Atmospheric aberrations in coherent laser systems Snowmass, July 12, 2007 Aniceto Belmonte [email_address]
Atmospheric Optical Systems
<ul><li>Simulated Experiments on Atmospheric Propagation </li></ul><ul><li>Compensation Methods on Coherent Measurements <...
Work Basis <ul><li>O ptical phase perturbations  destroy the spatial coherence  of a laser beam as it propagates through t...
Atmospheric Effects on Received Signal WIDE-BAND SIGNAL-TO-NOISE RATIO PHASE DISTORTION BEAM WANDER BEAM SPREADING SCINTIL...
Available Techniques !? Rytov Simulations Asymptotic Heuristic ?
Split-Step Solution <ul><li>Based on the Fresnel approximation to the wave equation </li></ul><ul><li>Atmosphere is modele...
Receiver Plane Formulation LO Beam Receiver Transmitted Beam i Reflected Beam Scatters Turbulence
Target Plane Formulation Receiver Transmitted Beam i BPLO Scatters LO Beam
Simulated Performance: Monostatic 0 1000 2000 3000 4000 5000 -6 -4 -2 0 2 4 Coherent Power Gain [dB] Lidar Range [m] C n 2...
Simulated Performance: Bistatic T BPLO 0 1000 2000 3000 4000 5000 -8 -6 -4 -2 0 Lidar Range [m] Coherent Power Gain [dB] -...
Misalignment Effects 0 500 1000 1500 2000 2500 3000 -16 -12 -8 -4 0 4 Coherent Power Gain [dB] Monostatic Bistatic 10  μ r...
Coherent Power Fluctuations 0 0.1 0.2 0.3 0.4 0.5 0.6 Strong C n 2 Coherent Power Standard Deviation 0 1000 2000 3000 4000...
Uncertainty Temporal Averaging 10 0 10 1 10 2 10 3 10 4 10 -3 10 -2 10 -1 10 0 10 1 N -1/2 V   = 10 m/s R   = 5 km Pulses ...
Free-Space Optical Communication Systems <ul><li>Optical phase perturbations restricts the received power levels in optica...
<ul><li>Simulated Experiments on Atmospheric Propagation </li></ul><ul><li>Compensation Methods on Coherent Measurements <...
APERTURE INTEGRATOR/ARRAYS PHASE COMPENSATED RECEIVERS RECIPROCITY POINTING ATMOSPHERIC COMPENSATION TECHNIQUES PHASE DIST...
Phase Compensation on Coherent FSO <ul><li>In communication with optical heterodyne detection, as in imaging systems, the ...
Atmospheric Compensation Needs in FSO Detector-plane Intensity Distributions
Adaptive Optics in Direct-Detection FSO Transmitter High Transmission Bandwidth Any Coding Scheme Horizontal/Slant Line-of...
FSO Coherent Power Gain 0 10 20 30 40 50 60 70 80 0 2 4 6 8 10 12 14 Modes Removed C n 2  = 10 -13  m -2/3 R   = 3  k m 0 ...
<ul><li>The target is a distributed aerosol, which creates target speckle with decorrelation times in the order of 1  μ s....
The Optimization Problem <ul><li>We need to consider the speckle averaged coherent signal.  Consequently, a rapid pulse re...
Non-Conjugated Adaptive Optics  <ul><li>There is another wavefront control paradigm. Instead of considering the wavefront ...
Blind (Free-Model) Compensation LO Beam Receiver Transmitted Beam i Reflected Beam Scatters Controller
Blind (Free-Model) Algorithms <ul><li>The algorithm choose the mirror shape to maximize the speckle averaged coherent sign...
LO Atmospheric Beam Projection <ul><li>The problem of adaptive laser beam projection onto an extended aerosol target in th...
Coherent Power as Quality Metric 0 10 20 30 40 50 20 22 24 26 28 Overlap Integral (Coherent Power) Evolution Iteration Num...
LO Control Wavefront 0 5 10 15 20 25 -15 -10 -5 0 5 10 Zernike Order Energy [dB]] Defocus Astigmatism Coma Spherical Aberr...
Beam Projection
Index <ul><li>Simulated Experiments on Atmospheric Propagation </li></ul><ul><li>Compensation Methods on Coherent Measurem...
Coherent Power Gain vs Elevation Angle 0 10 20 30 40 50 0 1000 2000 3000 4000 5000 Coherent Power Gain [%] Altitude [m] Mo...
Coherent Power Gain 0 10 20 30 40 50 0 1000 2000 3000 4000 5000 Coherent Power Gain [%] Altitude [m] Moderate C n 2 30 ° 4...
