Atmospheric aberrations in coherent laser systems

Snowmass, July 12, 2007

Aniceto Belmonte

belmonte@tsc.upc.edu

2

Atmospheric Optical Systems

3

• Simulated Experiments on Atmospheric Propagation

• Compensation Methods on Coherent Measurements

• Beam Projection on Coherent Lidars

• Conclusions

Index

Work Basis

•Optical phase perturbations destroy the spatial coherence of a laser beam as it propagates through the atmosphere. It restricts the received power levels in optical coherent systems.

•Temporal fading associate with optical amplitude fluctuations increases the uncertainty in the measurements.

•Performance limitations imposed by atmospheric turbulence on specific coherent systems need to be quantify.

•Main task is the quantification of the performance achievable in coherent optical systems using atmospheric compensation techniques.

5

Atmospheric Effects on Received Signal

WIDE-BANDSIGNAL-TO-NOISE RATIO

PHASE DISTORTION BEAM WANDER BEAM SPREADING SCINTILLATION

RECEIVED POWER UNCERTAINTYRECEIVED POWER LEVEL

SENSITIVITY LINK QUALITY

SIGNALRELATIVE ERROR

6

Available Techniques

!?Rytov

Simulations

Asymptotic

Heuristic ?

7

Split-Step Solution

R z

GaussianBeam

px

Aperture

AtmosphericTurbulence

DistortedBeam

py

vx

vy

• Based on the Fresnel approximation to the wave equation

• Atmosphere is modeled as a set of two-dimensional random phase screens

• All simulations use the Hill turbulence spectrum (1-mm to 5-m scales)

• Uniform and Non-Uniform (Hufnagel-Valley model) turbulence profiles

• Temporal and spatial analysis

8

*, ,S LO

DETECTOR

M M d d 1 2 1 2 1 2w w w w w w

LOBeam

Receiver

TransmittedBeam

i

ReflectedBeam

Scatters

Turbulence

Receiver Plane Formulation

9

I z I z dT BPLO

TARGET

( , ) ( , )p p p

Receiver

TransmittedBeam

i

BPLO

Scatters

LOBeam

Target Plane Formulation

10

Simulated Performance: Monostatic

0 1000 2000 3000 4000 5000-6

-4

-2

0

2

4

Coh

eren

t Pow

er G

ain

[dB

]

Lidar Range [m]

Cn2 = 10-12 m-2/3

λ = 2 μm

Cn2 = 10-13 m-2/3

11

T BPLO

0 1000 2000 3000 4000 5000

-8

-6

-4

-2

0

Lidar Range [m]

Coh

eren

t Pow

er G

ain

[dB

]

-10

Cn2 = 10-12 m-2/3

λ = 2 μm

Cn2 = 10-13 m-2/3

Simulated Performance: Bistatic

12

0 500 1000 1500 2000 2500 3000-16

-12

-8

-4

0

4

Coh

eren

t Pow

er G

ain

[dB

]

Monostatic

Bistatic

10 μrad20 μrad30 μrad40 μrad

D=36 cm

Cn2 = 10-12 m-2/3

λ = 2 μm

Range [m]

θ

0 500 1000 1500 2000 2500 3000-20

-15

-10

-5

0

5

Range [m]

Monostatic

Bistatic

D= 9 cm

Coh

eren

t Pow

er G

ain

[dB

]

Misalignment Effects

13

Coherent Power Fluctuations

0 0.1 0.2 0.3 0.4 0.5 0.6

Strong Cn2

Coherent Power Standard Deviation

0

1000

2000

3000

4000

5000

Alti

tude

[m

]

0 0.1 0.2 0.3 0.4 0.5

Coherent Power Standard Deviation

30°

60°90° (Zenith)

Moderate Cn2

λ = 2 m

0

1000

2000

3000

4000

5000

14

Uncertainty Temporal Averaging

100

101

102

103

10410

-3

10-2

10-1

100

101

N-1/2

V = 10 m/s

R = 5 km

Pulses Averaged

1 kHz

5 kHz

10 kHz

Cn2 = 10-13 m-2/3

λ = 2 m

10-3

10-2

10-1

100

101

Nor

mal

ized

Sta

ndar

d D

evia

tion

N-1/2

100

101

102

103

104

Pulses Averaged

R = 3 km

Cn2 = 10-12 m-2/3

15

Free-Space Optical Communication Systems

•Optical phase perturbations restricts the received power levels in optical communications.

•Temporal fading associate with optical amplitude fluctuations increases the error in the communication link.

