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1<br />Analytical Modeling of Optical Polarimetric Imaging Systems<br />2011 IEEE International Geoscience and <br />Remot...
Outline<br /><ul><li>Introduction
Background
Motivation
Analytical Model of Optical Polarization
Scene Model
Sensor Model
Processing Model</li></ul>Application for Target Detection<br /><ul><li>Conclusions</li></ul>2<br />
Outline<br /><ul><li>Introduction
Background
Motivation
Analytical Model of Optical Polarization
Scene Model
Sensor Model
Processing Model</li></ul>Application for Target Detection<br /><ul><li>Conclusions</li></ul>3<br />
Polarization of Light<br />4<br />Circular polarization<br />Linear polarization<br />http://en.wikipedia.org/wiki/Polariz...
5<br />Polarization-sensitive Optical System<br />θ3<br />θ2<br />θ1<br />Linear Polarizer<br />Optical Filter<br />CCD Ca...
6<br />Example of Polarization Imagery<br />Image was collected by Dr. Michael D. Presnar on May 25 2010.<br />
7<br />Polarization-sensitive Optical System<br />Linear Polarizer<br />Optical Filter<br />CCD Camera<br />S0<br />Iθ1<br...
Outline<br /><ul><li>Introduction
Background
Motivation
Analytical Model of Optical Polarization
Scene Model
Sensor Model
Processing Model</li></ul>Application for Target Detection<br /><ul><li>Conclusions</li></ul>8<br />
Analytical Modeling Framework<br />9<br />Processing Algorithm Description<br />Sensor Parameter Files<br />Material Datab...
Characterize Material Reflectance<br />Bidirectional reflectance distribution function (BRDF)<br />10<br />
Characterize Material Reflectance<br />Polarimetric BRDF (pBRDF)<br />The pBRDF can be expressed as the sum of a polarized...
12<br />pBRDF Model Determined DoLP<br />0<br />0<br />0<br />0<br />0<br />0<br />Vegetation DoLP <br />Glass DoLP<br />C...
13<br />Polar Coordinate Definition<br />
14<br />Polar Coordinate Definition<br />Sensor zenith angle<br />Radial coordinate<br />
15<br />Polar Coordinate Definition<br />Relative azimuth angle<br />Angular coordinate<br />
16<br />pBRDF Model Determined DoLP<br />0<br />0<br />0<br />0<br />0<br />0<br />Vegetation DoLP <br />Glass DoLP<br />C...
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  1. 1. 1<br />Analytical Modeling of Optical Polarimetric Imaging Systems<br />2011 IEEE International Geoscience and <br />Remote Sensing Symposium<br />LingfeiMeng: lxm8537@rit.edu<br />John P. Kerekes: kerekes@cis.rit.edu<br />Rochester Institute of Technology<br />29 July 2011<br />This work was supported by the AFOSR under agreement FA9550-08-1-0028.<br />
  2. 2. Outline<br /><ul><li>Introduction
  3. 3. Background
  4. 4. Motivation
  5. 5. Analytical Model of Optical Polarization
  6. 6. Scene Model
  7. 7. Sensor Model
  8. 8. Processing Model</li></ul>Application for Target Detection<br /><ul><li>Conclusions</li></ul>2<br />
  9. 9. Outline<br /><ul><li>Introduction
  10. 10. Background
  11. 11. Motivation
  12. 12. Analytical Model of Optical Polarization
  13. 13. Scene Model
  14. 14. Sensor Model
  15. 15. Processing Model</li></ul>Application for Target Detection<br /><ul><li>Conclusions</li></ul>3<br />
  16. 16. Polarization of Light<br />4<br />Circular polarization<br />Linear polarization<br />http://en.wikipedia.org/wiki/Polarizer<br />
