Evaluation of Spectral Issues in Sparse Aperture Imaging ... · TerraPix Digital Aerial Camera 4080...

R I T Rochester Institute of Technology

Evaluation of Spectral Issues inEvaluation of Spectral Issues inSparse Aperture Imaging SystemsSparse Aperture Imaging Systems

R.E. Introne

Digital Imaging and Remote Sensing LaboratoryChester F. Carlson Center for Imaging Science

Rochester Institute of Technology

The views expressed in this briefing are those of the author and do not reflect the policy or position of theUnited States Air Force, Department of Defense, or the U.S. Government.


OverviewOverview

• Theory

• Approach

• Results

• Summary


Sparse Aperture SystemsSparse Aperture Systems

Goal: Synthesize a larger effective collection aperture with a configuration of smaller phased subapertures

Multiple Phased Telescopes

Secondary

Primary

Tertiary

Focal Plane

Common Secondary Mirror

•• Includes multiple aperture & common secondary,Includes multiple aperture & common secondary,sparse & dilute telescope conceptssparse & dilute telescope concepts

•• Emphasize extended scene, remote sensing applications Emphasize extended scene, remote sensing applications

Image courtesy of HarveyImage courtesy of Boucher

Image courtesy of Fiete


Research ObjectivesResearch Objectives

• Develop understanding of Sparse Aperture phenomenology– System-level diffraction (OTF/PSF) effects

– Photon, dark current & read noise effects

– Image restoration techniques

• Develop theoretical basis for modeling spectrally diverse SparseAperture system performance

– Target source spectral radiance

– Polychromatic system OTF

– Spectrally diverse noise

• Implement strawman model for spectrally diverse Sparse Aperture collection systems

– Scene spectral radiance

– Polychromatic system OTF

– Spectrally diverse system noise


Signal ModelSignal Model

[ ] [ ] [ ] [ ]λλλλ ,,,,,,,, objincoh yxnyxyxfyxg +∗= h

Imaging System (Frequency Domain)

Imaging System (Space Domain)

where:

[ ] [ ] [ ] [ ]ληξληξληξληξ ,,,,,,,, objincoh NFG +⋅= H

Fourier Transform Pairs

[ ] [ ]{ }λληξ ,,,OTF x,yhFH =≡[ ]λ,,PSF yxh≡

[ ] [ ] [ ]( )

[ ] [ ] ( ) ( ) λλληλτληξληξπ

ληξληξηξ dLhcfFTA

FS fillopt

0FTsource,2

intdetobj ,,,,

#4,,,,,out

freq ∫∞

=⋅= HH

[ ] [ ] [ ] [ ] ( ) [ ] [ ]yxnyxnTyxnyxyxfyxn ,,,,,,,,, 3read2intdc1obj σσλλλ ++∗≅ h

Noise Model

Signal Frequency Spectrum

incohADC

elecconvcounts

2 gSGGI

n

=

Quantization


Image RestorationImage Restoration

1.0

ρco

[ ]ηξ ,MTF H=

1.0

ρco

threshold

Inverse Filter

Pseudo-Inverse Filter

ξ ξ

Transfer Function Inverse Filtering Wiener Filtering

1.0

ρco

Inverse Filter

Wiener Filter

ξ

[ ] [ ] [ ]

[ ]

<

≥=

threshold, when 0

threshold, when ,

1,pseudo

ηξ

ηξηξηξ

H

HHW

[ ] [ ]ηξηξ

,1,inverse H

=W

• Inverse Filters tend to over-boost the noise or be non-optimum at high frequencies

• Optimum solution from a mean-square error viewpoint is the Wiener-Helstrom Filter

[ ] [ ][ ] [ ]

