1

VIS-SPEAR Calibration Update

Prepared forAir Force Research Laboratory

AFRL/VS

Aerodyne Research, Inc.

45 Manning Road

Billerica, MA 01821-3976

12 March 2002

2

Agenda

•VIS SPEAR Status – Calibration and Early Retrieval Examples Jones (45)

•VMP Calibration Procedures? Fetrow (15)

•MODTRAN 4-P Validation Status Conant (45)

•Feedback on the MODTRAN 4-P Validation Plan and Implementation Fetrow (15)

•Coordinated Measurements for VIS SPEAR and VMP at KAFB? All (15)

– Multiple Objectives

– Other Sensors: Research Scanning Polarimeter; AERONET Cimel

– Anticipated Schedule

•LWIR SPEAR Status Scott (15)

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Meta-Agenda

• Recently achieved key SPEAR-TIP/PolTran milestones:– VIS-SPEAR is now working & field-worthy– VIS-SPEAR is spectro/polar/radiometrically calibrated– We are retrieving Stokes spectrum– Remote Surface Orientation Measurement (RSOM) patent

submitted– PolTran validation plan & results synergistic w/ NASA effort

• ~ $50K funded ARI effort remaining; additional $50K funded ARI set-aside for “field test”

Where-To From Here?

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Where-To From Here?

• We ask both (1) for optimally directing remaining funds, and (2) to anticipate prospective efforts

• Possible Paths– VIS-SPEAR field collects -

• Targets; surfaces

• Atmospherics (IAW PolTran validation plan)– Likely NASA synergy

– PolTran aerosol parametric sensitivity determination– RSOM exploitation for target discrimination– (XX)IR-SPEAR?

Can we discuss (our roles in) AFRL SpectroPolarimetry Roadmap?

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Recent & Prospective Progress

• We demonstrated calibrated “narrowband” (~14nm resolution) polarimetry against data.

• VIS-SPEAR is ready for local field data collects (FEB02)

• Steps remaining for VIS-SPEAR readiness for field test campaigns:– Improve mounting (CNC table too cumbersome)– Refine calibration; test against independent calibration

standards– Devise field-deployable calibration apparatus (existing lab

standard too cumbersome)– Integrate calibration/Stokes retrieval into data acquisition

program

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Fringe Image

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Fringe Spectra

Developed utility for real-time display of fringes to align sensor

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SPEAR/AERONET Correlative Experiments

• Perform measurements with VIS-SPEAR and AERONET photometer collocated to assess radiometric and polarimetric performance of VIS-SPEAR.

• AERONET photometers have a long legacy (since 1993) and well planned calibration program.

• Experiment serves the interests of both AFRL and NASA.

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Cimel Robotic Photometer

• Direct solar and sky radiance measurements.

• Sunrise to sunset.• Solar principal planes and

solar almucantars.• 8 pos. filter wheel w/ 4

interference filters. Additional 3 for polarization at 870 nm.

• Satellite feed and automatic data processing available via web.

• Rigorous calibration plan.

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VIS-SPEAR Field Mounts

• Scans performed manually:– Almucantars: VIS-SPEAR mounted on

heavy duty tripod Alt-Az head w/ graduations.

– Principal Planes: VIS-SPEAR mounted on equatorial telescope mount adjusted for operation at 0 deg latitude.

• Scans performed automatically:– Full imagery: VIS-SPEAR mounted on

CNC rotary table. Very bulky – needs to be replaced for future field measurements.

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Sensor ComparisonPrincipal Plane Scan

02/19/2002

0

5

10

15

20

-40 -20 0 20 40 60 80 100 120 140 160

View Angle [degrees]

Sky

Ra

dia

nce

[m

W/c

m^

2/sr

/um

]

CIMEL 675 nm 16:07UT

SPEAR 680 nm 16:35UT

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VIS-SPEAR

Principal Plane Scan2/19/2002 16:33UT

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9

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-90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90

View Zenith Angle [degrees]

Sky

Rad

ian

ce [

mW

/cm

^2/

sr/u

m] 480 nm BW=40 nm

520

560

600

640

680

720

760

800

820

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Cimel Photometer

AERONET Sun Photometer02/19/2002

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-10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170

View Angle [degrees]

Sky

Rad

ian

ce [

mW

/cm

^2/

sr/u

m]

1020 nm

675

441

870

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SPEAR/CIMEL DoLPPrincipal Plane Scan

2/19/200216:30UT

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-90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90

View Zenith Angle [degrees]

De

gre

e o

f L

ine

ar P

ola

riza

tio

n

CIMEL 870 nm

SPEAR 520 nm

SPEAR 680 nm

SPEAR 800 nm

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VIS-SPEAR DoLPPrincipal Plane Scan

VIS-SPEAR2/19/2002

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0.3

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-90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90

View Zenith Angle [degrees]