Coherent Power Gain 0 5 10 15 20 25 0 1000 2000 3000 4000 5000 Coherent Power Gain [%] Altitude [m] Moderate C n 2 30 ° 45...
Coherent Power Gain vs Aperture Size 0 10 20 30 40 50 0 1000 2000 3000 4000 5000 Coherent Power Gain [%] Altitude [m] Mode...
0 10 20 30 40 50 0 1000 2000 3000 4000 5000 Coherent Power Gain [%] Altitude [m] Moderate C n 2 0 10 20 30 40 50 0 1000 20...
Misalignment Compensation 0 5 10 15 0 1000 2000 3000 4000 5000 Coherent Power Gain [dB] Moderate C n 2 λ   = 1   m D = 20...
Misalignment Compensation 0 5 10 15 20 0 1000 2000 3000 4000 5000 Coherent Power Gain [dB] Altitude [m] 30  μ m Moderate C...
<ul><li>Simulated Experiments on Atmospheric Propagation </li></ul><ul><li>Compensation Methods on Coherent Measurements <...
Technique Summary <ul><li>Feasibility of Beam Propagation Technique Well-known Limits of Applicability </li></ul><ul><li>S...
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Belmonte

  1. 1. Atmospheric aberrations in coherent laser systems Snowmass, July 12, 2007 Aniceto Belmonte [email_address]
  2. 2. Atmospheric Optical Systems
  3. 3. <ul><li>Simulated Experiments on Atmospheric Propagation </li></ul><ul><li>Compensation Methods on Coherent Measurements </li></ul><ul><li>Beam Projection on Coherent Lidars </li></ul><ul><li>Conclusions </li></ul>Index
  4. 4. Work Basis <ul><li>O ptical 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 . </li></ul><ul><li>T emporal fading associate with optical amplitude fluctuations increases the uncertainty in the measurements. </li></ul><ul><li>P erformance limitations imposed by atmospheric turbulence on specific coherent systems need to be quantify. </li></ul><ul><li>Main task is the quantification of the performance achievable in coherent optical systems using atmospheric compensation techniques . </li></ul>
  5. 5. Atmospheric Effects on Received Signal WIDE-BAND SIGNAL-TO-NOISE RATIO PHASE DISTORTION BEAM WANDER BEAM SPREADING SCINTILLATION RECEIVED POWER UNCERTAINTY RECEIVED POWER LEVEL SENSITIVITY LINK QUALITY SIGNAL RELATIVE ERROR
  6. 6. Available Techniques !? Rytov Simulations Asymptotic Heuristic ?
  7. 7. Split-Step Solution <ul><li>Based on the Fresnel approximation to the wave equation </li></ul><ul><li>Atmosphere is modeled as a set of two-dimensional random phase screens </li></ul><ul><li>All simulations use the Hill turbulence spectrum (1-mm to 5-m scales) </li></ul><ul><li>Uniform and Non-Uniform (Hufnagel-Valley model) turbulence profiles </li></ul><ul><li>Temporal and spatial analysis </li></ul>R z Gaussian Beam p x Aperture Atmospheric Turbulence Distorted Beam p y v x v y
  8. 8. Receiver Plane Formulation LO Beam Receiver Transmitted Beam i Reflected Beam Scatters Turbulence
  9. 9. Target Plane Formulation Receiver Transmitted Beam i BPLO Scatters LO Beam
  10. 10. Simulated Performance: Monostatic 0 1000 2000 3000 4000 5000 -6 -4 -2 0 2 4 Coherent Power Gain [dB] Lidar Range [m] C n 2 = 10 -12 m -2/3 λ = 2 μ m C n 2 = 10 -13 m -2/3
  11. 11. Simulated Performance: Bistatic T BPLO 0 1000 2000 3000 4000 5000 -8 -6 -4 -2 0 Lidar Range [m] Coherent Power Gain [dB] -10 C n 2 = 10 -12 m -2/3 λ = 2 μ m C n 2 = 10 -13 m -2/3
  12. 12. Misalignment Effects 0 500 1000 1500 2000 2500 3000 -16 -12 -8 -4 0 4 Coherent Power Gain [dB] Monostatic Bistatic 10 μ rad 20 μ rad 30 μ rad 40 μ rad D=36 cm C n 2 = 10 -12 m -2/3 λ = 2 μ m Range [m] θ 0 500 1000 1500 2000 2500 3000 -20 -15 -10 -5 0 5 Range [m] Monostatic Bistatic D= 9 cm Coherent Power Gain [dB]
  13. 13. Coherent Power Fluctuations 0 0.1 0.2 0.3 0.4 0.5 0.6 Strong C n 2 Coherent Power Standard Deviation 0 1000 2000 3000 4000 5000 Altitude [m] 0 0.1 0.2 0.3 0.4 0.5 Coherent Power Standard Deviation 30 ° 60 ° 90 ° (Zenith) Moderate C n 2 λ = 2  m 0 1000 2000 3000 4000 5000
