Download Low Order Wavefront Sensing and Control for WFIRST

Jet Propulsion Laboratory
California Institute of Technology
WFIRST-AFTA Coronagraph Instrument
Low Order Wavefront Sensing & Control
Fang Shi, R. Bartos, R. Hein, B. Kern, R. Lam, J. Moore, K. Patterson,
O. Santos, E. Sidick, H. Tang, T. Truong, B. Tweddle, K. Wallace, and
X. Wang
Jet Propulsion Laboratory
California Institute of Technology
Pasadena, California 91109
Oct 8, 2014
Copyright 2014 California Institute of Technology. Government sponsorship acknowledged
1
Jet Propulsion Laboratory
Outline
California Institute of Technology
• WFIRT-AFTA coronagraph overview
• AFTA telescope wavefront drift and line-of-sight jitter
• Low order wavefront sensor (LOWFS) description
• LOWFS performance analysis
• LOWFS testbed
• Challenges of correcting low order WFE
• Summary
2
Jet Propulsion Laboratory
WFRIST-AFTA Coronagraph Instrument
California Institute of Technology
Coronagraph
Instrument
Exo-planet
Direct imaging
Telescope
Diameter
2.4 m
Band pass
430 – 980nm
Measured sequentially in
five ~10% bands
Inner working
angle
100 – 250 mas
~3λ/D, driven by science
Outer working
angle
0.75 – 1.8
arcsec
Detection
Limit
Contrast ≤ 10-9
After post
processing)
Imaging
Spectral
Resolution
Center obscuration and
SM support struts
By 48X48 DM
Cold Jupiters, not exoearths. Deeper contrast
looks unlikely due to
pupil shape and extreme
stability requirements
4.8" FoV 0.009" pixel
scale, 1kX1K EMCCD
~70
Exo-planet
Spectroscopy
With IFS, R~70 across
600 – 980 nm
AFTA Coronagraph Instrument will:
• Characterize the spectra of over a dozen
radial velocity planets.
• Discover and characterize up to a dozen
more ice and gas giants.
• Provide crucial information on the physics of
planetary atmospheres and clues to planet
formation.
• Respond to decadal survey to mature
coronagraph technologies, leading to first
images of a nearby Earth.
3
WFIRST-AFTA Coronagraph Functional Block Diagram
Jet Propulsion Laboratory
California Institute of Technology
Star light
suppression optics
High contrast
loop during
initialization
1kX1K, EMCCD; 150K,
IWA 3λ/D, OWA 12λ/D,
λ(0.43-0.98um)
Coronagraph
FPA
OTA
(PM, SM)
TM, relay,
FSM
DM #1,
DM #2
Relay,
Occulting
Masks &
Filters
LOWFS
Telemetry
IFS
LOWFS
FPA
Drift control
loop
Jitter
control loop
The function of LOWFS is to measure
the LoS jitter and the low order WF
changes
Post
processing
IFS FPA
1kX1k, EMCCD; 150K,
λ(0.6-0.98um), R~70,
17mas sampling
Optics
Control
Detector
Post processing on ground
AFTA Telescope LoS Jitter and WFE Drift
Jet Propulsion Laboratory
California Institute of Technology
• Current understanding comes from
WFIRST-AFTA Cycle 3 study
– Line-of-sight WFE:
• Goal for LOWFS sensor:
– Line-of-sight: 0.4 milli-arcsec
• LoS jitter requirement may be
loosened from better coulter design
• Drift (<2Hz): ~14 mas
• Jitter (>2Hz): ~ 4 mas
– Dominant frequency around 10 Hz
– Low order WFE sensing: ~10 pm at
much slower rate (> minutes)
– Thermal drift WFE:
• Maximum ~ 50 pm over 24 hours
• Typically with rate <10 pm/hour
• Dominant mode: focus and coma
LoS vs Wheel Speed
WFE RB Thermal Drift
WFE PM Thermal Drift
Coronagraph RMS Contrast Sensitivity to WFE
Jet Propulsion Laboratory
California Institute of Technology
HLC RMS Contrast vs. 0.1 nm WFE
SPC RMS Contrast vs. 0.1 nm WFE
• RMS contrast sensitivity curves from PROPER model
– X-axis is the field distance in unit of λ/D
– Y-axis is the coronagraph’s RMS contrast changes due the WFE
• Contract sensitivity depends on type (Hybrid Lyot vs. Shape Pupil) and design
– Shape Pupil Coronagraph (right plot) has much less sensitivity than that of Hybrid Lyot
Coronagraph (left plot)
• Contract sensitivity depends on WFE mode
– For HLC is very sensitive to coma and spherical WFE
Jet Propulsion Laboratory
LOWFSC Concepts
California Institute of Technology
• LOWFS uses the rejected star light from the coronagraph for wavefront sensing
– The rejected star light is picked from the occulter (HLC) or the field stop (SPC), hence
spatially filtered to contain low order WF information only
– LOWFS senses only low order wavefront changes (differential instead of absolute WFS)
• Senses WF jitter at high speed needed to suppress the jitter
• Senses slow varying low order WFE such as focus, astigmatism, and coma caused by the WFIRST-AFTA
telescope thermal drift
– Recorded WF will be used for coronagraph image post processing
– Use one camera to sense both LoS jitter and low order WFE
• Frame average when sense low order WFE to increase the SNR
