1. Digital Imaging and Remote Sensing Laboratory An Atmospheric Correction Algorithm for Hyperspectral Imagery Ph.D. Dissertation Defense by: Lee C. Sanders Advisor: Dr. John R. Schott

2. Digital Imaging and Remote Sensing Laboratory Outline Radiometry Overview Overview of atmospheric correction Elevation,column water vapor, and aerosol extraction methods: NLLSSF APDA RIMAC Inversion from sensor radiance to ground reflectance Contribution from the surround using the phase function Results Summary

3. Digital Imaging and Remote Sensing Laboratory Hyperspectral Data

4. Digital Imaging and Remote Sensing Laboratory Radiative Transfer Paths Trapping EffectEnvironmental/Adjacency Effect

5. Digital Imaging and Remote Sensing Laboratory Radiative Transfer Paths Upwelled RadianceDownwelled Radiance

6. Digital Imaging and Remote Sensing Laboratory Radiative Transfer Paths Direct Solar

7. Digital Imaging and Remote Sensing Laboratory The Governing Radiative Transfer Equation

8. Digital Imaging and Remote Sensing Laboratory MODTRAN 4 Look-Up Table Surface Elevation Water Vapor Amount Visibility Channel # L grnd L u S L d L env

9. Digital Imaging and Remote Sensing Laboratory Outline Radiometry Overview Overview of atmospheric correction Elevation,column water vapor, and aerosol extraction methods: NLLSSF APDA RIMAC Inversion from sensor radiance to ground reflectance Contribution from the surround using the phase function Results Summary

10. Digital Imaging and Remote Sensing Laboratory Why Atmospheric Correction?  Make better quantitative estimates of absolute surface reflectances.  Improve existing climatology models for weather forecasting.  Monitor pollution.  Determine how atmospheric chemistry impacts the trend of global warming.

11. Digital Imaging and Remote Sensing Laboratory Atmospheric Correction 1) Determine terrain elevation by surface pressure depth in 760nm oxygen band using NLLSSF. 2) Determine the visibility for a given aerosol type using a NLLSSF over the.4-.7µm range or use the RIMAC method from.55-.7µm range. 3) Determine atmospheric column water vapor content using the NLLSSF technique or the APDA technique on the.940µm absorption band. 4) From the calculated aerosol profile, determine the phase function-derived convolution kernel.

12. Digital Imaging and Remote Sensing Laboratory Outline Radiometry Overview Overview of atmospheric correction Elevation,column water vapor, and aerosol extraction methods: NLLSSF APDA RIMAC Inversion from sensor radiance to ground reflectance Contribution from the surround using the phase function Results Summary

13. Digital Imaging and Remote Sensing Laboratory Non-Linear Least-Squared Spectral Fit (NLLSSF) Technique  g : Lambertian ground reflectance LSE = L sensor - ( L U + L env  g + [E o cos(  )  1  2 + L d  2 ]  g /  (1-S  g ) ) Minimize the difference between the sensor radiance and the MODRAN-derived sensor radiance by changing parameters in the governing radiative transfer equation:

14. Digital Imaging and Remote Sensing Laboratory NLLSSF Flex Parameters.760µm Oxygen Band  surface elevation.94µm H2O Band  water vapor .4-.70 µm Aerosol Band  visibility

15. Digital Imaging and Remote Sensing Laboratory NLLSSF Model of Reflectance  =  +  +  (H 2 O l ) In the case of the aerosol and water vapor bands the equation includes a non-linearity for liquid water : In the.760µm oxygen band, the target reflectance is assumed linear with  =  + 

16. Digital Imaging and Remote Sensing Laboratory General Flow Chart of Algorithm Input Constant Parameters (i.e geometry, particle density,etc) Solve for Total Column Water Vapor Using the.94µm band. Using all Solved Parameters, Invert Governing Radiometric Equation and Calculate Ground Reflectance. Input Image Pixel: Solve for Surface Pressure Depth in.76µm O 2 band. Solve for Atmospheric Visibility Given an Aerosol Type Using.4-7µm bands

17. Digital Imaging and Remote Sensing Laboratory Surface Pressure Elevation

18. Digital Imaging and Remote Sensing Laboratory NLLSSF Curve Fit

19. Digital Imaging and Remote Sensing Laboratory The APDA (Atmospheric Pre- Corrected Differential Absorption) Technique A water vapor band depth ratio method that relates an Rapda value to a atmospheric columnar water vapor value.