*, ,S LO

DETECTOR

M M d d 1 2 1 2 1 2w w w w w w DETECTOR

I d w w

LOBeam

Receiver TransmitterSignalBeam

i

16

• Simulated Experiments on Atmospheric Propagation

• Compensation Methods on Coherent Measurements

• Beam Projection on Coherent Lidars

• Conclusions

Index

17

APERTURE INTEGRATOR/ARRAYS

PHASE COMPENSATED

RECEIVERS

RECIPROCITYPOINTING

ATMOSPHERIC COMPENSATION TECHNIQUES

PHASE DISTORTION BEAM WANDER BEAM SPREADING SCINTILLATION

ATMOSPHERIC EFFECTS ON RECEIVED SIGNAL

DIRECT DETECTIONGROUND, DOWNLINK

DIRECT, HETERODYNEGROUND, DOWNLINK

DIRECT, HETERODYNEGROUND, DOWN/UP LINKS

Atmospheric Compensation Techniques

18

Phase Compensation on Coherent FSO

•In communication with optical heterodyne detection, as in imaging systems, the aim of phase compensation is to restore diffraction-limited resolution. Technology of adaptive optics communications is identical to that of adaptive optics imaging: Measurement, reconstruction, and conjugation of the wavefront (spatial phase conjugation of Zernike modes).

1

, ,N

n nn

c ZR

LOBeam

Receiver

Transmitter

Wavefront Sensor&

Controller

SignalBeam

i

19

Atmospheric Compensation Needs in FSO

X [m]

Y [

m]

-800 -600 -400 -200 0 200 400 600 800

-800

-600

-400

-200

0

200

400

600

800

X [m]

Y [

m]

-800 -600 -400 -200 0 200 400 600 800

-800

-600

-400

-200

0

200

400

600

800

X [m]

Y [

m]

-800 -600 -400 -200 0 200 400 600 800

-800

-600

-400

-200

0

200

400

600

800

Detector-plane Intensity Distributions

20

Adaptive Optics in Direct-Detection FSO

Transmitter

Optical Power Any

Wavelength Near IR/Visible

Divergence Angle Any

Line-of-Sight Path Horizontal/Slant

Transmission Bandwidth High

Deployment Distance Near and Far Field

Coding Scheme Any

Medium

Visibility Any

Atmospheric Seeing Low (Day Time)

Scintillation Any

Solar Background High (Day Time)

Receiver

Receiver Sensitivity Any

Receive Lens Diameter >10 cm

Receiver Field of View Small (<1 mrad)

Detector Active Area Small (APD)

Reception Diversity Single/Multiaperture

21

0 10 20 30 40 50 60 70 800

2

4

6

8

10

12

14

Modes Removed

Cn2 = 10-13 m-2/3

R = 3 km

0 10 20 30 40 50 60 70 800

2

4

6

8

10

Modes Removed

Coh

eren

t Pow

er G

ain

(dB

)

Cn2 = 10-14 m-2/3

λ = 1.55 μmD=30 cmD=20 cmD=10 cm

FSO Coherent Power Gain

22

•The target is a distributed aerosol, which creates target speckle with decorrelation times in the order of 1 μs.

•Mirror segments response times are about 0.1―1ms, hence compensation system allows system bandwidths of about 1 kHz. Any phase conjugation system will be too slow to compensate for target speckle.

Speckle in Coherent Lidar

LOBeam

Receiver

Wavefront Sensor&

Controller

i TransmittedBeam

ReflectedBeam

Scatters

23

The Optimization Problem

•We need to consider the speckle averaged coherent signal. Consequently, a rapid pulse repetition rate is required from the laser. Nowadays systems have the required specifications.

•The power level reaching the receiver is extremely low and wavefront sensor should use coherent detection. Also, wavefront conjugation technique has problems related to the presence of intensity scintillation.

•Wavefront correctors based on MEM systems have large bandwidth and a reduced tag price. The wavefront sensor and the phase reconstruction hardware are the major obstacles to achieving fast, inexpensive adaptive systems.

24

Non-Conjugated Adaptive Optics

•There is another wavefront control paradigm. Instead of considering the wavefront conjugation based on the reciprocity principle, it is possible to compensate wavefront distortion using direct system performance metric optimization.

•We analyze a system implementing a non-conjugate adaptive optics with use efficient parallel model-free optimization algorithms (Gradient descent optimization).

•The metric can be considered as a functional that depends on the phase aberrations introduced by atmospheric turbulence.

25

Blind (Free-Model) Compensation

LOBeam

Receiver

TransmittedBeam

i

ReflectedBeam

Scatters

Controller

26

Blind (Free-Model) Algorithms

•The algorithm choose the mirror shape to maximize the speckle averaged coherent signal power. Compensation can consider either the transmitted beam or the local oscillator beam.

•Compensation algorithms can be associated with a metric defined in terms of the overlap integral of the transmitted and BPLO irradiances at the target plane. The speckle averaged coherent signal power P is defined through the overlap integral:

2( ) , ,T BPLOP R C R j R j R d

p p p

27

LO Atmospheric Beam Projection

•The problem of adaptive laser beam projection onto an extended aerosol target in the atmosphere needs to be considered. Beam compensation is considered through conjugation of the wave phase.

