Transcript ao2004 3674

Fundamentals of closed loop
wave-front control
M. Le Louarn
ESO
Many thanks to
E. Fedrigo
for his help !
Introduction
Atmospheric turbulence: structure &
temporal evolution
 AO control and why a closed loop ?
 Optimal modal control & AO temporal model
 A real world example: MACAO
 Advanced concepts: Predictive control,
MCAO et al.
 Future directions

Temporal evolution of atmospheric turbulence

Model phase perturbations as thin turbulence
layers
 Temporal evolution: only shift of screens, i.e.
assume frozen flow (“Taylor hypothesis”)
 There is experimental evidence for this:



Gendron & Léna, 1996
Schöck & Spillar, 2000
Idea: predict WFS measurements, if wind
speed & direction are known/measured
 But, when there are several layer, things get
complicated
Atmospheric structure (Cn2)
Atmospheric structure (v(h))
AO Closed loop
AO and atmospheric turbulence
AO must be fast enough to follow
turbulence evolution
 Greenwood & Fried (1976), Greenwood
(1977), Tyler 1994
 BW requirements for AO



5
6 / 5
2
3
f G(λ)  0.1024 λ  v (h)C n (h)dh 
0



Greenwood
frequency
Correlation
time



5
2
2
3
0 ()  2.91k sec(z) v (h)Cn (h)dh
0


3
5
3
5
fG~10-30 Hz
at 0.5 um
0  3-6 ms at
0.5 um
Errors in AO

photon noise
+
 read-out noise
+
 aliasing
gather enough photons to reduce measurement noise
read the detector
compute the DM commands
 atmosphere has evolved between measurement and command
 temporal delay error:
+
 fitting
+
 temporal delay
 5/3
 ( )
0
2
 : delay between the beginning of the measurement and
the actuation of the DM
0 : atmospheric correlation time
Rousset 94, Parenti & Sasiela 94
Why closed loop ?

There is a good reconstruction algo (=get the right
answer in 1 iteration).
 Hardware issues:



DM hysteresis (i.e. don’t know accurately what shape
DM has)
WFS dynamic range: much reduced if need only to
measure residuals.
E.g. on SH, Open loop requires more pixels more
noise
WFS linearity range : for some WFSs, this is critical: SH
with quad-cell, Curvature WFS…
 Closed loop hides calibration / non-linearity
problems
 Closed loop statistics harder to model



PSF reconstruction gets harder
Loop optimization harder
Interaction matrix in (MC)AO

Move one actuator on the deformable mirror

response DM  influence function
Propagate this DM shape to the conjugation height of the
WFS (usually ground)


measure of the response current WFS ( b )
 store b in the interaction matrix (M)

as many rows as measurements and columns as actuators

Invert that matrix (+ filter some modes)
 command matrix: M+ (LS estimate)
  command vector c of the DM :




t
1
t
c  M  b  (M M ) M  b
Optimizing control matrix

Problem: previous method doesn’t know
anything about:

Atmospheric turbulence power spectrum
 A priori knowledge



MAP
Minumum variance methods (e.g. Ellerbroek 1994)
[…]
Guide star magnitude
 Temporal evolution (turbulent speed, system
bandwidth)
  See talks by Marcos van Dam & J.M. Conan

A word on modal control

The previously generated command matrix controls
“mirror modes”
 Some filtering is usually required (there are ill
conditioned modes)
 Strategy: filter out “unlikely” modes

Project system control space on some orthogonal
polynomials, like:




Zernike polynomials
KL-polynomials
[…]
Use atmospheric knowledge to guess which of those
modes are not likely to appear in the atmosphere (see talk
by J.-M. Conan)
Optimized modal control

Must evaluate S/N of measurements and include it in
command matrix
 Gendron & Léna (1994, 1995)
 Ellerbroek et al., 1994
 Idea: low order modes should have better S/N because they
have lower spatial frequencies




 Compute, for each corrected mode, the optimal
bandwidth: allows in effect to change integration time
Need to estimate




E.g. Tip-tilt has a lot of signal (measured over a large pupil)
High orders need more integration time to get enough signal.
Noise variance (at first in open loop)
PSD of mode fluctuations
Sys transfer fn
Include these gains in the
command matrix:

M  VGoptWU
t
Requirements

We need to:
Identify delays in the system
  Model system’s transfer function
 Measure the measurement noise in the
WFS
 Atmospheric noise

Major AO delay sources
Integration time: need to get photons
 CCD read-out time ~ integration time
 WFS measurement processing:

~4ms
Flat-fielding
 Thresholding
 CCD de-scrambling

~1ms
Matrix multiplication
 Actuation (time between sending
command and new DM shape)
 NOTE: some of these operation can be (and
are) pipelined to increase performance

MACAO Control Loop Model
Aberrated
Wavefront
Corrected
Wavefront
Digital System
+
-
WFS
RTC
DAC
HVA
DM
WFS: integrator from t to t+T
RTC: computational delay + digital controller
DAC: zero-order holder
HVA: low-pass filter, all pass inside our bandwidth
DM: low-pass filter, all pass inside our bandwidth (first approximation)
System frequency: 350 Hz
T = 2.86ms
τ = 0.5 ms
HVA bandwidth: 3Khz
E. Fedrigo
DM first resonance: 200 Hz
AO open loop transfer function
1  exp[Ts ] 
H ( s)  
exp[s]C ( s)

