1. 1 Analytical Modeling of Optical Polarimetric Imaging Systems 2011 IEEE International Geoscience and Remote Sensing Symposium LingfeiMeng: lxm8537@rit.edu John P. Kerekes: kerekes@cis.rit.edu Rochester Institute of Technology 29 July 2011 This work was supported by the AFOSR under agreement FA9550-08-1-0028.

3. Background

4. Motivation

5. Analytical Model of Optical Polarization

6. Scene Model

7. Sensor Model

10. Background

11. Motivation

12. Analytical Model of Optical Polarization

13. Scene Model

14. Sensor Model

16. Polarization of Light 4 Circular polarization Linear polarization http://en.wikipedia.org/wiki/Polarizer

17. 5 Polarization-sensitive Optical System θ3 θ2 θ1 Linear Polarizer Optical Filter CCD Camera Conventional Operation Methods Pickering: 0°, 45°, 90° Fessenkov: 0°, 60°, 120° M-Pickering: 0°, 45°, 90°, 135° Iθ1 S0 S1 DoLP Iθ2 S2 Iθ3 Stokes Images Multi-channel Intensity Images

18. 6 Example of Polarization Imagery Image was collected by Dr. Michael D. Presnar on May 25 2010.

19. 7 Polarization-sensitive Optical System Linear Polarizer Optical Filter CCD Camera S0 Iθ1 S1 DoLP Iθ2 S2 Iθ3 Stokes Images Multi-channel Intensity Images

21. Background

22. Motivation

23. Analytical Model of Optical Polarization

24. Scene Model

25. Sensor Model

27. Analytical Modeling Framework 9 Processing Algorithm Description Sensor Parameter Files Material Database Stokes Radiance Statistics Intensity Signal Statistics Processing Model Performance Metrics Sensor Model Scene Model User Inputs Scene Description Processing Settings Sensor Settings 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.

28. Characterize Material Reflectance Bidirectional reflectance distribution function (BRDF) 10

29. Characterize Material Reflectance Polarimetric BRDF (pBRDF) The pBRDF can be expressed as the sum of a polarized specular component and an unpolarized diffuse component 11 M. W. Hyde, J. D. Schmidt, and M. J. Havrilla, “A geometrical optics polarimetric bidirectional reflectance distribution function for dielectric and metallic surfaces,” Opt. Express, vol. 17, no. 24, pp. 22138–22153, Nov 2009.

30. 12 pBRDF Model Determined DoLP 0 0 0 0 0 0 Vegetation DoLP Glass DoLP Concrete DoLP

31. 13 Polar Coordinate Definition

32. 14 Polar Coordinate Definition Sensor zenith angle Radial coordinate

33. 15 Polar Coordinate Definition Relative azimuth angle Angular coordinate

34. 16 pBRDF Model Determined DoLP 0 0 0 0 0 0 Vegetation DoLP Glass DoLP Concrete DoLP

36. With the upwelled radiance , the total sensor reaching radiance can be found as 17

37. 18 MODTRAN-P Predicted Downwelled Radiance

38. 19 MODTRAN-P Predicted Downwelled Radiance S1 S0 W/sr/cm2/μm Normalized Unit S2 DoLP Normalized Unit Normalized Unit

39. 20 MODTRAN-P Predicted Skylight DoLP

40. MODTRAN-P Predicted Skylight DoLP 21

42. Analytical Modeling Framework 23 Processing Algorithm Description Sensor Parameter Files Material Database Stokes Radiance Statistics Intensity Signal Statistics Processing Model Performance Metrics Sensor Model Scene Model User Inputs Scene Description Processing Settings Sensor Settings

46. Model Validation 29 Real data Analytical model

47. Analytical Modeling Framework 30 Processing Algorithm Description Sensor Parameter Files Material Database Stokes Radiance Statistics Intensity Signal Statistics Processing Model Performance Metrics Sensor Model Scene Model Signal-to-clutter ratio (SCR) User Inputs Processing Settings Scene Description Sensor Settings Interested vector space Target mean Background mean Background covariance

49. Background

50. Motivation

51. Analytical Model of Optical Polarization

52. Scene Model

53. Sensor Model

55. Adaptive Polarimetric Target Detector (APTD) 32 RX GLRT ROC Curve Comparison 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) .

57. Background

58. Motivation

59. Analytical Model of Optical Polarization

60. Scene Model

61. Sensor Model

63. Conclusions An analytical model for optical polarization has been designed, and initial validations have shown encouraging results. A system performance metric based on signal-to-clutter ratio (SCR) has been suggested, and can be potentially used for system optimization. 34 Thank you!