•Using the target-plane formulation and our simulation techniques, it is straightforward to estimate the phase-correction system reliability and its effects on the coherent lidar performance.

Receiver

TransmittedBeam

i

Scatters

Controller

BPLO

28

0 10 20 30 40 5020

22

24

26

28Overlap Integral (Coherent Power) Evolution

Iteration Number

Qua

lity

Met

ric

0 10 20 30 40 50-0.4

-0.2

0

0.2

0.4

Qua

lity

Met

ric

Gra

dien

t

0 1000 2000 3000 4000 5000 6000 700016

18

20

22

24

26

28

30

Range [m]

Ove

rlap

Int

egra

l

Overlap Integral (Coherent Power) Range Dependency

Coherent Power as Quality Metric

29

0 5 10 15 20 25-15

-10

-5

0

5

10

Zernike Order

Ene

rgy

[dB

]]

Defocus

Astigmatism

Coma

Spherical Aberration

Distortion

LO Control Wavefront

30

Beam Projection

31

Index

• Simulated Experiments on Atmospheric Propagation

• Compensation Methods on Coherent Measurements

• Beam Projection on Coherent Lidars

• Conclusions

32

0 10 20 30 40 500

1000

2000

3000

4000

5000

Coherent Power Gain [%]

Alti

tude

[m]

Moderate Cn2

30°45°60°

λ = 1 m

90° (Zenith)

D = 40 cm

0 5 10 15 20 25Coherent Power Gain [%]

Strong Cn2

0

1000

2000

3000

4000

5000

Coherent Power Gain vs Elevation Angle

33

0 10 20 30 40 500

1000

2000

3000

4000

5000

Coherent Power Gain [%]

Alti

tude

[m

]

Moderate Cn2

30°45°60°

λ = 1 m

90° (Zenith)

D = 20 cm

0 5 10 15 20 250

1000

2000

3000

4000

5000

Coherent Power Gain [%]

Strong Cn2

Coherent Power Gain

34

0 5 10 15 20 250

1000

2000

3000

4000

5000

Coherent Power Gain [%]

Alti

tude

[m

]

Moderate Cn2

30°45°60°

λ = 1 m

90° (Zenith)

D = 10 cm

0 5 10 15 20 250

1000

2000

3000

4000

5000

Coherent Power Gain [%]

Strong Cn2

Coherent Power Gain

35

0 10 20 30 40 500

1000

2000

3000

4000

5000

Coherent Power Gain [%]

Alti

tude

[m

]

Moderate Cn2

0 10 20 30 40 500

1000

2000

3000

4000

5000

Coherent Power Gain [%]

Strong Cn2

λ = 1 m

D = 10 cm

θ = 90° (Zenith)

D = 20 cmD = 40 cm

Coherent Power Gain vs Aperture Size

36

0 10 20 30 40 500

1000

2000

3000

4000

5000

Coherent Power Gain [%]

Alti

tude

[m

]

Moderate Cn2

0 10 20 30 40 500

1000

2000

3000

4000

5000

Coherent Power Gain [%]

λ = 1 m

D = 10 cm

θ = 45°

D = 20 cmD = 40 cm

Strong Cn2

Coherent Power Gain

37

0 5 10 150

1000

2000

3000

4000

5000

Coherent Power Gain [dB]

Moderate Cn2

λ = 1 m

D = 20 cm

90° (Zenith)

60°

30°

Misalignment 20 μm

0 5 10 150

1000

2000

3000

4000

5000

Coherent Power Gain [dB]

Alti

tude

[m

]

Moderate Cn2Misalignment 20 μm

λ = 1 m

D = 10 cm

θ = 90° (Zenith)

D = 20 cmD = 40 cm

Misalignment Compensation

38

0 5 10 15 200

1000

2000

3000

4000

5000

Coherent Power Gain [dB]

Alti

tude

[m

]

30 μm

Moderate Cn2

λ = 1 mD = 20 cm

θ = 90° (Zenith)20 μm

10 μm

5 μm

Misalignment Compensation

39

• Simulated Experiments on Atmospheric Propagation

• Compensation Methods on Coherent Measurements

• Beam Projection on Coherent Lidars

• Conclusions

Index

40

Technique Summary

• Feasibility of Beam Propagation Technique

Well-known Limits of Applicability

• Simulation of Coherent Laser System Performance

Practical Systems Analysis

• Results are encouraging

Compensation techniques may extend the deployment distance

and/or quality of atmospheric optical systems.

• Room for improvement

New algorithms and Full Field Compensation

• Results must be viewed as benchmarks whose achievements may

require the development of devices.