20. Digital Imaging and Remote Sensing Laboratory The APDA Technique The single channel/band Rapda: which can be extended to more channels:

21. Digital Imaging and Remote Sensing Laboratory The APDA Technique Relate R ratio with the corresponding water vapor amount (PW)  wv (PW) = R APDA = e -(  +  (PW)  ) Solving for water vapor: PW(R APDA )= ( -ln (R APDA ) -   ) 1/ 

22. Digital Imaging and Remote Sensing Laboratory The Regression-Intersection Method for Aerosol Correction (RIMAC) RIM depends on classification of homogenous areas with varying spectral contrasts. Band pair by band pair, the DCs for each class are regressed toward the origin and the intersections of all the classes are determined. Intersections below the “toe” of the histogram are discarded. The mean intersection becomes the estimate of total upwelling radiance.

23. Digital Imaging and Remote Sensing Laboratory Regression Intersection Method (RIM) R.E. Crippen (1987) DC band1 DC band2 DC u1 DC u2 class a class b Extrapolate data to intersection representing zero ground reflectance and upwelled radiance. Intersections determined for many classes in each band pair.

24. Digital Imaging and Remote Sensing Laboratory Regression Intersection Method for Aerosol Correction (RIMAC) Structural regression of bispectral classes. Classified Image Intersect class lines by extrapolation to zero reflectance point. Fit to MODTRAN LUT Extract spectral upwelled radiance from intersections’ averages.

25. Digital Imaging and Remote Sensing Laboratory Finding Atmospheric Visibility The total upwelled radiance is a combination of atmospheric upwelled scattered and environmental radiance. The average reflectance of the background is estimated either by Kaufman’s correlation with the 2.1µm band or by a simple linear fit to RIM total upwelled radiance estimate given an aerosol visibility.

26. Digital Imaging and Remote Sensing Laboratory Finding Atmospheric Visibility The visibility estimate is that which gives the minimum squared spectral radiance error compared to the RIM-derived total upwelled radiance. MODTRAN- Derived

27. Digital Imaging and Remote Sensing Laboratory Outline Radiometry Overview Overview of atmospheric correction Elevation,column water vapor, and aerosol extraction methods: APDA NLLSSF RIMAC Inversion from sensor radiance to ground reflectance Contribution from the surround using the phase function Results Summary

28. Digital Imaging and Remote Sensing Laboratory

29. First Pass Solve for Reflectance Once the atmospheric parameters have been set, the radiometric terms can be extracted from the MODTRAN 4 Look-Up Table and the sensor radiance can be inverted to ground reflectance for each pixel.

30. Digital Imaging and Remote Sensing Laboratory Second Pass Solve for Reflectance In the first pass, the surround reflectance was set to be equal to the target reflectance. To be rigorous, an approach had to be derived that estimated the aggregate reflectance contribution of the surround and the magnitude of the adjacency radiance.

31. Digital Imaging and Remote Sensing Laboratory Outline Radiometry Overview Overview of atmospheric correction Elevation,column water vapor, and aerosol extraction methods: APDA NLLSSF RIMAC Inversion from sensor radiance to ground reflectance Contribution from the surround using the phase function Results Summary

32. Digital Imaging and Remote Sensing Laboratory Environmental Contribution Light from the target surround is scattered into the sensor path The intensity distribution of radiance depends on the angle from sensor optical path and the aerosol phase function. The magnitude of the radiance depends on the target reflectance, the aerosol particle density, and the aerosol scattering cross-section.