[ ]ηξηξηξ

ηξηξ

,,,

,,

f

n2

*wiener

SSW

+=

H

H


Modeling Approach OverviewModeling Approach Overview

PupilFunction

PhaseErrors

UnaberratedOptics OTF

OpticsOTF

DetectorMTF

ObjectRadiance

DetectorNoise

RestorationFilter

RestoredImage

X

MotionMTF

X XX +

DIRSIG

MODTRAN

X

AberratedPSF

UnaberratedPSF

{}⋅F {}⋅-1F RawImage {}⋅-1F

{}⋅-1F

{}⋅-1F

{}⋅F

{}2⋅F

{}2⋅F

{}∑ ⋅λ

iλ iλ iλ iλ iλ iλ iλ

WavefrontError

Estimate

ObjectEstimate


Strawman Collection ScenarioStrawman Collection Scenario

Panchromatic(polychromatic world)

Sparse Aperture Configurations:Annulus, Tri-arm, Golay-6

Pupil Function Phase Profile

Scenario #1Parameter Value

Spectral passband 0.4-0.7 µmSystem f-number (f#) 18.0Optical sampling (Q=λf/pD) 2.0 (Nyquist)Ground Sample Distance (GSD) 0.4572 m (18 in)Optical Transmission (τopt) 0.9Secondary Obscuration (εsub) 0.24Focal Plane Array (FPA) Staring Frame CCDRead Noise 50 rms electronsDynamic Range 11 bitsImage Smear 0.25 pixelsrms Wavefront Error 0.12 waves (λ = 0.65 µm)Atmosphere MODTRAN 4.0 mid-latitude summerVisibility 17.0 kmSimulation Time ~1700 GMT (~79° sun angle)Target Location 43.2° N Lat, 77.6° W Lon


Orbital AnalysisOrbital Analysis

Orbit design and collection geometry evaluation performed

through use of STK

1 Jun 2003 16:48:00.00

Access Summary Report

Start Time (UTCG) Stop Time (UTCG)---------------------- ----------------------1 Jun 2003 16:33:33.66 1 Jun 2003 17:41:17.55

Duration (sec)--------------4063.893


Imagery Collection GeometryImagery Collection Geometry

STK enables detailed evaluation of vehicle pointing (az, el) and position

(lat, lon, alt) required for DIRSIG

Performed arbitrary simulated nadir ascending pass at

~1300 local time on 1 Jun 03


Suburban Scene RadiometrySuburban Scene RadiometryRochester Megascene

– Complex scene representative of typical remotely sensed targets

– Greater Rochester suburban area modeled with good fidelity

– Advertised to be accurate at 1-m (39.4-in) Ground Sample Distance

– Underlying texture map sampled at 6-in GSD

– Features within scene modeled well below 6 inches

Scene Attributes:

Simulations were performed using collection geometry acquired from STK and oversampled by 3:1(6 in to support 18-in GSD in sparse aperture simulation)

RGB spectral radiance image: 0.65µm (R), 0.55µm (G), 0.45µm (B)

1 Jun 2003 12:56:59.00


Rural Scene RadiometryRural Scene RadiometryRochester Microscene

1 Jun 2003 12:56:59.00

Simulations were performed using collection geometry acquired from STK and oversampled between 3:1(6 in) and 18:1 (1 in)

Concealed MilitaryVehicles


Alternative Scene OptionsAlternative Scene Options

TerraPix Digital Aerial Camera

4080 x 4080 pixel frame

0.4 – 0.9 µmRGB

~7 in GSD

12 bits

CitiPix Aerocolor Film Camera

9.5in film

0.38 – 0.7 µmRGB

~6 in GSD

8 bits (digitized)

Hymap Hyperspectral Sensor

512 pixel scanner

0.45 – 2.5 µm144 hyperspectral bands

~20 ft GSD

16 bits

Potential Aerial Object Scenes


Complex Exit PupilComplex Exit Pupil

[ ] [ ]

= yxwiyxpyx ,2exp,],[λπ

p

[ ] [ ]

−−−−= ∑

=iii

N

iiii yyxxwiyyxxpyx ,2exp,],[

1 λπ

p

Conventional Pupil Function :

Sparse Aperture Pupil Function :

[ ] [ ] ( )

( ) ( )