  14. 14. Uncertainty Temporal Averaging 10 0 10 1 10 2 10 3 10 4 10 -3 10 -2 10 -1 10 0 10 1 N -1/2 V = 10 m/s R = 5 km Pulses Averaged 1 kHz 5 kHz 10 kHz C n 2 = 10 -13 m -2/3 λ = 2  m 10 -3 10 -2 10 -1 10 0 10 1 Normalized Standard Deviation N -1/2 10 0 10 1 10 2 10 3 10 4 Pulses Averaged R = 3 km C n 2 = 10 -12 m -2/3
  15. 15. Free-Space Optical Communication Systems <ul><li>Optical phase perturbations restricts the received power levels in optical communications. </li></ul><ul><li>Temporal fading associate with optical amplitude fluctuations increases the error in the communication link. </li></ul>LO Beam Receiver Transmitter Signal Beam i
  16. 16. <ul><li>Simulated Experiments on Atmospheric Propagation </li></ul><ul><li>Compensation Methods on Coherent Measurements </li></ul><ul><li>Beam Projection on Coherent Lidars </li></ul><ul><li>Conclusions </li></ul>Index
  17. 17. APERTURE INTEGRATOR/ARRAYS PHASE COMPENSATED RECEIVERS RECIPROCITY POINTING ATMOSPHERIC COMPENSATION TECHNIQUES PHASE DISTORTION BEAM WANDER BEAM SPREADING SCINTILLATION ATMOSPHERIC EFFECTS ON RECEIVED SIGNAL DIRECT DETECTION GROUND, DOWNLINK DIRECT, HETERODYNE GROUND, DOWNLINK DIRECT, HETERODYNE GROUND, DOWN/UP LINKS Atmospheric Compensation Techniques
  18. 18. Phase Compensation on Coherent FSO <ul><li>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). </li></ul>LO Beam Receiver Transmitter Wavefront Sensor & Controller Signal Beam i
  19. 19. Atmospheric Compensation Needs in FSO Detector-plane Intensity Distributions
  20. 20. Adaptive Optics in Direct-Detection FSO Transmitter High Transmission Bandwidth Any Coding Scheme Horizontal/Slant Line-of-Sight Path Near and Far Field Deployment Distance Any Divergence Angle Near IR/Visible Wavelength Any Optical Power Medium Low (Day Time) Atmospheric Seeing High (Day Time) Solar Background Any Scintillation Any Visibility Receiver Single/Multiaperture Reception Diversity Small (APD) Detector Active Area Small (<1 mrad) Receiver Field of View >10 cm Receive Lens Diameter Any Receiver Sensitivity
  21. 21. FSO Coherent Power Gain 0 10 20 30 40 50 60 70 80 0 2 4 6 8 10 12 14 Modes Removed C n 2 = 10 -13 m -2/3 R = 3 k m 0 10 20 30 40 50 60 70 80 0 2 4 6 8 10 Modes Removed Coherent Power Gain (dB) C n 2 = 10 -14 m -2/3 λ = 1.55 μ m D=30 cm D=20 cm D=10 cm
  22. 22. <ul><li>The target is a distributed aerosol, which creates target speckle with decorrelation times in the order of 1 μ s. </li></ul><ul><li>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 . </li></ul>Speckle in Coherent Lidar LO Beam Receiver Wavefront Sensor & Controller i Transmitted Beam Reflected Beam Scatters
  23. 23. The Optimization Problem <ul><li>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. </li></ul><ul><li>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. </li></ul><ul><li>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. </li></ul>
  24. 24. Non-Conjugated Adaptive Optics <ul><li>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. </li></ul><ul><li>We analyze a system implementing a non-conjugate adaptive optics with use efficient parallel model-free optimization algorithms (Gradient descent optimization). </li></ul><ul><li>The metric can be considered as a functional that depends on the phase aberrations introduced by atmospheric turbulence. </li></ul>
  25. 25. Blind (Free-Model) Compensation LO Beam Receiver Transmitted Beam i Reflected Beam Scatters Controller
  26. 26. Blind (Free-Model) Algorithms <ul><li>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. </li></ul><ul><li>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: </li></ul>
