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Elastic LADAR Modeling for Synthetic Imaging Applications

Elastic LADAR Modeling for Synthetic Imaging Applications. By: Robin R. Burton. Topics to Be Covered. Overview Theory Approach Preliminary Results. Topics to Be Covered. Overview Theory Approach Preliminary Results. Topics to Be Covered. Overview Theory Approach

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Elastic LADAR Modeling for Synthetic Imaging Applications

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  1. Elastic LADAR Modeling for Synthetic Imaging Applications By: Robin R. Burton

  2. Topics to Be Covered • Overview • Theory • Approach • Preliminary Results

  3. Topics to Be Covered • Overview • Theory • Approach • Preliminary Results

  4. Topics to Be Covered • Overview • Theory • Approach • Preliminary Results

  5. Peak Power cL Time 1 Power Time 2 Time 3 R1 R2 R3 R4 R5 R6 R7 R8 R9 cL / 2 Range R Basic Elastic Equation Overlap Factor

  6. Pulse Characteristics Spatial Temporal

  7. Difference Between Basic Elastic and Topographic Equation Topographic Elastic

  8. Elastic Is Already Convolved

  9. Topographic Is Not

  10. The GFF Is a Combination of the Laser Beam and Sensor Field of View Overlap

  11. AND Signal Compression Due to the Optics Being Focused at Infinity

  12. GFF Equations What I call the GFF

  13. Noise Sources • Atmospheric Turbulence • Speckle • Temporal • Multiple Scatter • Multiple Bounce • Diffraction • Passive

  14. Noise Sources • Atmospheric Turbulence • Speckle • Temporal • Multiple Scatter • Multiple Bounce • Diffraction • Passive

  15. Source of Optical Turbulence Wind and convection produce air motion Air motion produces random temperature variations Random temperature variations produce small index-of-refraction fluctuations Optical Turbulence = Index-of-refraction fluctuations

  16. Source of Optical Turbulence • Two regimes of fluid flow • Laminar • Each parcel of fluid stays nearly || to adjacent parcels • Turbulent • Portions of the flow move radially as well as axially, forming eddies and vortices • Reynold’s number – index of the tendency of the flow to become turbulent • Identified in 1883 by British engineer and physicist Osborne Reynolds •  fluid velocity •  modulus of viscosity •  density • L characteristic length http://www.sigmaxi.org/amsci/articles/97articles/Hademenos-5.html

  17. Source of Optical Turbulence • Nonlinear process • Not derived from 1st principles • Velocity of sections fluctuate about the mean velocity of the entire flow • Continuous power spectrum • Kolmogorov • Valid 1/L0 <<  << 1/l0 • Tatarskii • Valid  >> 1/L0 • Von Kármán • Valid 0   <  Wind – velocity increases until crosses from laminar to turbulent flow Macroscopic to microscopic (Heat)

  18. Optical Turbulence Parameter • Index-of-Refraction Structure Constant • Measure of turbulence strength

  19. Index-of-Refraction Structure Constant • Several Models • Nonparametric • Submarine Laser Communication (SLC) Day and Night • Median values above Mt. Haleakala, Maui, Hawaii • AFGL AMOS night model • Mean values of Cn2 • Disagrees with SLC night • CLEAR I • Same procedure as AMOS • New Mexico desert • Parametric • Hufnagel ( 3-24 km) • Mid-latitude model, assumes a low tropopause • Since does not include the boundary layer can be used both day and night • 1 parameter = rms wind speed between 5-20 km in m/s • Hufnagel-Valley Model • Extension of Hufnagel model into the boundary layer • 2 parameters • RMS wind speed between 5-20 km in m/s • Value of Cn2 one meter above the ground • 5/7 model (coherence = 5 cm, isoplanatic angle = 7 rad

  20. Index-of-Refraction Structure Constant • Tatarski M = gradient of the refractive index L0 = outer scale of turbulence • NOAA (VanZandt) model • Excellent agreement with measurement • Most complex model and requires an expert to use • No boundary layer • Uses meteorological data • Other simpler Tatariski-based models exist

  21. Atmospheric Turbulence • Scintillation • Beam Effects • Beam Spread • Beam Wander • Image Effects • Image Blurring • Image Dancing

  22. Scintillation • Fluctuations in intensity due to turbulence • Spatial • Temporal (twinkling of a star) • Statistics are log amplitude • Experiment shows intensity is log-normal • Bx = amplitude covariance • <I> exact solution for all order perturbations • Rytov, <I> = 1

  23. Scintillation

  24. Scintillation • Normalized Intensity Variance Solutions • Plane Wave • Cn2 = index of refraction structure constant • Assumes a Point Receiver • I2(L) only valid for the optical axis