( )

sorder termhigher

,,,

406

305

22204

20

23

2202

2221

20302

2210

distortion curvature field

mastigmatis coma spherical

piston tilt defocus

+

++++

+++++

+++=≡

xbxxbyxxb

xxbyxxxbyxb

xaxxayxaxyxwyxw

Aberration (wavefront error) function:


Imaging System OTFImaging System OTF

[ ]∏=

=N

ii

1sys ,,MTFMTF ληξ

[ ] [ ] [ ] [ ] [ ] [ ]ληξηξηξηξληξληξ ,,MTF,MTF,MTF,MTF,,OTF,,OTF diffjittersmeardetapsys ⋅⋅⋅⋅=

[ ] [ ] [ ]

[ ]dxdyyxp

zzzz

∫ ∫∞+

∞−

=

,

, ,,,OTF 2222ap

ηλξληλξλληξ pp 9

System Transfer Function developed by cascading individual component OTF :

[ ]∏=

=N

ii

1sys ,,OTFOTF ληξ

Optical Transfer Function Modulation Transfer Function

Complex Aperture OTF:

0 20 40 60 80 100 1200.0

0.2

0.4

0.6

0.8

1.0

MTF

Optics

OQF

Det

Jit

Atm

Smear

Diff

CTE

TOTAL

Freq (mm-1)Data courtesy of Boucher

Note: normalized autocorrelationof the scaled pupil function


Sparse Aperture AutocorrelationSparse Aperture Autocorrelation

• Unaberrated System Pupil:

• Optical Transfer Function (OTF):

[ ] [ ] [ ]∑∑==

−−=−−∗=N

iii

N

iii yyxxsyyxxyxsyxp

11,,,],[ δ

[ ] [ ] [ ]ηλξληλξληξ 22*

22 , ,, zzpzzp −−−−∝ 9H

[ ] [ ] [ ]( ) [ ]∑∑= = =

=−+−+∗−−−−∝N

j

N

k zyzxkjkj yyyxxxyxsyxs

1 1

*

22,,,,ηλξλδηξ 9 H

Pupil

x

y

x1-x1

-d = -(x12+y1

2)1/2

y1

-y1

cross-correlationpairss[x,y]

p[x,y]OTF

ξ

η

y1

-y1

x1-x1-2x1 2x1

d+y1

-d

d

-d-y1

H[ξ,η]


DiffractionDiffraction--Limited MTF ComparisonLimited MTF Comparison

FilledFill Factor: 1.000

CassegrainFill Factor: 0.942

Golay-6Fill Factor: 0.170

AnnularFill Factor: 0.190

Tri-armFill Factor: 0.170


Polychromatic OTF IssuesPolychromatic OTF Issues

– Traditional approaches resample high-resolution panchromatic imagery

– Spectrally weighted polychromatic MTF computed to apply to gray-world scene

– This technique fails to accurately account for scene spectral content and MTF spectral artifacts

– Direct spectral integration of radiance frequency spectrum and system OTF desirable

[ ]( )

[ ] [ ] ( ) ( ) λλληλτληξληξπ

ηξ dLhcf

FTAS

GGS filln

opt0

FTsource,2intdet

ADC

elecconv ,,,,OTF#4

2,out

freq ∫∞

=

[ ]( )

[ ][ ] [ ] ( ) ( ) ( ) λλληλτληξηξπ

ηξ dLFF

hcf

FTASGG

S filln

opt0

sourcepolygrayobj,

grayobj,2

intdet

ADC

elecconvoutfreq ,MTF

0,0,

#42

, ∫∞

=

[ ][ ] ( ) ( ) ( )

( ) ( ) ( )∫

∫=

max

min

max

min

optsource

optsource

poly

,,MTF

,MTF λ

λ

λ

λ

λλληλτλ

λλληλτλληξ

ηξdL

dL


Spectral MTF VariationSpectral MTF VariationComparison of Filled versus Sparse Aperture MTFs

Sparse Aperture MTF:Aberrated 0.24-waves rms

Filled Aperture MTF:Unaberrated

• Oscillatory behavior of sparse aperture MTF versus wavelength creates concern over spectral artifact image quality issues