33. Digital Imaging and Remote Sensing Laboratory Scattering From Surround Into The Sensor Path Is Governed By The Aerosol Phase Function Single Atmospheric Layer Diagram

34. Digital Imaging and Remote Sensing Laboratory The scattering function for a unit layer is weighted by the solid angle subtended by the layer pixel at altitude h. Sensor IFOV of An Atmospheric Layer

35. Digital Imaging and Remote Sensing Laboratory Atmospheric Layers 1 2 3 4 5 6

36. Digital Imaging and Remote Sensing Laboratory Calculating Average Reflectance The scattering contributions are summed over all the atmospheric layers: For this algorithm, the real interest is the fractional reflectance contribution of each pixel in the surround:

37. Digital Imaging and Remote Sensing Laboratory 0.400µm & 2.1µm Scattering Kernels of HYDICE Run 29

38. Digital Imaging and Remote Sensing Laboratory Western Rainbow Scattering Kernel

39. Digital Imaging and Remote Sensing Laboratory

40. Second Pass  Once a  avg map is created, the algorithm can proceed using the first pass atmospheric parameters as initial estimates.  The atmospheric parameters are re- calculated using the same methodology as the first pass except a different radiative transfer equation is used.  Final output is the reflectance map of the scene and the solved atmospheric parameters.

41. Digital Imaging and Remote Sensing Laboratory Outline Radiometry Overview Overview of atmospheric correction Elevation,column water vapor, and aerosol extraction methods: APDA NLLSSF RIMAC Inversion from sensor radiance to ground reflectance Contribution from the surround using the phase function Results Summary

42. Digital Imaging and Remote Sensing Laboratory Ground Target Layout

43. Digital Imaging and Remote Sensing Laboratory

58. Outline Radiometry Overview Overview of atmospheric correction Elevation,column water vapor, and aerosol extraction methods: APDA NLLSSF RIMAC Inversion from sensor radiance to ground reflectance Contribution from the surround using the phase function Results Summary

59. Digital Imaging and Remote Sensing Laboratory Summary A modular algorithm for inverting hyperspectral imagery from sensor radiance to ground reflectance has been constructed and validated. A new method for in-scene determination of aerosol-dependent visibility called RIMAC has been developed and tested. A new concept for adjacency-effect correction using the atmospheric scattering phase function has been implemented.

60. Digital Imaging and Remote Sensing Laboratory Possible Future Upgrades X Make option to take in DEM for surface elevation. X Incorporate Henyey-Greenstein phase function for multiple scattering. X Explore ratio technique on 760nm oxygen band for surface elevation. X Include a spectral correlation method to correct for spectral mis-matches in sensor radiance.

61. Digital Imaging and Remote Sensing Laboratory Acknowledgements Advisor: Dr. John R. Schott Staff Scientists: Rolando Raqueño and Scott Brown Special Thanks To: Dr. Robert Green, JPL (NLLSSF) Dr. Daniel Schlaepfer (APDA) Christopher Borel (APDA) Lex Berk and Dr. Stephen Adler-Golden, Spectral Sciences, Inc. Dr. Eric Crist, ERIM International, Inc. Sue Michel and Bob Krzaczek, Center for Imaging Science

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63. Amoeba Algorithm

64. Digital Imaging and Remote Sensing Laboratory

69. Amoeba Algorithm in Simplex Space

70. Digital Imaging and Remote Sensing Laboratory Compute LUT w/ L T (wv,h, )@  =0.4 and L atm (wv,h,  Calculate R APDA for each MODTRAN run by applying APDA equation to the LUT. Fit ratio values to PW and store the regression parameters. Assume starting PW 1 and subtract height dependent L u from image. Calculate APDA ratio and transform R APDA values to PW 2 using inverse mapping eq. Substitute the L atm in eq. with new PW dpndt values derived from LUT. Calculate RAPDA a 2nd time and trans- form to final PW 3 (x,y). General APDA Procedure

71. Digital Imaging and Remote Sensing Laboratory The purpose of this research is to contribute to the precision and accuracy of atmospheric characterization by developing an algorithmic approach that will:  Be computationally feasible,  Be radiometrically sound,  Include column water vapor determination  Be able to use in-scene techniques that preclude using radiosonde or ground truth. Atmospheric Correction