Atmospheric aberrations in coherent laser systems               Snowmass, July 12, 2007                  Aniceto Belmonte ...
Atmospheric Optical Systems                              2
Index•   Simulated Experiments on Atmospheric Propagation•   Compensation Methods on Coherent Measurements•   Beam Project...
Work Basis•Optical phase perturbations destroy the spatial coherence of a laser beamas it propagates through the atmospher...
Atmospheric Effects on Received SignalPHASE DISTORTION           BEAM WANDER   BEAM SPREADING         SCINTILLATION       ...
Available Techniques                                           !?Rytov              Simulations                           ...
Split-Step Solution•   Based on the Fresnel approximation to the wave equation•   Atmosphere is modeled as a set of two-di...
Receiver Plane Formulation                                LO                               Beam                           ...
Target Plane Formulation                           LO                          Beam                                       ...
Simulated Performance: Monostatic                           4                                                       λ = 2 ...
Simulated Performance: Bistatic                            0                           -2                            λ = 2...
Misalignment Effects                           4                                                         Monostatic       ...
Coherent Power Fluctuations               5000                                                                    5000    ...
Uncertainty Temporal Averaging                                     1                                                      ...
Free-Space Optical Communication Systems•Optical phase perturbations restricts the received power levels in opticalcommuni...
Index•   Simulated Experiments on Atmospheric Propagation•   Compensation Methods on Coherent Measurements•   Beam Project...
Atmospheric Compensation Techniques                      ATMOSPHERIC EFFECTS ON RECEIVED SIGNALPHASE DISTORTION       BEAM...
Phase Compensation on Coherent FSO•In communication with optical heterodyne detection, as in imagingsystems, the aim of ph...
Atmospheric Compensation Needs in FSO         -800                                                                        ...
Adaptive Optics in Direct-Detection FSO                  Transmitter                                                   Rec...
FSO Coherent Power Gain                           10                                                                  14  ...
Speckle in Coherent Lidar•The target is a distributed aerosol, which creates target speckle withdecorrelation times in the...
The Optimization Problem•We need to consider the speckle averaged coherent signal. Consequently,a rapid pulse repetition r...
Non-Conjugated Adaptive Optics•There is another wavefront control paradigm. Instead of considering thewavefront conjugatio...
Blind (Free-Model) CompensationController                   LO                  Beam                              Reflecte...
Blind (Free-Model) Algorithms•The algorithm choose the mirror shape to maximize the speckleaveraged coherent signal power....
LO Atmospheric Beam Projection•The problem of adaptive laser beam projection onto an extended aerosoltarget in the atmosph...
Coherent Power as Quality Metric                          Overlap Integral (Coherent Power) Evolution                     ...
LO Control Wavefront               10                         Defocus       Coma                5 Astigmatism             ...
Beam Projection                  30
Index•   Simulated Experiments on Atmospheric Propagation•   Compensation Methods on Coherent Measurements•   Beam Project...
Coherent Power Gain vs Elevation Angle               5000                                                         5000    ...
Coherent Power Gain               5000                                                                   5000             ...
Coherent Power Gain               5000                                                            5000                    ...
Coherent Power Gain vs Aperture Size               5000                                                       5000        ...
Coherent Power Gain               5000                                                     5000                           ...
Misalignment Compensation               5000                                                           5000               ...
Misalignment Compensation               5000               4000Altitude [m]               3000               2000         ...
Index•   Simulated Experiments on Atmospheric Propagation•   Compensation Methods on Coherent Measurements•   Beam Project...
Technique Summary•   Feasibility of Beam Propagation Technique         Well-known Limits of Applicability•   Simulation of...
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Atmospheric aberrations in coherent laser systems

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Atmospheric aberrations in coherent laser systems

  1. 1. Atmospheric aberrations in coherent laser systems Snowmass, July 12, 2007 Aniceto Belmonte belmonte@tsc.upc.edu
  2. 2. Atmospheric Optical Systems 2
  3. 3. Index• Simulated Experiments on Atmospheric Propagation• Compensation Methods on Coherent Measurements• Beam Projection on Coherent Lidars• Conclusions 3
  4. 4. Work Basis•Optical phase perturbations destroy the spatial coherence of a laser beamas it propagates through the atmosphere. It restricts the received powerlevels in optical coherent systems.•Temporal fading associate with optical amplitude fluctuations increasesthe uncertainty in the measurements.•Performance limitations imposed by atmospheric turbulence on specificcoherent systems need to be quantify.•Main task is the quantification of the performance achievable incoherent optical systems using atmospheric compensation techniques.