Simulation OverviewSimulation Overview

Top-level simulation methodology:– Develop geometric pupil function

– Add phase via Zernike polynomials to incorporate aberrations

– Evaluate aberrated system OTF

– Perform Fourier Optical prediction of noise-free degraded image

– Add uncorrelated noise

– Restore imagery via conventional Wiener-Helstrom filter

Original Object

Wiener Filter Restoration

Sparse Aperture PredictionAberrated Sparse Aperture


MTF EvaluationMTF Evaluation(Effects of Aberrations)(Effects of Aberrations)

0.07-wave rms MTFSparse Aperture w/Piston Error

0.10-wave rms MTF 0.20-wave rms MTF

Diffraction-Limited MTF

0.14-wave rms MTF


Modulation Transfer FunctionModulation Transfer Function

Comparison of Filled versus Sparse Aperture MTFs

Aberrated Sparse Aperture MTF: 0.20-wave rms


Point Spread FunctionPoint Spread Function

Comparison of Filled versus Sparse Aperture PSFs

Sparse Aperture PSF:Aberrated 0.20-waves rms

Filled Aperture PSF:Unaberrated

Sparse Aperture PSF:Unaberrated


Quality ImpactsQuality Impacts

Image Quality Comparisonof Filled versus Sparse Aperture

Sparse Aperture:Aberrated 0.20-waves rms

Filled Aperture:Unaberrated

Sparse Aperture:Unaberrated


Wiener Filter ExampleWiener Filter Example

WFE: 0.20-waves rms

Wiener Filtered Image

SNR: 18.5 db

Original Object Noisy Degraded Image

Aperture Comparison Wiener Filtered ImageNoisy Degraded Image

Sparse Aperture Sparse Aperture

Filled Aperture Filled Aperture

Fill Factor: 0.173

SNR: 6.0 db


Image Restoration Example (1)Image Restoration Example (1)Wavefront Error: 0.10-waves rms PTT

Restored RGB Image

SNR: 25.3 db

Sparse Aperturew/Piston Tip/Tilt Errors

Original Object Predicted RGB Image

Aperture Phase Profile Aberrated MTF

Fill Factor: 0.173



Restored RGB Image

SNR: 25.3 db




Fill Factor: 0.173


Closer Examination of RestorationCloser Examination of Restoration

Original Object


Image Restoration Example (1)Image Restoration Example (1)Wavefront Error: 0.10-waves rms PTT SNR: 25.3 dbFill Factor: 0.173

Note correlated noise amplification & presence of color artifacts due to Wiener

filter frequency boost mismatch

Precise knowledge of phase errors assumed

Individual spectral bands restored via central wavelength OTF to simulate physics associated with wideband collection


Image Restoration Example (4)Image Restoration Example (4)Wavefront Error: 0.30-waves rms defocus

Restored RGB Image

SNR: 16.5 db

Filled Aperturew/Focus Errors



Fill Factor: 1.000


Criticality of Phase KnowledgeCriticality of Phase KnowledgeWavefront Error: 0.25-wave rms PTT

Restored RGB Image(RGB OTF - perfect phase knowledge)

Restored RGB Image(RGB OTF - no phase knowledge)

Restored RGB Image(central OTF - perfect phase knowledge)

SNR: 25.3 db


Original Object Predicted Noisy ImageAperture Phase Profile

Fill Factor: 0.173


SummarySummary

• Strawman spectra-radiometric sparse aperture model demonstrated

• Includes effects of spectrally-dependent OTF, phase errors, noise, spectral radiance

• Moderately aberrated, low-fill factor sparse aperture systems appear to demonstrate spectral issues

Evaluation of Spectral Issues in Sparse Aperture Imaging ... · TerraPix Digital Aerial Camera 4080...

Documents

Transcript of Evaluation of Spectral Issues in Sparse Aperture Imaging ... · TerraPix Digital Aerial Camera 4080...