digital imaging and remote sensing laboratory an atmospheric correction algorithm for hyperspectral...

Digital Imaging and Remote Sensing Laboratory

An Atmospheric CorrectionAlgorithm for Hyperspectral

Imagery

Ph.D. Dissertation Defense by:

Lee C. Sanders

Advisor: Dr. John R. Schott


Outline

Radiometry OverviewOverview of atmospheric correctionElevation,column water vapor, and aerosol extraction methods:

NLLSSFAPDARIMAC

Inversion from sensor radiance to ground reflectanceContribution from the surround using the phase functionResultsSummary


Hyperspectral Data


Radiative Transfer Paths

Trapping Effect Environmental/Adjacency Effect



Upwelled Radiance Downwelled Radiance



Direct Solar


The Governing Radiative Transfer Equation

Lsensor=

ρ Lgrnd +LD( )1−ρS( )

+Lenvρ+Lu


MODTRAN 4 Look-Up Table

Surface ElevationWater Vapor AmountVisibilityChannel # Lgrnd Lu S Ld Lenv

1 0.3970 0.002090 0.002636 0.3270 0.009838 0.01263 2 0.4003 0.003521 0.004220 0.3238 0.01614 0.02048 3 0.4036 0.003754 0.004298 0.3207 0.01680 0.02111 4 0.4069 0.003828 0.004173 0.3176 0.01671 0.02076 5 0.4103 0.004131 0.004294 0.3146 0.01759 0.02163 6 0.4137 0.004340 0.004309 0.3116 0.01805 0.02196 7 0.4171 0.004393 0.004169 0.3087 0.01785 0.02151 8 0.4205 0.004350 0.003944 0.3057 0.01726 0.02059 9 0.4240 0.004342 0.003765 0.3028 0.01684 0.01989 10 0.4276 0.004077 0.003389 0.3000 0.01547 0.01811


Outline


NLLSSFAPDARIMAC



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.


Atmospheric Correction1) 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.


Outline


NLLSSFAPDARIMAC



Non-Linear Least-Squared Spectral Fit (NLLSSF) Technique

ρg: Lambertian ground reflectance

LSE = Lsensor - ( LU + Lenv ρg + [Eocos()12+ Ld2 ]ρg/ (1-Sρg) )

Minimize the difference between the sensor radiance and the MODRAN-derived sensor radiance by changing parameters in the governing radiative transfer equation:


NLLSSF Flex Parameters

.760µm Oxygen Band

surface elevation

.94µm H2O Band

water vapor

.4-.70 µm Aerosol Band

visibility


NLLSSF Model of Reflectance

ρ=++(H2Ol)

In the case of the aerosol and water vapor bandsthe equation includes a non-linearity for liquid water :

In the .760µm oxygen band, thetarget reflectance is assumed linear with

ρ = +


General Flow Chart of Algorithm

Input ConstantParameters(i.e geometry,particle density,etc)

Solve for TotalColumn Water Vapor Using the .94µm band.

Using all Solved Parameters, Invert Governing Radiometric Equation and Calculate Ground Reflectance.

Input Image Pixel:Solve for SurfacePressure Depth in.76µm O2 band.

Solve for AtmosphericVisibility Given an Aerosol Type Using.4-7µm bands


Surface Pressure Elevation

0.015

0.0175

0.02

0.0225

0.025

0.0275

0.03

0.745 0.75 0.755 0.76 0.765 0.77 0.775 0.78 0.785

HYDICE Channel Center Wavelength (micron)

Radiance (W/cm^2/sr/micron)

HYDICE Sensor

MODTRAN Calculated


NLLSSF Curve Fit

0

0.005

0.01

0.015

0.02

0.025

0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 1.02

HYDICE Channel Center Wavelength (microns)

Radiance (W/cm^2/sr/micron)

HYDICE Sensor

MODTRAN Calculated


The APDA (Atmospheric Pre-Corrected Differential Absorption)

Technique

A water vapor band depthratio method that relatesan Rapda value to a atmospheric columnar water vapor value.


The APDA TechniqueThe single channel/band Rapda:

Rapda =Lm−Latm,m(PW)

ω 1r (L 1r −Latm, 1r )+ω 2r (L 2r −Latm, 2r )

which can be extended to more channels:

RAPDA =

[Lm −Latm ,m] i

LIR ([ r ] j , [Lm −Latm ,m] j ) |[ m]i


The APDA Technique

Relate R ratio with the corresponding water vapor amount (PW)

wv(PW) = RAPDA = e -(+(PW))

Solving for water vapor:

PW(RAPDA)= ( -ln (RAPDA) -

)1/


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.


Regression Intersection Method (RIM)Regression Intersection Method (RIM)R.E. Crippen (1987)R.E. Crippen (1987)

DCband1

DCband2

DCu1

DCu2

class a

class b

• Extrapolate data to intersection representing zero ground reflectance and upwelled radiance.