  5. 5. Atmospheric Effects on Received SignalPHASE DISTORTION BEAM WANDER BEAM SPREADING SCINTILLATION RECEIVED POWER LEVEL RECEIVED POWER UNCERTAINTY WIDE-BAND SIGNAL SIGNAL-TO-NOISE RATIO RELATIVE ERROR SENSITIVITY LINK QUALITY 5
  6. 6. Available Techniques !?Rytov Simulations Asymptotic Heuristic ? 6
  7. 7. Split-Step Solution• 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 px• Temporal and spatial analysis vx R z py Distorted Beam vy Atmospheric Turbulence Aperture Gaussian Beam 7
  8. 8. Receiver Plane Formulation LO Beam TurbulenceReceiver Scatters i Reflected Beam Transmitted Beam ∫∫ M S ( w1 , w2 ) M LO ( w1 , w2 ) dw1 dw2 * DETECTOR 8
  9. 9. Target Plane Formulation LO Beam BPLOReceiver i Scatters Transmitted Beam ∫ TARGET IT ( p, z ) I BPLO ( p, z ) dp 9
  10. 10. Simulated Performance: Monostatic 4 λ = 2 μm 2 Cn2 = 10-12 m-2/3Coherent Power Gain [dB] Cn2 = 10-13 m-2/3 0 -2 -4 -6 0 1000 2000 3000 4000 5000 Lidar Range [m] 10
  11. 11. Simulated Performance: Bistatic 0 -2 λ = 2 μmCoherent Power Gain [dB] Cn2 = 10-12 m-2/3 -4 T BPLO Cn2 = 10-13 m-2/3 -6 -8 -10 0 1000 2000 3000 4000 5000 Lidar Range [m] 11
  12. 12. Misalignment Effects 4 Monostatic D=36 cm 0Coherent Power Gain [dB] θ -4 λ = 2 μm Cn2 = 10-12 m-2/3 Bistatic -8 10 μrad 20 μrad -12 30 μrad 40 μrad 5 -16 D= 9 cm 0 500 1000 1500 2000 2500 3000 0 Coherent Power Gain [dB] Range [m] Monostatic -5 -10 -15 Bistatic -20 0 500 1000 1500 2000 2500 3000 Range [m] 12
  13. 13. Coherent Power Fluctuations 5000 5000 Strong Cn2 Moderate Cn2 4000 4000Altitude [m] 3000 3000 λ = 2 µm 30° 2000 2000 60° 90° (Zenith) 1000 1000 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 Coherent Power Standard Deviation Coherent Power Standard Deviation 13
  14. 14. Uncertainty Temporal Averaging 1 1 10 10 R = 3 km R = 5 kmNormalized Standard Deviation 0 0 10 Cn2 = 10-12 m-2/3 10 N -1/2 Cn2 = 10-13 m-2/3 N -1/2 -1 -1 10 10 1 kHz -2 -2 V = 10 m/s 10 10 5 kHz λ = 2 µm 10 kHz -3 -3 10 0 1 2 3 4 10 0 1 2 3 4 10 10 10 10 10 10 10 10 10 10 Pulses Averaged Pulses Averaged 14
  15. 15. Free-Space Optical Communication Systems•Optical phase perturbations restricts the received power levels in opticalcommunications.•Temporal fading associate with optical amplitude fluctuations increases theerror in the communication link. LO Beam Signal Receiver Beam Transmitter i ∫∫ M S ( w1 , w2 ) M LO ( w1 , w2 ) dw1 dw2 * ∫∫ I ( w ) dwDETECTOR DETECTOR 15
  16. 16. Index• Simulated Experiments on Atmospheric Propagation• Compensation Methods on Coherent Measurements• Beam Projection on Coherent Lidars• Conclusions 16
  17. 17. Atmospheric Compensation Techniques ATMOSPHERIC EFFECTS ON RECEIVED SIGNALPHASE DISTORTION BEAM WANDER BEAM SPREADING SCINTILLATION ATMOSPHERIC COMPENSATION TECHNIQUES PHASE APERTURE RECIPROCITY COMPENSATED INTEGRATOR/ARRAYS POINTING RECEIVERS DIRECT DETECTION DIRECT, HETERODYNE DIRECT, HETERODYNE GROUND, DOWNLINK GROUND, DOWNLINK GROUND, DOWN/UP LINKS 17
  18. 18. Phase Compensation on Coherent FSO•In communication with optical heterodyne detection, as in imagingsystems, the aim of phase compensation is to restore diffraction-limitedresolution. Technology of adaptive optics communications is identical tothat of adaptive optics imaging: Measurement, reconstruction, andconjugation of the wavefront (spatial phase conjugation of Zernike modes). Signal Beam Transmitter LO Beam Receiver i N ρ  Φ ( ρ , ϕ ) = ∑ cn Z n  , ϕ ÷ n =1 R  Wavefront Sensor & Controller 18
