N

i

xixNdx

�

(9)

� ��

��

�� N

i

xixNdd 1

203

2)(2� (10)

� �

� � dxix

Nd

xixNd

d N

i

N

i 2

)(1

)(21

1

202

1

2032

2 ��

�

�

��

��

��

�

�

��

(11)

So, the combined standard uncertainty is given as follows,

)(2

)()()()(

1)( 222

02

2

0

22

22

22

2

dud

dud

xux

xuix

uC

�

��

��

��

��

�

��

��

��

�

��

��

��

��

��

(12) Choosing the standard uncertainty of <�2> as its

combined standard uncertainty, namely )()( 22 �� Cuu (13)

we could gain

)(2)(2

2du

du

��

��

�� (14)

Taking u(d) = 0.5mm and d = 1.0m, we can get %1.0

0.1105.02)(2)( 3

2

2�

��

��

��

dud

u�� (15)

Inserting equations (6) and (15) into equation (5) gives

%1.0)(

0

0 �r

ruC (16)

This uncertainty of measurement of r0 is very small and this very small uncertainty of measurement of r0 profits from measurements of differential angle-of-arrival and a geometrical quantity, length. The differential angle-of-arrival gives the fluctuations relative to average centroid. In this case the absolute values of centroid at instantaneous times are not important and the relative fluctuations play a important role in the measurements. In this way, the measurements of absolute quantities should be transformed into measurements of relative quantities, namely, fluctuations. So, a small uncertainty of measurement of r0 is gained.

B. Uncertainty of measurement of r0 by experiments

To validate theoretical analysis results of uncertainty of measurement of r0, type A evaluation of uncertainty was performed utilized experiments data.

For every r0, five values of measurements were obtained by experiments and the experimental standard deviation, �(r0), were calculated from measuring data. In Fig. 8, the type A evaluation of uncertainty of r0 are presented for various air temperature at wind velocity 0.7m/s, and the relative values of the type A evaluation of uncertainty of r0 are presented in Fig. 10. In Fig. 9, the type A evaluation of uncertainty of r0 are presented for various wind velocity at air temperature 40 Celsius degree, and the relative values of the type A evaluation of uncertainty of r0 are presented in Fig. 11.

From these figures, it shows that maximum of the type A evaluation of uncertainty of r0 is about 2.3mm, and the maximum of relative values for the type A evaluation of uncertainty of r0 is about 2%.

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20 25 30 35 40 45 50 55

2

4

6

8

10

12 =0.7m/s

r 0/mm

Temperature/oC Fig. 8 The type A evaluation of uncertainty of r0

for various air temperature (wind velocity = 0.7m/s)

Uncertainty of measurement of r0 given by

experimental data is about 2% and this values is larger than theoretical values presented above. The primary reason may be unstable air temperature and wind velocity controlled by fluctuant voltages.

0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.11.8

1.9

2.0

2.1

2.2

2.3

2.4

2.5 Temperature=40oC

r 0/mm

/m.s-1

Fig. 9 The type A evaluation of uncertainty of r0 for

various wind velocity (Air Temperature = 40 )

20 25 30 35 40 45 50 550.0

0.5

1.0

1.5

2.0

2.5

Temperature/oC

=0.7m/s

� (r

0)/r0(%

)


various air temperature (wind velocity = 0.7m/s)

VI. CONCLUSION

A simulated-turbulence generator was built in laboratory. The angle-of-arrival fluctuations of laser light flux could be measured by PSD. The turbulence parameters, Fried coherence length and refractive - index structure constant could be calculated from measurement data. The results show that simulated-turbulence could

be 1000 times stronger than that in the real atmosphere and applied in the experiments for wireless laser communication and other laser propagation. These differential angle-of-arrival measurements could give very small uncertainty of measurements. To improve simulated-turbulence quality and make it homogeneous, controlling parameters such as air temperature and wind velocity should be improved by some techniques in the future.

0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.10.0

0.2

0.4

0.6

0.8

1.0

Temperature=40oC

� (r

0)/r0(%

)

/m.s-1


various wind velocity (Air Temperature = 40 )

ACKNOWLEDGMENT

The author wishes to thank the IEEE for providing this template and all colleagues who previously provided technical support.

REFERENCES

[1] S. Ohmori, Y. Yamao, and N. Nakajima, “The Future Generation of Mobile Communications based on Broadband Access Methods”. J. Wireless Personal Commun., Vol. 17, pp. 175 – 190, Mar. 2001.

[2] Y. Hase, R. Miura, and S. Ohmori, “A Novel Broadband All-wireless Access Network using Stratospheric Radio Platform”. The Forty-eighth Vehicular Technology Conference, Ottawa, Canda, 18 – 21 May 1998.

[3] P. Greiling and N. Ho, “Commercial Satellite Applications for Heterojunction Microelectronics Technology”. IEEE Trans. Microwave Theory Tech., Vol. 46, pp. 734 – 738, June 1998.

[4] L. R. Bissonnette, “Atmospheric Scintillation of Optical and Infrared Waves: a Laboratory Simulation”. Applied Optics, Vol. 16, No. 8, pp. 2242 – 2251, Aug. 1977.

[5] H. Gamo and A. K. Majumdar, “Atmospheric Chamber for Optical Transmission Experiment: Characterization by Thermal Method”. Applied Optics, Vol. 17, No. 23, pp. 2242 – 2251, Dec. 1978.

[6] A. K. Majumdar, J. A. DiUbaldo, and A. Brown-Vanhoozer, “Measurement and Characterization of Laboratory-Simulated Turbulence Parameters of Interest to Adaptive Optics Imaging and Laser Communications”. Proceedings of SPIE, Vol. 3760, pp. 123 – 128, July 1999.

[7] O. Keskin, L. Jolissaint, C. Bradley, S. Dost, and I. Sharf, “Hot air turbulence generator for multi-conjugate adaptive optics”. Proceedings of SPIE, Vol. 5162, pp. 49 – 57, 2003.

[8] F. Roddier, “The Effects of Atmospheric Turbulence in Optical Astronomy”. Progress in Optics, Vol. 19, 99. 281 – 376, 1981.

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[ieee instruments (icemi) - beijing, china (2009.08.16-2009.08.19)] 2009 9th international...

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