Meng.pptx

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Analytical Modeling of Optical Polarimetric Imaging Systems

2011 IEEE International Geoscience and Remote Sensing Symposium

Lingfei Meng: [email protected]

John P. Kerekes: [email protected]

Rochester Institute of Technology

29 July 2011This work was supported by the AFOSR under agreement FA9550-08-1-0028.

mailto:[email protected]

mailto:[email protected]

Outline

• Introduction− Background− Motivation

• Analytical Model of Optical Polarization− Scene Model− Sensor Model− Processing Model

• Application for Target Detection• Conclusions

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Outline




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Polarization of Light

4

http://en.wikipedia.org/wiki/Polarizer

Circular polarization

Linear polarization

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Iθ3

Optical Filter CCD CameraLinear Polarizer

Stokes Images

Multi-channel Intensity Images

θ1θ2θ3

Iθ2

Iθ1S1S2

S0DoLP

Conventional Operation MethodsPickering: 0°, 45°, 90°Fessenkov: 0°, 60°, 120°M-Pickering: 0°, 45°, 90°, 135°

Polarization-sensitive Optical System

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Example of Polarization Imagery

Image was collected by Dr. Michael D. Presnar on May 25 2010.

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Iθ3

Optical Filter CCD CameraLinear Polarizer

Stokes Images

Multi-channel Intensity Images

Iθ2

Iθ1S1S2

S0DoLP

Polarization-sensitive Optical System

Outline




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Analytical Modeling Framework

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ProcessingModel

SensorModel

SceneModel

PerformanceMetrics

Material Database

Sensor Parameter

Files

Processing Algorithm

Description

SceneDescription

SensorSettings

ProcessingSettings

UserInputs

Stokes RadianceStatistics

Intensity Signal

Statistics

,S LSL , II

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.

Characterize Material Reflectance• Bidirectional reflectance distribution function (BRDF)

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( , )

( , )r r

i i

Lf

E

( , )i iE

( , )r rL

ir

i

r

Characterize Material Reflectance

• Polarimetric BRDF (pBRDF)The pBRDF can be expressed as the sum of a polarized specular component and an unpolarized diffuse component

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00 01 02

10 11 12

20 21 22

f f f

f f f

f f f

F

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.

0 00 01 02 0

1 10 11 12 1

2 20 21 22 2out in

S f f f S

L S f f f E S

S f f f S

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Glass DoLP Concrete DoLP Vegetation DoLP

60i

80i

pBRDF Model Determined DoLP

0 0 0

0 0 0

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Polar Coordinate Definition

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Sensor zenith angle Radial coordinate

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Relative azimuth angle Angular coordinate

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Glass DoLP Concrete DoLP Vegetation DoLP

60i

80i

pBRDF Model Determined DoLP

0 0 0

0 0 0

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• Direct solar reflected radiance

0 1 2 00 10 20cosr i sr r r

T TL L E fL f f L

• Surface reflected radiance from sky

• With the upwelled radiance , the total sensor reaching radiance can be found as

0 1 2 ,( , ) cosT

d i d i id d dL L dL L F L

0 1 2

T

u u u uL L LL

0 1 2

T

S d uS S rSL L L L L L L

• The solar illumination and polarized atmospheric radiance are computed using MODTRAN-P.

Modeling Sensor Reaching Radiance

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MODTRAN-P Predicted Downwelled Radiance

MODTRAN-P Input Parameter Setting

Atmospheric Model 1976 US Standard

Haze Parameter Rural Extinction

Surface Meteorological Range 23 km

Scattering Type Single

Solar Zenith Angle 60°

Day of the Year 170

Center Wavelength 450 nm

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S1

S2 DoLP

MODTRAN-P Predicted Downwelled RadianceS0

W/s

r/cm

2 /μm

Nor

mal

ized

Uni

t

Nor

mal

ized

Uni

tN

orm

aliz

ed U

nit

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MODTRAN-P Predicted Skylight DoLP

MODTRAN-P Predicted Skylight DoLP

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Sensor Reaching Radiance Statistics• Mean

