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Op#mal Es#ma#on of Starlight and Incoherent Light
A.J. Riggs, Tyler Groff, and Jeremy Kasdin Princeton University
February 12, 2015
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Work supported by the NASA Space Technology Research Fellowship
Overview: High Order Wavefront Sensing & Control
Main Goal: Image faint exoplanets & disks.
HOWFSC Methodology: a) Use DMs to provide diversity in focal plane. b) Es#mate focal plane E-‐field from intensity measurements. c) Calculate control signal and apply to DMs. d) Repeat (a)-‐(c) un#l desired contrast is reached.
Main Points: 1) Use recursive es)ma)on for faster, more robust WFC. 2) Can also recursively es)mate incoherent light during WFC.
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Recursive Wavefront Es#ma#on • Observa#ons:
– Most of dark hole acquisi#on (wavefront correc#on) #me is spent ge\ng last order of magnitude in contrast.
– Measurements are dominated by readout noise. • Op#mal recursive es#ma#on (Kalman filtering) u#lizes all
measurements – Reduces measurement noise and limits model uncertainty. – Less total #me is required for correc#on:
40 60 80 100 120 140 160 180 200 220 24010
−7
10−6
Total Image Count
Measu
redContrast
2−Pair Batch
2−Pair KF
1−Pair EKF
References: Riggs et al., “Demonstra#on of Symmetric Dark Holes Using Two Deformable Mirrors at the High-‐Contrast Imaging Testbed”,SPIE, 2013.
Groff & Kasdin, “Kalman filtering techniques for focal plane electric field es#ma#on”, JOSA-‐A, 2013.
Princeton HCIL: Best Monochroma#c Results with Ripple3 SPC (Riggs, February 3, 2015)
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Recursive WFE: Experimental Results
40 60 80 100 120 140 160 180 200 220 24010
−7
10−6
Total Image Count
Measu
redContrast
2−Pair Batch
2−Pair KF
1−Pair EKF
Princeton HCIL: Best Monochroma#c Results with Ripple3 SPC (Riggs, February 3, 2015)
Kalman filtering techniques for focal plane electric field es#ma#on
100 200 300 400 500 600 700 800
10−8
10−7
10−6
Total Image Count
Contrast
2−Pair Batch
1−Pair Kalman
JPL HCIT: Best Monochroma#c Results with Ripple SPC (Riggs, August, 2013) In Riggs SPIE 88640T, 2013.
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Recursive Incoherent Light Es#ma#on
• Can also es#mate incoherent light recursively using a nonlinear es#mator. – Currently trying extended Kalman filter (EKF). – EKF just as fast (exposure & computa#onal #me) as KF, but also provides less noisy incoherent es#mate
• Reason for not using nonlinear es#mator: Correc#on might be done on other, brighter star – What if there is zodi or exozodi? Need to es#mate incoherent light well and pre-‐subtract it from nominal PSF (or use just es#mated intensity of star)
– Helpful if any correc#on itera#ons required on science target star.
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Incoherent Light Es#mates • Recursive incoherent es#mate is less sensi#ve to
measurement noise and shot noise.
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x (λ/D)
y(λ
/D)
EKF: Starlight Estimate
−10 −5 0 5 10−2
0
2
−8
−7
−6
x (λ/D)
y(λ
/D)
EKF: Incoherent Estimate
−10 −5 0 5 10−2
0
2
−8
−7
−6
x (λ/D)
y(λ
/D)
KF: Starlight Estimate
−10 −5 0 5 10−2
0
2
−8
−7
−6
x (λ/D)
y(λ
/D)
KF: Incoherent Estimate
−10 −5 0 5 10−2
0
2
−8
−7
−6
• Data above are from the final itera#on of correc#on runs in Princeton’s HCIL. • KF and EKF data above are from separate correc#on runs • In Princeton’s HCIL, unclear if incoherent es#mate is stray light or something else.
§ 1-‐sigma readout noise at 8e-‐8 contrast (=5 ADU)
HOWFS Comparison Batch Process Kalman Filter (KF) Extended Kalman Filter (EKF)
Pros • Computa#onally fastest • No tuning
• Less exposure #me • Uses all probed images for recursive es#ma#on • Allows for a dynamic model
• Less exposure #me • Uses all images recursively • Recursively es#mates incoherent light • Allows for a dynamic model • Allows for parameter adap#ve es#ma#on
Cons • More exposure #me • Does not u#lize previous data • Sta#c model only
• Computa#onally slower • Must be well tuned
• Computa#onally slowest • Must be very well tuned • Less stable
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Sensor Fusion: LOWFS & HOWFS Main ques#on:
How best to combine LOWFS and HOWFS for a stable PSF?