  19. 19. Atmospheric Compensation Needs in FSO -800 -800 -800 -600 -600 -600 -400 -400 -400 -200 -200 -200 Y [ m]Y [µm] Y [ m] 0 0 0 µ µ 200 200 200 400 400 400 600 600 600 800 800 800 -800 -600 -400 -200 0 200 400 600 800 -800 -600 -400 -200 0 200 400 600 800 -800 -600 -400 -200 0 200 400 600 800 X [µm] X [µm] X [µm] Detector-plane Intensity Distributions 19
  20. 20. Adaptive Optics in Direct-Detection FSO Transmitter Receiver Optical Power Any Receiver Sensitivity Any Wavelength Near IR/Visible Receive Lens Diameter >10 cm Divergence Angle Any Receiver Field of View Small (<1 mrad) Line-of-Sight Path Horizontal/Slant Detector Active Area Small (APD)Transmission Bandwidth High Reception Diversity Single/Multiaperture Deployment Distance Near and Far Field Coding Scheme Any Medium Visibility Any Atmospheric Seeing Low (Day Time) Scintillation Any Solar Background High (Day Time) 20
  21. 21. FSO Coherent Power Gain 10 14 Cn2 = 10-14 m-2/3 Cn2 = 10-13 m-2/3 12 8Coherent Power Gain (dB) 10 6 8 4 6 4 D=30 cm λ = 1.55 μm 2 D=20 cm R = 3 km 2 D=10 cm 0 0 0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 70 80 Modes Removed Modes Removed 21
  22. 22. Speckle in Coherent Lidar•The target is a distributed aerosol, which creates target speckle withdecorrelation times in the order of 1 μs.•Mirror segments response times are about 0.1―1ms, hence compensationsystem allows system bandwidths of about 1 kHz. Any phase conjugationsystem will be too slow to compensate for target speckle. LO Beam Scatters Receiver Reflected Beam i Transmitted Beam Wavefront Sensor & Controller 22
  23. 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 systemshave the required specifications.•The power level reaching the receiver is extremely low and wavefrontsensor should use coherent detection. Also, wavefront conjugationtechnique has problems related to the presence of intensity scintillation.•Wavefront correctors based on MEM systems have large bandwidth and areduced tag price. The wavefront sensor and the phase reconstructionhardware are the major obstacles to achieving fast, inexpensive adaptivesystems. 23
  24. 24. Non-Conjugated Adaptive Optics•There is another wavefront control paradigm. Instead of considering thewavefront conjugation based on the reciprocity principle, it is possible tocompensate wavefront distortion using direct system performance metricoptimization.•We analyze a system implementing a non-conjugate adaptive opticswith use efficient parallel model-free optimization algorithms (Gradientdescent optimization).•The metric can be considered as a functional that depends on the phaseaberrations introduced by atmospheric turbulence. 24
  25. 25. Blind (Free-Model) CompensationController LO Beam Reflected Beam Scatters i Receiver Transmitted Beam 25
  26. 26. Blind (Free-Model) Algorithms•The algorithm choose the mirror shape to maximize the speckleaveraged coherent signal power. Compensation can consider either thetransmitted beam or the local oscillator beam.•Compensation algorithms can be associated with a metric defined interms of the overlap integral of the transmitted and BPLO irradiances atthe target plane. The speckle averaged coherent signal power P is definedthrough the overlap integral: +∞ P( R) = C ( R ) λ 2 ∫ jT ( p, R ) jBPLO ( p, R ) dp −∞ 26
