belmonte
DESCRIPTION
FGDFDDDTRANSCRIPT
Atmospheric aberrations in coherent laser systems
Snowmass, July 12, 2007
Aniceto Belmonte
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.