  27. 27. LO Atmospheric Beam Projection <ul><li>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. </li></ul><ul><li>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. </li></ul>Receiver Transmitted Beam i Scatters Controller BPLO
  28. 28. Coherent Power as Quality Metric 0 10 20 30 40 50 20 22 24 26 28 Overlap Integral (Coherent Power) Evolution Iteration Number Quality Metric 0 10 20 30 40 50 -0.4 -0.2 0 0.2 0.4 Quality Metric Gradient 0 1000 2000 3000 4000 5000 6000 7000 16 18 20 22 24 26 28 30 Range [m] Overlap Integral Overlap Integral (Coherent Power) Range Dependency
  29. 29. LO Control Wavefront 0 5 10 15 20 25 -15 -10 -5 0 5 10 Zernike Order Energy [dB]] Defocus Astigmatism Coma Spherical Aberration Distortion
  30. 30. Beam Projection
  31. 31. Index <ul><li>Simulated Experiments on Atmospheric Propagation </li></ul><ul><li>Compensation Methods on Coherent Measurements </li></ul><ul><li>Beam Projection on Coherent Lidars </li></ul><ul><li>Conclusions </li></ul>
  32. 32. Coherent Power Gain vs Elevation Angle 0 10 20 30 40 50 0 1000 2000 3000 4000 5000 Coherent Power Gain [%] Altitude [m] Moderate C n 2 30 ° 45 ° 60 ° λ = 1  m 90 ° (Zenith) D = 40 cm 0 5 10 15 20 25 Coherent Power Gain [%] Strong C n 2 0 1000 2000 3000 4000 5000
  33. 33. Coherent Power Gain 0 10 20 30 40 50 0 1000 2000 3000 4000 5000 Coherent Power Gain [%] Altitude [m] Moderate C n 2 30 ° 45 ° 60 ° λ = 1  m 90 ° (Zenith) D = 20 cm 0 5 10 15 20 25 0 1000 2000 3000 4000 5000 Coherent Power Gain [%] Strong C n 2
  34. 34. Coherent Power Gain 0 5 10 15 20 25 0 1000 2000 3000 4000 5000 Coherent Power Gain [%] Altitude [m] Moderate C n 2 30 ° 45 ° 60 ° λ = 1  m 90 ° (Zenith) D = 10 cm 0 5 10 15 20 25 0 1000 2000 3000 4000 5000 Coherent Power Gain [%] Strong C n 2
  35. 35. Coherent Power Gain vs Aperture Size 0 10 20 30 40 50 0 1000 2000 3000 4000 5000 Coherent Power Gain [%] Altitude [m] Moderate C n 2 0 10 20 30 40 50 0 1000 2000 3000 4000 5000 Coherent Power Gain [%] Strong C n 2 λ = 1  m D = 10 cm θ = 90° (Zenith) D = 20 cm D = 40 cm
  36. 36. 0 10 20 30 40 50 0 1000 2000 3000 4000 5000 Coherent Power Gain [%] Altitude [m] Moderate C n 2 0 10 20 30 40 50 0 1000 2000 3000 4000 5000 Coherent Power Gain [%] λ = 1  m D = 10 cm θ = 45° D = 20 cm D = 40 cm Strong C n 2 Coherent Power Gain
  37. 37. Misalignment Compensation 0 5 10 15 0 1000 2000 3000 4000 5000 Coherent Power Gain [dB] Moderate C n 2 λ = 1  m D = 20 cm 90° (Zenith) 60° 30° Misalignment 20 μ m 0 5 10 15 0 1000 2000 3000 4000 5000 Coherent Power Gain [dB] Altitude [m] Moderate C n 2 Misalignment 20 μ m λ = 1  m D = 10 cm θ = 90° (Zenith) D = 20 cm D = 40 cm
  38. 38. Misalignment Compensation 0 5 10 15 20 0 1000 2000 3000 4000 5000 Coherent Power Gain [dB] Altitude [m] 30 μ m Moderate C n 2 λ = 1  m D = 20 cm θ = 90° (Zenith) 20 μ m 10 μ m 5 μ m
  39. 39. <ul><li>Simulated Experiments on Atmospheric Propagation </li></ul><ul><li>Compensation Methods on Coherent Measurements </li></ul><ul><li>Beam Projection on Coherent Lidars </li></ul><ul><li>Conclusions </li></ul>Index
  40. 40. Technique Summary <ul><li>Feasibility of Beam Propagation Technique Well-known Limits of Applicability </li></ul><ul><li>Simulation of Coherent Laser System Performance Practical Systems Analysis </li></ul><ul><li>Results are encouraging Compensation techniques may extend the deployment distance and/or quality of atmospheric optical systems. </li></ul><ul><li>Room for improvement New algorithms and Full Field Compensation </li></ul><ul><li>Results must be viewed as benchmarks whose achievements may require the development of devices . </li></ul>
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