  17. 17. 5<br />Polarization-sensitive Optical System<br />θ3<br />θ2<br />θ1<br />Linear Polarizer<br />Optical Filter<br />CCD Camera<br />Conventional Operation Methods<br />Pickering: 0°, 45°, 90°<br />Fessenkov: 0°, 60°, 120°<br />M-Pickering: 0°, 45°, 90°, 135°<br />Iθ1<br />S0<br />S1<br />DoLP<br />Iθ2<br />S2<br />Iθ3<br />Stokes Images<br />Multi-channel Intensity Images<br />
  18. 18. 6<br />Example of Polarization Imagery<br />Image was collected by Dr. Michael D. Presnar on May 25 2010.<br />
  19. 19. 7<br />Polarization-sensitive Optical System<br />Linear Polarizer<br />Optical Filter<br />CCD Camera<br />S0<br />Iθ1<br />S1<br />DoLP<br />Iθ2<br />S2<br />Iθ3<br />Stokes Images<br />Multi-channel Intensity Images<br />
  20. 20. Outline<br /><ul><li>Introduction
  21. 21. Background
  22. 22. Motivation
  23. 23. Analytical Model of Optical Polarization
  24. 24. Scene Model
  25. 25. Sensor Model
  26. 26. Processing Model</li></ul>Application for Target Detection<br /><ul><li>Conclusions</li></ul>8<br />
  27. 27. Analytical Modeling Framework<br />9<br />Processing Algorithm Description<br />Sensor Parameter Files<br />Material Database<br />Stokes Radiance<br />Statistics<br />Intensity Signal<br />Statistics<br />Processing<br />Model<br />Performance<br />Metrics<br />Sensor<br />Model<br />Scene<br />Model<br />User<br />Inputs<br />Scene<br />Description<br />Processing<br />Settings<br />Sensor<br />Settings<br />J.P. Kerekes and J.E. Baum, "Spectral Imaging System Analytical Model for Subpixel Object Detection," IEEE Transactions on Geoscience and Remote Sensing, vol. 40, no. 5, pp. 1088-1101, May 2002.<br />
  28. 28. Characterize Material Reflectance<br />Bidirectional reflectance distribution function (BRDF)<br />10<br />
  29. 29. Characterize Material Reflectance<br />Polarimetric BRDF (pBRDF)<br />The pBRDF can be expressed as the sum of a polarized specular component and an unpolarized diffuse component<br />11<br />M. W. Hyde, J. D. Schmidt, and M. J. Havrilla, “A geometrical optics polarimetric bidirectional reflectance distribution<br />function for dielectric and metallic surfaces,” Opt. Express, vol. 17, no. 24, pp. 22138–22153, Nov 2009.<br />
  30. 30. 12<br />pBRDF Model Determined DoLP<br />0<br />0<br />0<br />0<br />0<br />0<br />Vegetation DoLP <br />Glass DoLP<br />Concrete DoLP<br />
  31. 31. 13<br />Polar Coordinate Definition<br />
  32. 32. 14<br />Polar Coordinate Definition<br />Sensor zenith angle<br />Radial coordinate<br />
  33. 33. 15<br />Polar Coordinate Definition<br />Relative azimuth angle<br />Angular coordinate<br />
  34. 34. 16<br />pBRDF Model Determined DoLP<br />0<br />0<br />0<br />0<br />0<br />0<br />Vegetation DoLP <br />Glass DoLP<br />Concrete DoLP<br />
  35. 35. Modeling Sensor Reaching Radiance<br /><ul><li>The solar illumination and polarized atmospheric radiance are computed using MODTRAN-P.</li></ul>Direct solar reflected radiance <br /><ul><li>Surface reflected radiance from sky
  36. 36. With the upwelled radiance , the total sensor reaching radiance can be found as </li></ul>17<br />
  37. 37. 18<br />MODTRAN-P Predicted Downwelled Radiance<br />
  38. 38. 19<br />MODTRAN-P Predicted Downwelled Radiance<br />S1<br />S0<br />W/sr/cm2/μm<br />Normalized Unit<br />S2<br />DoLP<br />Normalized Unit<br />Normalized Unit<br />
  39. 39. 20<br />MODTRAN-P Predicted Skylight DoLP<br />
  40. 40. MODTRAN-P Predicted Skylight DoLP<br />21<br />
  41. 41. 22<br />Sensor Reaching Radiance Statistics<br /><ul><li>Mean</li></ul>For object surfaceviewed by the sensor over K pixels within a viewing angle range of<br /><ul><li>Covariance matrix</li></ul>Variance due to viewing geometry<br />Covariance matrix of sensor reaching radiance<br />