• LOWFSC uses FSM for LOS jitter correction and a suitable corrector for low order
WFE correction
– FSM loop bandwidth is driven by AFTA LOS jitter
– Low order WFE corrector should avoid to corrupt coronagraph’s high order WF control
• LOWFS is closed-loop only for low order wavefront error. It lacks the sensitivity to high spatial order
WFE
• DM calibration is very important
• Combine the LOWFS mask (a phase dimple of π/2 in phase and diameter of ~1.2
λ/D) on the coronagraph star light rejection mask reduces the non-common path error
Jet Propulsion Laboratory
Zernike Wavefront Sensor
California Institute of Technology
ZWFS Fourier Modes
• Zernike WFS (ZWFS) measures WFE from interference between
the abberated WF and the reference WF generated by a phase
Input
plate
• Phase plate is at the center of occulting mask
• ZWFS sensed pupil is imaged to CCD at 8x8 pixels
• Phase shift of π/2 in ref portion to accentuate the WFE
–
CCD brightness variation proportional to the WFE: ∆Ι ~ ±2φ
–
ZWFS uses differential image to sense the delta WFE
Phase
Image
Plane
Pupil
• AFTA-C LOWFS mask will be reflective instead of transmissive Plane
Image
shown in this conceptual illustration
• Working with 10% band filters, higher bandwidth (20%) is ok
E (η ,υ ) = F [P(u , v )] ∗ F [A(1 + ε (u , v ) + i ϕ (u , v ))]
E (η ,υ ) = A PSF (η ,υ )ei θ + A PSF (η ,υ ) ∗
F [ε (u , v ) + i ϕ (u , v )]
E (u, v ) = P (u, v ) ⋅ A(1 + ε (u, v ))ei ϕ (u ,v )
(
I = E ⋅ E * = A2 1 + 2ϕ + ε 2 + ϕ 2
with θ = π/2
)
Jet Propulsion Laboratory
ZWFS Analysis Approach
California Institute of Technology
Diffraction model using “SemiAnalytical Method (SAM) or FFT:
Example on ZWFS Signal (FFT Model)
1. Generate ZWFS intensity
output (reference) with zero
input phase and down sampled
to 8x8
2. Adding photon noise and
detector read/dark noise and
down sampled to 8x8 pixels
3. Generate ZWFS intensity
output with aberration on the
input phase Φ
4. Adding photon noise and
detector read/dark noise and
down sampled to 8x8 pixels
5. Subtract out reference frame
and reconstruct the sensed
phase using signal-to-Zernike
coeff matrix which is precalculated at noise-free case
6. WFE is computed with pseudo
inverse of signal-to-Zernike coeff
matrix
Input Pupil & WFE
HLC configuration
LOWFS is illustrated
here. SPC LOWFS is
similar except the pupil
support is that of SPC
mask. Higher spatial
frequency contents (>6
λ/D) are not being
collected by LOWFS
High Resolution
ZWFS Signal
Pixelated
ZWFS Signal
*SAM reference: R. Soummer, etal, "Fast computation of Lyot-style coronagraph propagation", Optics Express, Vol. 15, No. 24, 26 Nov. 2007
Zernike WFS Pixelated Signals for each WFE Modes
Jet Propulsion Laboratory
California Institute of Technology
Pixelated ZWFS signals of Z2-Z11 WFE modes
• Used for WF sensing
• Noise will be applied on these signals for performance evaluation
ZWFS Noise Performance with AFTA-C HLC
Jet Propulsion Laboratory
California Institute of Technology
Noise Equivalent Angle (tilt)
Noise Equivalent Low Order WFE
• K0V star spectral profile
• ZWFS wavelength band shown in the plot: 561 nm ± 64 nm
• WFS camera exposure of 1 msec (read out at 1 KHz frame rate)
–
Low order WFE from thermal drift veries much slower which allows senso’s images to be averaged to impove S/N
• Include camera (CCD39) QE, readout noise, and dark current specifications
• Each result data point is a mean of 100 Monte-Carlo realizations
• Noise performance is very similar with & without WFE presence
Preliminary LoS Jitter Suppression Estimate
Jet Propulsion Laboratory
California Institute of Technology
• Simulink model for LoS loop
– Integrator for LOWFS over sampling period
– Normally distributed sensor noise based on star magnitude
ZWFS sensor study
– Karman filter to reduce servo’s response to ZWFS sensor noise
– Fitted model for FSM dynamics from measurement
– PID controller
• Primary limitation is photon noise/sensing speed
• Very quiet between 15 - 40 rev/s
• Strong resonances greater than ~130 Hz tough to kill
• Faint target stars may make it tough to meet jitter requirements
if wheel speed is not properly “selected” before observation
– Data editing / smart operation to avoid high wheel seed
Jitter
Amplifier & FSM
Controller
LOWFS
OTA Simulator and LOWFSC Testbed
Pinhole
PM
OAP1
OAP4
Jitter Mirr
OAP2
OAP3
FSM
(pupil)
Fold Mirr
Focusing
Fold Mirror
LOWFS OAP
Occulter &
ZWFS Mask
L2
L1
L3
4’ x 3’ LOWFS Bench
1.5’ x 2.5’
OTA Bench
SM
(pupil)
CCD
Coro Sci
• OTA simulator consists of miniature WFIRST-AFTA telescope, relay optics, and a small jitter mirror
conjugated to the pupil (PM)