  25. Scintillation • Covariance • Points in observation plane separated by a Fresnel length are alternately bright and dark • Fresnel length = [(L-z)]1/2 • Large Aperture • Average Scintillation • Intensity Variance Reduced • MCF = aperture mutual coherence function

  26. Beam Effects • Beam Spreading • long-term beam radius • scales small wrt beam size broaden the beam • scales large wrt beam size cause tilt and deflect the beam • short-term beam radius • valid for 0 << D < L0 • D = aperature diameter • L0 = outer scale of turbulence • valid for weak turbulence diffraction turbulence focusing

  27. Beam Effects • 0 = Gaussian transverse coherence length (TCL) • 0s = plane wave short-term TCL • valid for TCL > l0 plane wave TCL when TCL > Dx set = 1

  28. Beam Effects • Beam Wander • motion of the beam centroid from pulse to pulse • 0 << D < L0

  29. Image Effects • Image Blurring • Counterpart to beam spread • Image Dancing • Counterpart to beam wander

  30. Image Effects • Phase Distortions • Image Blurring (Coherence Loss) • Long and Short Term MTF • Short Term is valid for exposures of .01s or less • b=1 near-field propagation, b=.5 far-field • near-field, log-amplitude fluctuations are negligible • r0 = atmospheric coherence length (Fried) • Valid for  < l0 = inner scale of turbulence Plane Wave

  31. Image Effects

  32. Image Effects • Image Dancing • Overall tilt caused by the advection of large eddies • Mean-square displacement in focal plane Plane Wave

  33. Noise Sources • Atmospheric Turbulence • Speckle • Temporal • Multiple Scatter • Multiple Bounce • Diffraction • Passive

  34. Speckle • 1st order statistics • Ideal • Finite Detector Size • I(,) = intensity profile across the target • S = area of the aperture • RS = aperture autocorrelation function • Valid only for an ensemble of independent speckle patterns

  35. Speckle • 2nd order statistics • RI = autocorrelation of speckle intensity • (x, y) = power spectral density • For an imaging geometry replace I(,) with P (,) • P (,) = pupil function

  36. Noise Sources • Atmospheric Turbulence • Speckle • Temporal • Multiple Scatter • Multiple Bounce • Diffraction • Passive

  37. Temporal • Correlation length • Atmosphere “frozen” for approx. 1-3 msec • If capture within, get a single speckle pattern • Correlation coefficient • Strongly target dependent

  38. Temporal • Temporal variations of meterological quantities at a point are produced by advection of these quantities by the mean wind speed flow • Advection time scale = L0 / V • V = mean wind speed transverse to the observation path • Approx. 1 sec • Eddy turnover time • Aprrox. 10 s – can usually be neglected in comparison with the mean wind flow • Basis of the Taylor frozen turbulence hypothesis • Turbulence eddies treated as frozen in space and moved across the observation path by the mean wind speed • Fails when V less than the magnitude of turbulent fluctuations in wind velocity • When the mean wind speed is near parallel to the line of sight

  39. Noise Sources • Atmospheric Turbulence • Speckle • Temporal • Multiple Scatter • Multiple Bounce • Diffraction • Passive

  40. Multiple Scatter • Most articles discuss multiple scattering in clouds, fog, and water • Any photon deflected from the beam axis encounters a time delay in reaching the target plane • Multipath time =  = t – z/c • We will be modeling multiple bounce

  41. I Sun R, t 2RS1 2RS2 (RS2+RS2:S3+RS3:S4) Moon Multiple Bounce and Ray Tracing Time delay = ( RS3:S4 + RS2:S3) - (RS2 ) Specular (skylight) RS3:S4 IS3 RS1 IS1 Specular (skylight) RS1:S2 IS2 RS2:S3 IS2

  42. Noise Sources • Atmospheric Turbulence • Speckle • Temporal • Multiple Scatter • Multiple Bounce • Diffraction • Passive

  43. Passive Sources DIRSIG Already Models Starlight Sunlight Moonlight Inside Buildings Streetlights Carlights

  44. Topics to Be Covered • Overview • Theory • Approach • Preliminary Results

  45. To Calculate the GFF Perform numerical integration – test each point to determine if it is in the red area Beam FOV Contribution area in the object plane for point xf, yf on the focal plane Obscuration Shadow Actual contribution area Receiver FOV

  46. Beam Wander / Image Dancing

  47. Validation • Conversion Utilities • DIRSIG gdb to an IRMA facet file • DIRSIG material file and associated emissivity files to an IRMA monostatic BRDF file

  48. DIAL Technique

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