Key Points: – LOWFS sampling much faster than HOWFS – Will LOWFC residuals alter PSF above allowable contrast level? If yes: • Major problem for scheme to calibrate on different star • Must include in HOWFSC
Possible solu#ons: 1) HOWFS can be blind to LOWFSC if LOWFSC residuals are
negligible. 2) Include known LOWFC residuals and/or extra process noise in
recursive HOWFS.
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Extra Topics Best ways to speed up HOWFSC:
– Use broadband light. – Obtain a beker system model.
1. Broadband HOWFSC – Crucial for HOWFS to be fast enough. – Currently, no alterna#ve to (monochroma#c) pairwise es#ma#on and
EFC. – Limited filter wheel space on AFTA
2. Model-‐based es#ma#on & control are very sensi#ve to accuracy of model – How to use measurements to improve linear control response matrix? – How to obtain DM registra#on and ini#al wavefront at DMs without
phase retrieval on AFTA?
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References
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• EKF reference: • Riggs et al., “Op#mal Wavefront Es#ma#on of Incoherent Sources”,SPIE, 2014.
• Kalman filter references: • Groff & Kasdin, “Kalman filtering techniques for focal plane electric field
es#ma#on”, JOSA-‐A, 2013. • Riggs et al., “Demonstra#on of Symmetric Dark Holes Using Two Deformable
Mirrors at the High-‐Contrast Imaging Testbed”,SPIE, 2013.
• Stroke minimiza#on: • Pueyo et al., “Op#mal dark hole genera#on via two deformable mirrors with
stroke minimiza#on”, Applied Op#cs, 2009 • Groff & Kasdin, “Kalman filtering techniques for focal plane electric field
es#ma#on”, JOSA-‐A, 2013
• Pair-‐wise es#ma#on and EFC • Give’on et al., “Pair-‐wise, deformable mirror, image plane-‐based diversity
electric field es#ma#on for high contrast coronagraphy”, SPIE, 2011
Backup Slides
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Princeton HCIL Layout
Starlight Xpress SXV-‐M9
x (λ/D)
y(λ
/D)
Initial Image
ï10 ï5 0 5 10
ï5
0
5
ï8
ï7
ï6
ï5
ï4
ï3
x (λ/D)
y(λ
/D)
Final Image
ï10 ï5 0 5 10
ï5
0
5
ï8
ï7
ï6
ï5
ï4
ï3
WFC
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Diagram from [Groff JOSA-‐A 2013]
Es#mator Comparison: Princeton HCIL Results
50 100 150 200 25010
−7
10−6
10−5
Total Image Count
Measu
redContrast
Batch
2−Pair KF
1−Pair KF
2−Pair EKF
1−Pair EKF
0 10 20 30 40 50 60 7010
−7
10−6
10−5
Correction Iteration
MeasuredContrast
Batch
2−Pair KF
1−Pair KF
2−Pair EKF
1−Pair EKF
Exposure #me is constant for all images. One-‐sigma measurement noise at 8e-‐8 contrast.
All recursive es#mators are faster than the batch process es#mator.
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Incoherent Light Es#mates • In Princeton’s HCIL, unclear if incoherent es#mate is readout noise or stray light. § 1-‐sigma readout noise at 8e-‐8 contrast (=5 ADU)
50 100 150 200 250
10−7
10−6
10−5
Incoherent Estimate
Total Image Count
Measu
redContrast
Batch
2−Pair KF
1−Pair KF
2−Pair EKF
1−Pair EKF
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Example Contrast Correc#on Curves
0 5 10 15 20 25 30 35 40 45 50
10−7
10−6
10−5
10−4 2-Pair KF
Iterat ion
Contrast
Measured
Estimated
Incoherent Est.
Meas. Avg. Probe
Readout Std Dev
0 10 20 30 40 50 60 70 80
10−7
10−6
10−5
10−4 1-Pair EKF
Iterat ion
Contrast
Measured
Estimated
Incoherent Est.
Meas. Avg. Probe
Readout Std Dev
Princeton HCIL: 3 Feb 2015
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