For object surface viewed by the sensor over K pixels within a viewing angle range of

( , )r

,

1( )

r

r

S i Si rL LK

• Covariance matrix Variance due to viewing geometry

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1( )

1

r

r

g i Si r SiL LK

Covariance matrix of sensor reaching radiance

LS g v


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ProcessingModel

SensorModel

SceneModel

PerformanceMetrics

Material Database

Sensor Parameter

Files


Description

SceneDescription

SensorSettings

ProcessingSettings

UserInputs


Intensity Signal

Statistics

,S LSL , II

Sensor Model

• System matrix

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ψ1 ψiψN

m1

• Polarizer leakage effect

mi mN

• Sensor input radiance —> electrons —>output signal

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2

· · · · ·( ) ·

1 4 #i t

i d e

L tI R d N g

f h c

• The total sensor noise can be expressed as

2ni e i cg I

• The covariance matrix of the N-channel signal is as

TI LS n M M

Sensor Model (cont.)


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ProcessingModel

SensorModel

SceneModel

PerformanceMetrics

Material Database

Sensor Parameter

Files


Description

SceneDescription

SensorSettings

ProcessingSettings

UserInputs


Intensity Signal

Statistics

,S LSL , II

Processing Model

• Incident Stokes vector estimation

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1S M I

TS I W W

• DoLP calculation 2 2

1 22

0

S SDoLP

S

2 2 22 2

1 22 1 20 1 22 2 2 2 2

0 0 1 2 0 1 2

,

2 iji ji

DoLP S S S

Si

j

Sj

S S S S

S S S S S S S

DoLP DoLP

S S

1( )W M

Outdoor Imagery Collection

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0.05

0.1

0.15

0.2

0.25

0.3

0.35

White painted panel

Black painted panel

DoL

P

Model Validation

0 0.2 0.4 0.60

10

20

30

40

50

S1

Pro

babi

lity

Den

sity Black

White

−0.1 0 0.1 0.2 0.3 0.40

10

20

30

40

50

S2

BlackWhite

0 0.2 0.4 0.60

10

20

30

40

50

DoLP

BlackWhite

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0 0.2 0.4 0.60

10

20

30

40

50

S1

Pro

babi

lity

Den

sity Black

White

−0.1 0 0.1 0.2 0.3 0.40

10

20

30

40

50

S2

BlackWhite

0 0.2 0.4 0.60

10

20

30

40

50

DoLP

BlackWhite

Realdata

Analyticalmodel


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ProcessingModel

SensorModel

SceneModel

PerformanceMetrics

Material Database

Sensor Parameter

Files


Description

SceneDescription

SensorSettings

ProcessingSettings

UserInputs


Intensity Signal

Statistics

,S LSL , II

Signal-to-clutter ratio (SCR) 2 1( ) ( )T

t b t bSCR V V

t Target mean

b Background meanV Background covariance

V Interested vector space

Outline




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Adaptive Polarimetric Target Detector (APTD)

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1, , N initial

Acquire Intensity & Stokes

Images

Stokes Vector Statistical Model

Searching Optimal Multi-channel

s.t. Max(SCRV)V

, vSS ,t bμ μ Stop Criterion

Meet?

Multi-channel Setting 1, , N optimal No

Intensity Images

Target Detection

Yes

Initial Multi-channel Setting

Stokes Parameter Images

Sensor Noise Calibration

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) .

0 0.1 0.2 0.3 0.4 0.50

0.2

0.4

0.6

0.8

1

Probability of False Alam (PFA)

Prob

abili

ty o

f D

etec

tion

(PD

)

APTDM−PickeringFessenkovPickering

0 0.1 0.2 0.3 0.4 0.50

0.2

0.4

0.6

0.8

1

Probability of False Alam (PFA)

Prob

abili

ty o

f D

etec

tion

(PD

)

APTDM−PickeringFessenkovPickering

ROC Curve Comparison

RX GLRT

Outline




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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.

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Thank you!