Do

LP

480 nm BW=40 nm

520

560

600

640

680

720

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800

820

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AERONET Polarimetry

AERONET Billerica Raw Data 18 Feb 2002

0.1

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-90 -60 -30 0 30 60 90

View Zenith (deg)

Radi

ance

Pol Channel 1 Pol Channel 2 Pol Channel 3

Billerica 18 Feb 2002

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View Zenith (deg)

Do

LP

16:10:33

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Retrieval Context

• Retrieve Stokes spectrum from x(i)– x(i) is output of i-th pixel– Sensor input Stokes vector S().– Gaussian spectral blur h(), gain R(), and offset C(i).– Mueller matrix M; P-SIM crystals (lengths and birefringence of

material). Integration “over blur” – x(i) includes tails of x(i-1) and x(i-1).

• Retrieval first requires estimation of system parameters

)()())(,,()()()( 21 iCdSnMhRix

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Calibration Sequence

• Cal Sequence - designed to estimate parameters of the system equation

– Spectral cal: • Mapping between wavelength vs. pixel index;

• Spectral blur h().

– NUC (Non-Uniformity Correction):• R and C

– Retardance cal: • L1, L2, n• and any additional system retardance

)()())(,,()()()( 21 iCdSnMhRix

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Spectral Cal• Infer from spectral line source images:

– wavelength vs. pixel index; blur {h[] and }

• Hg(Ar) and Kr vapor lamps– line widths << pixel bin

• Non-linear regression using multiple lines:– retrieves: quadratic polynomial mapping between

and pixel index I; and (gaussian blur)

NLR retrieval matched the Andor and slit blur estimates

pixel bin: 2.3nm

0 50 100 150 200

5000

10000

15000

20000

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Non-Uniformity Correction (NUC)

• NUC accounts for:– Spatial non-uniformity of pixel gain & offset

– Equalization of aperture shading (Cos4), spectral transmittance

– Maps raw digital counts to radiance units

• Requires spectrally-calibrated sources– Unlike conventional 2D imaging flat-fielding

Sli

t

500 1000 1500 2000Nanometers

0

50

100

150

200

250

300

A.U.

Cal source spectrum

0 50 100 150 200 2500

50

100

150

200

250

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Retardance Cal

• Global non-linear regression retrieves from known input Stokes spectra (“Charlie Brown” frames):– crystal lengths L1, L2, quadratic polynomial n – nuisance parameters (for the calibration itself):

• i0 (intensity scale) • raop (unknown polarizer alignment offset angle)

• Employs Labsphere source (known spectral intensity) and rotating polarizer– absolute polarizer rotation alignment presently

unknown - known relative rotations between frames– assumes perfect, spectrally flat polarizer

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Retardance Cal

550 600 650 700

0.0089

0.0091

0.0092

0.0093

Nominal vs. fitted polynomial n

900000950000

1´106

1.05´106

1.1´1061.9´106

1.95´106

2´106

2.05´1062.1´106

0100000200000300000400000

900000950000

1´106

1.05´106

1.1´106

• The objective (error) function for global NLR: – sum of squared errors:– error=data vs. parametric

signal model– Model parameters are L1,

L2, n, i0, raopError surface vs. crystal length

parameters L1 and L2

Highly non-smooth error surface requires Global NLR

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Retardance Cal

0 20 40 60 80 1000

200000

400000

600000

800000

1´106

1.2´106

1.4´106

0 20 40 60 80 1000

250000

500000

750000

1´106

1.25´106

1.5´106

• Excellent model fit (calibration), except at short wavelength end for sideband-rich AoPs

• Fit error consistent with NUC, other errors ~1-2% (for now)A

oP=

6deg

AoP

=13

6deg

DataModel

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Stokes Retrieval Strategy

• Invert the system equation– linear (pseudoinverse-”PI”) for Stokes parameters

• assumes spectrally-constant source across – non-linear regression (“NLR”) for:

• spectrally-constant {I,dop,aop,} across • parametric spectral source models (Sellmeier, Lorentz)• requires global solver

2

2 1

2 1

1

2

212 2

2 [ ]2

2 [ ]2 2

T

L nCos I

Q I dop Cos aopY L n L n

U I dop Sin aop CosSin Sin

V I dop Sin aop SinL n L n

Sin Cos

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Stokes Retrieval to Date

• 6-sample (~14nm) Stokes retrieval achieved from PseudoInverse and NLR– Assuming flat source spectum

over 14nm band– But works nonetheless against

blackbody-like spectrum

• Handling spectral structure:– Will try NLR against spectral

models– Actual implementation: basis

pursuit?

0 20 40 60 80 1000

200000

400000

600000

800000

1´106

1.2´106

1.4´106

0 20 40 60 80 1000

250000

500000

750000

1´106

1.25´106

1.5´106

AoP

=6d

egA

oP=

136d

eg

DataModel