  42. 42. Analytical Modeling Framework<br />23<br />Processing Algorithm Description<br />Sensor Parameter Files<br />Material Database<br />Stokes Radiance<br />Statistics<br />Intensity Signal<br />Statistics<br />Processing<br />Model<br />Performance<br />Metrics<br />Sensor<br />Model<br />Scene<br />Model<br />User<br />Inputs<br />Scene<br />Description<br />Processing<br />Settings<br />Sensor<br />Settings<br />
  43. 43. Sensor Model<br />System matrix <br />24<br />m1<br />mi<br />mN<br />ψi<br />ψN<br />ψ1<br /><ul><li>Polarizer leakage effect</li></li></ul><li>Sensor input radiance —> electrons —>output signal<br />25<br />Sensor Model (cont.)<br /><ul><li>The total sensor noise can be expressed as
  44. 44. The covariance matrix of the N-channel signal is as</li></li></ul><li>Analytical Modeling Framework<br />26<br />Processing Algorithm Description<br />Sensor Parameter Files<br />Material Database<br />Intensity Signal<br />Statistics<br />Stokes Radiance<br />Statistics<br />Processing<br />Model<br />Performance<br />Metrics<br />Sensor<br />Model<br />Scene<br />Model<br />User<br />Inputs<br />Scene<br />Description<br />Processing<br />Settings<br />Sensor<br />Settings<br />
  45. 45. Processing Model<br />Incident Stokes vector estimation<br />27<br /><ul><li>DoLPcalculation </li></li></ul><li>Outdoor Imagery Collection<br />28<br />White painted panel<br />DoLP<br />Black painted panel<br />
  46. 46. Model Validation<br />29<br />Real<br />data<br />Analytical<br />model<br />
  47. 47. Analytical Modeling Framework<br />30<br />Processing Algorithm Description<br />Sensor Parameter Files<br />Material Database<br />Stokes Radiance<br />Statistics<br />Intensity Signal<br />Statistics<br />Processing<br />Model<br />Performance<br />Metrics<br />Sensor<br />Model<br />Scene<br />Model<br />Signal-to-clutter ratio (SCR)<br />User<br />Inputs<br />Processing<br />Settings<br />Scene<br />Description<br />Sensor<br />Settings<br />Interested vector space<br />Target mean<br />Background mean<br />Background covariance<br />
  48. 48. Outline<br /><ul><li>Introduction
  49. 49. Background
  50. 50. Motivation
  51. 51. Analytical Model of Optical Polarization
  52. 52. Scene Model
  53. 53. Sensor Model
  54. 54. Processing Model</li></ul>Application for Target Detection<br /><ul><li>Conclusions</li></ul>31<br />
  55. 55. Adaptive Polarimetric Target Detector (APTD)<br />32<br />RX<br />GLRT<br />ROC Curve Comparison<br />L. Meng and J. P. Kerekes, Adaptive Target Detection with a Polarization-sensitive Optical System, Applied Optics, Vol. 50, Issue 13, pp. 1925-1932 (2011) .<br />
  56. 56. Outline<br /><ul><li>Introduction
  57. 57. Background
  58. 58. Motivation
  59. 59. Analytical Model of Optical Polarization
  60. 60. Scene Model
  61. 61. Sensor Model
  62. 62. Processing Model</li></ul>Application for Target Detection<br /><ul><li>Conclusions</li></ul>33<br />
  63. 63. Conclusions<br />An analytical model for optical polarization has been designed, and initial validations have shown encouraging results.<br />A system performance metric based on signal-to-clutter ratio (SCR) has been suggested, and can be potentially used for system optimization.<br />34<br />Thank you!<br />
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