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

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

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

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 2 + 𝑛 𝑘 . 4/6/2019

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

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

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

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

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

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

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

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

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

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