• Intersections determined for many classes in each band pair.


Regression Intersection Method for Regression Intersection Method for Aerosol Correction (RIMAC)Aerosol Correction (RIMAC)

Structural regression of bispectral classes.

Classified Image

Intersect class lines by extrapolationto zero reflectance point.

Fit to MODTRAN LUT

Extract spectral upwelled radiance from intersections’ averages.


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.

Ltotal_upwelled=Lenvρavg+Latmos_upwelled


Finding Atmospheric Visibility

• The visibility estimate is that which gives the minimum squared spectral radiance error compared to the RIM-derived total upwelled radiance.

MSSE= LRIM _ upwelled−(Lu +Lenvρavg)∑

MODTRAN-Derived


Outline


APDANLLSSFRIMAC



First Pass Solve for Reflectance

Lsensor=

ρ Es cos12 + LD2[ ]1.0 −ρS( )

+ Lenvρ+ L u

Once the atmospheric parameters have been set, theradiometric terms can be extracted from the MODTRAN 4 Look-Up Table and the sensor radiancecan be inverted to ground reflectance for each pixel.


Second Pass Solve for Reflectance

Lsensor=

ρ Es cos12 + L D2[ ]1.0 −ρavgS( )

+ Lenvρavg + L u

In the first pass, the surround reflectance was set tobe equal to the target reflectance. To be rigorous,an approach had to be derived that estimatedthe aggregate reflectance contribution of the surround and the magnitude of the adjacency radiance.


Outline


APDANLLSSFRIMAC



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.

Lenv_total ( ) = (L θ,φ,)θ=0

π2

∫φ=0

2π

∫ layer(1)

layer(h)

∫ P(θ,, H)T2 (θ, )ρ (θ,φ, )d (sinθ )dθ dφ


Scattering FromSurround IntoThe Sensor PathIs Governed ByThe AerosolPhase Function

Single AtmosphericLayer Diagram


The scattering function for aunit layer is weightedby the solid anglesubtended by the layerpixel at altitude h.

Sensor IFOV of An AtmosphericLayer


Atmospheric Layers

1

2

3

4

5

6


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:

PSFunnorm(i, j) = (P θ, )Ω( ,i )j e-( 2aecθ+2b)Δyeρyeρ∑

PSF(i, j) =

(P θ, )Ω( ,i )j e-( 2asecθ+ 2b)

layers∑

(P θ, )Ω( ,i )j e-( 2asecθ+2b)

layers∑

j∑

i∑


0.400µm & 2.1µm Scattering Kernels of HYDICE Run 29


Western Rainbow Scattering Kernel


Adjacency Effect Radiance for HYDICE Run 29

0

0.002

0.004

0.006

0.008

0.01

0.012

0.4 0.65 0.9 1.15 1.4 1.65 1.9 2.15 2.4

Wavelength (µm)


Second PassOnce a ρavg 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.


Outline


APDANLLSSFRIMAC



Ground Target Layout


Error in Recovered Reflectance for HYDICE Run 29 Using Def_RIMAC_NL Options

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Wavelength (µm)

Reflectance Error

2% Delta r4% Delta r8% Delta r16% Delta r32% Delta r64% Delta r


Error in Second Pass Recovered Reflectance for HYDICE Run 29 Using Def_RIMAC_NL Options

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Wavelength (µm)

Reflectance Error



Error in Recovered Reflectance for HYDICE Run 29 Using All NLLSSF Options

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Wavelength (µm)

Reflectance Error



Error in Second Pass Recovered Reflectance for HYDICE Run 29 Using All NLLSSF Options

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Wavelength (µm)

Reflectance Error



Recovered Reflectance Second Pass Comparison for Total Inversion Using ALL NLLSSF Options on HYDICE Run 29

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

Wavelength (µm)

Reflectance

Truth 2%Tot_Inv 2%Truth 4%Tot Inv 4%Truth 8%Tot Inv 8%Truth 16%Tot Inv 16%Truth 32%Tot Inv 32%Truth 64%Tot Inv 64%


0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

2 4 8 16 32 64

ARMs Site Gray Panel Nominal Reflectance

RMS Reflectance Error

Default

NLLSSF

Def_RIMAC_NL

NLavg_RIMAC_NL

NLLSSF 2nd Pass

Def_RIMAC_NL 2nd Pass


Error in Recovered Reflectance for cr08m33 Using NLavg_RIMAC_NL Options on Old Panels

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

400 600 800 1000 1200 1400 1600 1800

Wavelength (nm)

Reflectance Error



Error in Second Pass Recovered Reflectance for cr08m33 Using NLavg_RIMAC_NL Options on Old Panels

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

400 600 800 1000 1200 1400 1600 1800

Wavelength (nm)