• OTA simulator uses the precision motion of the powered optics to simulate the telescope jitter and drifts
–
Line-of-sight jitter is simulated by a small mirror conjugated to pupil on a PZT stage
–
Small (~nm) low order (focus, stigmatism, coma, and spherical) wavefront error can be generated by moving powered
optics on OTA simulator (PM, SM, and OAP2) using PZT actuators
–
All PZT actuators have strain gauge to ensure the precision of their motion
Input WF Errors and Resulted Pre-Control 10%
Mean Contrast
Jet Propulsion Laboratory
California Institute of Technology
• Simulation of LOWFSC correction to a hypothetical thermal drift using a
DM which has calibration error and fitting error (preliminary results)
– Three commonly occurred wavefront drift (focus, astigmatism, and coma) are
used as the WFE input to examine the WFC with DM
• Based on the analysis of WFIRST-AFTA telescope thermal drift
• 0.1 nm WFE in 24 hour thermal cycle (lower left plot)
– The coronagraph (HLC) contrast corresponding to the three WFE modes(lower
right plot)
• Coronagraph has larger sensitivity to Coma.
Jet Propulsion Laboratory
DM Gain Calibration Errors Model
California Institute of Technology
DM w/ Act. Err. Example
OPDnom = Nominal OPD without thermal errors (post EFC)
OPDpre = Thermal + Previous Residual + OPDnom
OPDsense = Z4-Z11 Fit to (Thermal + Previous Residual)
OPDwfc = G x ∆u’
OPDpost = OPD after Z4-Z11 control = OPDpre - OPDwfc
∆OPDres(i) = OPDpost - OPDnom
= Residual OPD after ith time-series
Z4-Z11 control
∆OPDres(i) is introduced into DM1 before (i+1)th time-series Z4Z11 control
Incremental
Commands:
Modified
Static Gain Errors


∆u' = ∆u × (1 + δ ) × (1 + γ )
True
(OPDsense)
Time-dependent gain errors
(Different at different time
cases)
RMS Residual Wavefront Errors After LOWFSC
Correction Using DM with Calibration Error
Jet Propulsion Laboratory
California Institute of Technology
• Post low order wavefront correction using DM
– No WFE sensing error in this simulation. WFSC is quasi-static: the thermal drift is very slow compared to
WFSC loop bandwidth
– WFS senses only low order wavefront (Z2 - Z11) but WFE is calculated to include DM calibration error
and fitting error induced high order WFE
– DM gain calibration error varies from 5% to 30%
• The post-WFSC residual WFE shows the DM calibration gain error greatly impact the system
WF after the chasing the thermal disturbance
Broadband (10%) Contrast: After LOWFSC
Control Using DM with Calibration Error
Jet Propulsion Laboratory
California Institute of Technology
• HLC broadband (10%) contrast after the low order wavefront correction using DM
• The DM calibration gain error greatly impact the coronagraph contrast after the chasing the
thermal disturbance
• This type of DM may not be ideal for low order WF correction. Options for LOWFSC:
– Better DM calibration and smarter control. Can we do smatter things about DM act influence function?
– Using powered optics to correct low order wavefront correction. This will make the system more
complicated
– Low order wavefront sensing only and use the recorded WF information to do the post-PSF processing
Jet Propulsion Laboratory
Summary
California Institute of Technology
• Wavefront error from the WIRST-AFTA telescope jitter and thermal drift
creates many challenges for the coronagraph’s performance
• Zernike WFS is used to sense the low order wavefront drift and line-ofsight jitter using the rejected star light from the coronagraph
• Working in differential mode the ZWFS can provide the sensitivity
needed for the coronagraph
• A testbed is being built to simulate WFIRS-AFTA telescope jitter & drift
and to test the LOWFSC sub-system
• Tight requirement for deformable mirror actuator calibration is needed if
the DM is to be used for low order wavefront correction
• This work is funded by NASA Exoplanet program.
18
Backups
19
ZWFS Phase Mask Manufacturing Error Tolerance
Jet Propulsion Laboratory
California Institute of Technology
Noise Equivalent Angle (tilt)
•
•
•
•
Noise Equivalent Low Order WFE
SPC characterization mask is used for this analysis (similar result for other
configurations)
When phase-shift mask depth is off from its design specification, without
resconstructor re-calibration, phase-shift mask depth error translates directly to
sensing slope error and noise performance is degraded as expected
However, with reconstructor recalibrated using the measured mask depth, noise
performance is improved dramatically
5% manufacturing error on mask depth does not change much the noise performance