Ts


2

H(s): Open loop transfert function
 C(s): Compensator’s continuous transfer
function (usually ~integral…)
K
C (s) 

s
T: Integration time (= sampling period (+ readout))
 : Pure delay
 Simplistic model (continuous, not all errors…),
can of course be improved
Noise estimation

It is possible to compute (Gendron & Léna
1994):
 0 ( g )   Hcor ( f , g )  (T ( f )  B( f )  b0 )df  b0   H ( f , g )df
n
Residual error
on a mode
Bandwidth error
Noise error
Noise estimation

It is possible to compute (Gendron &
Léna, 1994):
 0 ( g )   Hcor ( f , g )  (T ( f )  B( f )  b0 )df  b0   H ( f , g )df
n
where :
0(g): residual phase error on a mode (for a mode)
g: modal gain for mode ( BW), Fe: sampling freq
Hcor(f,g): correction transfer function
T(f): PSD of fluctuations due to turbulence
B(f): PSD of noise propagated on mode
b0: average level of B(f): b0  2 F / 2B( f ) df
e
Fe

0
Hn: transfer fn white noise input  noise output on
mirror mode controls.
Measuring the noise variance
Gendron
&
Lena
1994
Optimized modal control
Gendron
&
Lena
1994
Correction BW not very
sensitive to b0 estimate
Optimized modal control
High order modes have
less BW
than low order modes
Gendron
&
Lena
1994
Closed loop optimization

Problems:




noise estimation+transfer function model need (too)
good accuracy
Turbulence is evolving rapidly must adapt gains
Non linearity problems in WFS possible (e.g. curvature)
Rigaut, 1993: Use closed-loop data as well
 Dessenne et al 1998:
(PUEO)
Minimization of residuals of WFS error
 Reconstruction of open loop data from CL
measurements
Algorithm must be quick to follow turbulence evolution (few
minutes)



Iterative process: initial gain “guess” (from simulation) improved with
closed-loop data, by minimizing WFE estimate.
An example AO system: MACAO
Multi Application Curvature Adaptive Optics system

60 elements Curvature System (vibrating membrane, radial
geometry micro-lenses, Bimorph Deformable Mirror and TipTilt mount)
 2.1 kHz sampling, controlled 350 Hz, expected bandwidth ~50
Hz
 Real Time Software running a PowerPC 400 MHz Real Time
Computer

WaveFrontSensor detector: APD coupled with optical fibers 
no significant RON, or read-out time

Modular approach (4 VLTI units+SINFONI/CRIRES+spares)
Strap quadrant detector tip-tilt sensor+ TCCD (VLTI)

A real system: MACAO
Telescope
Control
M2
Guide
Probe
Corrected
Wavefront
1Hz
ATM+TEL
CWFS
Adaptive
Control
DM
TTM
350Hz
5Hz
Low Pass
Low Pass
E. Fedrigo
1Hz
LGS Control
Telescope
Control
M2
LGS
Defocus
Guide
Probe
Corrected
Wavefront
Airmass
Trombone
Low Pass
1Hz
ATM+TEL
CWFS
Adaptive
Control
DM
TTM
500Hz
5Hz
E. Fedrigo
0.03Hz
Low Pass
Low Pass
1Hz
System Bandwidth
Measured Close-Loop Error Transfer Function
10
10
M A C A O 1 in n e r rin g c lo s e d -lo o p e rro r t ra n s fe r fu n c t io n fo r g = 7 0 % , t u rb = 1 0 , 2 5 , 5 0 %
M A C A O 1 in n e r rin g c lo s e d -lo o p e rro r t ra n s fe r fu n c t io n fo r g = 7 0 % , t u rb = 1 0 , 2 5 , 5 0 %
0
0
g a in (d B )
g a in (d B )
-1 0
-1 0
-2
-200
-3
-300
-4
-400
-5
-500 0
1100 0
(0.45” seeing in V)
1
1100 1
fre
freqquueennccyy (H
(Hzz) )
Plots: courtesy of Liviu Ivanescu, ESO
2
1100 2
Predictive & more elaborate control


How to improve control BW ?
Turbulence is predictable



Several approaches (at least):









Schwarz, Baum & Ribak, 1994
Aitken & McGaughey, 1996
Madec et al., 1991, Smith compensator : takes lag into account
Paschall & Anderson, 1993 : Kalman filtering : see talk by Don Gavel
Wild, 1996 : cross covariance matrices
Dessenne, Madec, Rousset 1997: predictive control law
There is a performance increase in BW limited system
Layers are not separated, so “hard job”
Unfortunately, gain seems small for current single GS AO systems.
Static aberrations need to be taken into account: residual mode error  0
Telescope vibrations need special attention
Predictive control
Dessenne, Madec, Rousset, 1999
MCAO / GLAO

General case of AO, Several WFSs, several
DMs
Observation / optimization
direction
Measurement
Direction 1
Challenge:find clever ways to work in closed loop !
Are the sensors always seeing the correction ?
Measurement
Direction 2
The future

MCAO



ELTs / ExAO: fast reconstructors, because MVM grows
quickly w/ number of actuators





FFT-based
Sparse matrix
[…]
 predictive methods to the rescue !?
Segmentation


Allow better temporal predictability if layers are separated
Control of several DMs, WFSs, possibly in “open loop”
Algorithms investigated to use AO WFS info to co-phase
segmented telescopes
Kalman filtering


Optimize correction in closed loop, reliable noise estimates,
complex systems
Applicable to MCAO