Reflectance Error



0

0.01

0.02

0.03

0.04

0.05

0.06

2 12 24 36 48 60Yuma Site Gray Panel Nominal Reflectance

Old Panels Run cr08m33


Default

NLLSSF

Def_RIMAC_NL

NLavg_RIMAC_NL

NLLSSF 2nd Pass

NLavg_RIMAC_NL 2ndPass


Error in Recovered Reflectance for cr15m50 Using NLLSSF Options for New Panels

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

400 600 800 1000 1200 1400 1600 1800

Wavelength (nm)

Reflectance Error



Error in Second Pass Recovered Reflectance for cr15m50 Using NLLSSF Options for New Panels

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

400 600 800 1000 1200 1400 1600 1800

Wavelength (nm)

Reflectance Error



0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

2 12 24 36 48 60Yuma Site Gray Panel Nominal Reflectance

New Panels Run cr15m50


Default

NLLSSF

Def_RIMAC_NL

NLavg_RIMAC_NL

Default_2nd Pass

NLLSSF 2nd Pass

Def_RIMAC_NL 2nd Pass

NLavg_RIMAC_NL 2ndPass


Estimated Average Image-Wide Reflectance Error for HYDICE Run 29 from Def_RIM_NLLSSF 2nd Pass

(average of all panel reflectances less than 18%)

-0.05

-0.045

-0.04

-0.035

-0.03

-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

Wavelength (µm)


Estimated Average Image-Wide Reflectance Error for HYDICE Run cr08m33 from NLLSSF 2nd Pass

(average of all Old panel reflectances less than 18%)

-0.05

-0.045

-0.04

-0.035

-0.03

-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800

Wavelength (nm)


Estimated Average Image-Wide Reflectance Error for HYDICE Run cr15m50 from NLLSSF 2nd Pass

(average of Old panel reflectances less than 18%)

-0.05

-0.045

-0.04

-0.035

-0.03

-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800

Wavelength (nm)


Outline


APDANLLSSFRIMAC



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.


Possible Future Upgrades

Make option to take in DEM for surface elevation.

Incorporate Henyey-Greenstein phase function for multiple scattering.

Explore ratio technique on 760nm oxygen band for surface elevation.

Include a spectral correlation method to correct for spectral mis-matches in sensor radiance.


Acknowledgements

Advisor: Dr. John R. SchottStaff 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


Radiometric Parameters for HYDICE Run 29

0

0.005

0.01

0.015

0.02

0.025

0.03

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

Wavelength (µm)

Lgrnd

Lu

Ld

Lenv

Ltrap


Amoeba Algorithm


-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

Wavelength (µm)

Reflectance Unit Error

Average Reflectance Error for HYDICE Run 29 2-64% Gray Panels


Error in Recovered Reflectance for Four Ground Truth Sites in AVIRIS Boreas Imagery (NLLSSFavg_RIMAC_NLLSSF Multiple Scattering Model)

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

400 450 500 550 600 650 700 750 800 850 900

Wavelength (nm)

Diff 535_97

Diff 193_256Diff 250_290

Diff 144_195


Error in Recovered Reflectance (Second Pass) for Four Ground Truth Sites in AVIRIS Boreas Imagery (NLLSSFavg_RIMAC_NLLSSF Multiple

Scattering Model)

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

400 450 500 550 600 650 700 750 800 850 900

Wavelength (nm)

Diff 535_97

Diff 193_256Diff 250_290

Diff 144_195


Comparison of Different Inversion Techniques from AVIRIS Boreas Image in Multiple Scattering Model

0.00

0.01

0.02

0.03

0.04

0.05

0.06

Diff 535_97 Diff 193_256 Diff 250_290 Diff 144_195

Truth Pixel Evaluated

RMS Error in Reflectance

NLavg_RIMAC_NL

Def_RIMAC_NL

NLLSSF

NLavg_RIMAC_NL 2nd Pass

NLLSSF 2nd Pass


Comparison of Recovered Reflectance for the 64% Gray Panel from HYDICE Run 29

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Wavelength (µm)

Truth

NLLSSF_avg

NLLSSF_Flat_avg


Amoeba Algorithm in Simplex Space


Compute LUTw/ LT(wv,h,)@ρ=0.4 and Latm (wv,h,)

Calculate RAPDA foreach MODTRAN runby applying APDAequation to the LUT.

Fit ratio values toPW and store theregressionparameters.

Assume startingPW1 and subtractheight dependentLu from image.

Calculate APDA ratioand transform RAPDA

values to PW2 usinginverse mapping eq.

Substitute the Latm

in eq. with newPW dpndt valuesderived from LUT.

Calculate RAPDA a2nd time and trans-form to final PW3(x,y).

General APDA Procedure


The purpose of this research is to contributeto 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

digital imaging and remote sensing laboratory an atmospheric correction algorithm for hyperspectral...

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