1. Intelligent wavefront sensing and control for exoplanet coronagraphic imaging instrument
He Sun
Advisor: N. Jeremy Kasdin
Mechanical and Aerospace Engineering
Princeton University
4/6/2019

2. High Contrast Coronagraph Imaging
Coronagraph = series of masks, stops, and/or apodizers to remove starlight but transmit off-axis sources (e.g., exoplanets)
Quasi-static aberrations from in the system degrade the contrast in the dark holes
Shaped Pupil Lyot Coronagraph (WFIRST CGI)
Zimmerman+ 2016
Shaped Pupil
Focal
Plane
Mask
On-axis PSF
at camera
Lyot Stop
10-9 contrast
10-4 contrast
4/6/2019

3. Wavefront Sensing and Control for CGI
Deformable Mirror #1
Light field
Controller
Estimator
Camera Image
Deformable Mirror #2
Coronagraph
Star and planet Light
1. Sensing commands and images for estimation;
2. Control commands for correction;
4/6/2019

4. Wavefront Sensing and Control for CGI
3. Wavefront Control:
𝑢 𝑘+1 =𝜋 𝐸 𝑘
Wavefront Sensing (Estimation):
𝐸 𝑘 ~𝑝( 𝐸 𝑘 | 𝐸 𝑘−1 , 𝐼 𝑘 𝑝 , 𝑢 𝑘 , 𝑢 𝑘 𝑝 )
Science Camera
Controller
Optical System
Deformable Mirrors
Coronagraph
Telescope
Images
Estimator
Commands
Focal Plane Wavefront Control
Estimated
States
𝐸 𝑎𝑏
𝑒 𝑖 Δ 𝜙 𝑘
𝐶 ∙
𝐸 𝑘
𝐼 𝑘 , 𝐼 𝑘 𝑝
𝑢 𝑘 , 𝑢 𝑘 𝑝
𝐸 𝑘
Light
Field
System modeled as state space model with Gaussian noises:
𝐸 𝑘 = 𝑓(𝐸 𝑘−1 , 𝑢 𝑘 )+ 𝑤 𝑘 , 𝐼 𝑘 𝑝 = 𝑓 𝐸 𝑘 , 𝑢 𝑘 𝑝 𝑛 𝑘 .
4/6/2019

5. Princeton High Contrast Imaging Lab
4/6/2019
High Contrast Imaging Lab, Princeton University

6. Wavefront Sensing and Control Simulation (Monochromatic)
Model accuracy is one of the key limitations.
Biased model: not know the surface aberrations on mirrors or lenses and the accurate DM surface response
4/6/2019

7. Adaptive Wavefront Sensing and Control
Model
Fitting
Wavefront
Estimator
Estimated
States
E-M Model Identification
Commands,
Images
A reinforcement learning algorithm:
Improve the control based on past experience
Focal Plane Wavefront Control
Controller
Estimator
Estimated
States
Commands
Images
Light
Telescope
Deformable Mirrors
Coronagraph
Science Camera
Optical System
4/6/2019
Sun, He, et al., Identication and adaptive control of a high-contrast focal plane wavefront correction system, JATIS., 2018

8. E-M Model Identification
𝑬 𝒌
𝒀 ={ 𝑰 𝒌 𝒑 , 𝒖 𝒌 , 𝒖 𝒌 𝒑 }
𝑰 𝒌 𝒑 = 𝒇 𝜽 ( 𝑬 𝒌 , 𝒖 𝒌 𝒑 ) 𝟐 + 𝒏 𝒌
𝑬 𝒌 = 𝒇 𝜽 ( 𝑬 𝒌−𝟏 , 𝒖 𝒌 )+ 𝒘 𝒌
Model
Fitting
Wavefront
Estimator
Estimated
States
E-M Model Identification
Commands,
Images
E-M algorithm: iterative method for identifying system with hidden states
E-step: Estimate the hidden state using data, 𝐸 𝑘 ~ 𝑝 𝜃 ( 𝐸 𝑘 | 𝐼 𝑘 𝑝 , 𝑢 𝑘 , 𝑢 𝑘 𝑝 )
M-step: Fit state and data to the model parameters, 𝜃=𝑎𝑟𝑔𝑚𝑎 𝑥 𝜃 𝑝 𝜃 ( 𝐸 𝑘 , 𝐼 𝑘 𝑝 | 𝑢 𝑘 , 𝑢 𝑘 𝑝 )
4/6/2019

9. Adaptive Wavefront Sensing and Control Simulation (Monochromatic)
Adaptive control helps close the gap between the biased model and the true model.
4/6/2019

10. Experimental Results (Monochromatic)
Log scale
Control Step
4/6/2019

11. Active Wavefront Sensing
Wavefront estimator predicts the estimation covariance.
𝐸 𝑘 ~𝑁(𝜇 𝐼 𝑘 𝑝 , 𝑢 𝑘 𝑝 , 𝐸 𝑘−1 , 𝑢 𝑘 ,Σ 𝐸 𝑘−1 , 𝑢 𝑘 , 𝑢 𝑘 𝑝
In each control step, we can optimally choose the DM sensing commands by minimizing the estimation uncertainty,
𝑢 𝑘 𝑝∗ =𝑎𝑟𝑔𝑚𝑖 𝑛 𝑢 𝑘 𝑝 𝑙𝑜𝑔 Σ 𝐸 𝑘−1 , 𝑢 𝑘 , 𝑢 𝑘 𝑝 +𝛼 𝑢 𝑘 𝑝 2 2
It considers the estimation uncertainties of last step to design a optimal sensing command.
An active sensing (optimal experiment design) algorithm: optimally acquire the needed knowledge
4/6/2019

12. Active Wavefront Sensing Simulation
1DM
Optimized DM sensing commands lead to more accurate estimation, higher contrast, and faster wavefront correction.
4/6/2019

13. Summary Two new AI techniques for improving WFSC for CGI:
Reinforcement learning improves model accuracy and enables online adaptive wavefront control;
Active sensing reduces the wavefront estimation uncertainties, improve the contrast and correction speed.
Future work:
Adaptive identification and control
with broadband measurements from IFS;
4/6/2019

14. Acknowledgements Princeton High Contrast Imaging Lab 10/05/2018
4/6/2019