  27. 27. LO Atmospheric Beam Projection•The problem of adaptive laser beam projection onto an extended aerosoltarget in the atmosphere needs to be considered. Beam compensation isconsidered through conjugation of the wave phase.•Using the target-plane formulation and our simulation techniques, it isstraightforward to estimate the phase-correction system reliability and itseffects on the coherent lidar performance. Scatters Receiver BPLO i Transmitted Beam Controller 27
  28. 28. Coherent Power as Quality Metric Overlap Integral (Coherent Power) Evolution Overlap Integral (Coherent Power) Range Dependency 28 0.4 30 28 26 0.2 Quality Metric Gradient 26Quality Metric Overlap Integral 24 24 0 22 22 -0.2 20 18 20 -0.4 16 0 10 20 30 40 50 0 1000 2000 3000 4000 5000 6000 7000 Iteration Number Range [m] 28
  29. 29. LO Control Wavefront 10 Defocus Coma 5 Astigmatism Distortion Spherical AberrationEnergy [dB]] 0 -5 -10 -15 0 5 10 15 20 25 Zernike Order 29
  30. 30. Beam Projection 30
  31. 31. Index• Simulated Experiments on Atmospheric Propagation• Compensation Methods on Coherent Measurements• Beam Projection on Coherent Lidars• Conclusions 31
  32. 32. Coherent Power Gain vs Elevation Angle 5000 5000 30° 45° 4000 4000 60° 90° (Zenith)Altitude [m] 3000 3000 D = 40 cm λ = 1 µm 2000 2000 1000 1000 Moderate Cn2 Strong Cn2 0 0 0 10 20 30 40 50 0 5 10 15 20 25 Coherent Power Gain [%] Coherent Power Gain [%] 32
  33. 33. Coherent Power Gain 5000 5000 30° 45° 4000 60° 4000 90° (Zenith)Altitude [m] D = 20 cm 3000 3000 λ = 1 µm 2000 2000 1000 1000 Moderate Cn2 Strong Cn2 0 0 0 10 20 30 40 50 0 5 10 15 20 25 Coherent Power Gain [%] Coherent Power Gain [%] 33
  34. 34. Coherent Power Gain 5000 5000 D = 10 cm 30° λ = 1 µm 45° 60° 4000 90° (Zenith) 4000Altitude [m] 3000 3000 2000 2000 1000 1000 Moderate C n 2 Strong Cn2 0 0 0 5 10 15 20 25 0 5 10 15 20 25 Coherent Power Gain [%] Coherent Power Gain [%] 34
  35. 35. Coherent Power Gain vs Aperture Size 5000 5000 D = 10 cm 4000 4000 D = 20 cm D = 40 cmAltitude [m] 3000 3000 θ = 90° (Zenith) λ = 1 µm 2000 2000 1000 1000 Strong Cn2 Moderate C n 2 0 0 0 10 20 30 40 50 0 10 20 30 40 50 Coherent Power Gain [%] Coherent Power Gain [%] 35
  36. 36. Coherent Power Gain 5000 5000 D = 10 cm 4000 4000 D = 20 cm D = 40 cmAltitude [m] 3000 3000 θ = 45° λ = 1 µm 2000 2000 1000 1000 Strong Cn2 Moderate Cn2 0 0 0 10 20 30 40 50 0 10 20 30 40 50 Coherent Power Gain [%] Coherent Power Gain [%] 36
  37. 37. Misalignment Compensation 5000 5000 4000 4000Altitude [m] 3000 3000 D = 10 cm 30° D = 20 cm 60° 2000 D = 40 cm 2000 90° (Zenith) θ = 90° (Zenith) D = 20 cm 1000 λ = 1 µm 1000 λ = 1 µm Misalignment 20 μm Moderate C n 2 Misalignment 20 μm Moderate Cn2 0 0 0 5 10 15 0 5 10 15 Coherent Power Gain [dB] Coherent Power Gain [dB] 37
  38. 38. Misalignment Compensation 5000 4000Altitude [m] 3000 2000 θ = 90° (Zenith) 30 μm D = 20 cm 20 μm 1000 λ = 1 µm 10 μm Moderate Cn2 5 μm 0 0 5 10 15 20 Coherent Power Gain [dB] 38
  39. 39. Index• Simulated Experiments on Atmospheric Propagation• Compensation Methods on Coherent Measurements• Beam Projection on Coherent Lidars• Conclusions 39
  40. 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. 40

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