Tomographic phase diversity for non-common path ... - AO4ELT 2

Tomographic phase diversity for
non-common path aberration
retrieval on wide field AO
systems
F.Rigaut (1) , D.Gratadour (2) & B.Neichel (1)
(1) Gemini Observatory
(2) LESIA, Observatoire de Paris-Meudon
OSA, AO Session, Toronto, July 10-14, 2011
Wednesday, 28 September 11
1

Motivations
Wide field AO systems require dedicated methods for
non-common path aberration (NCPA) correction to
cancel aberrations simultaneously over the entire FoV
Use a focal-based approach:
optimize image where it needs to be optimized
easy to acquire many measurement points simultaneously
saves hardware
Leverage Phase Diversity (PD), a known and proven
technique (Paxman et al 1982, Blanc et al 2003,
Hartung et al 2003)
On cal source: simplified PD, straightforward object
Kolb (2006): wide field capable but not intrinsically
tomographic
OSA, AO Session, Toronto, July 10-14, 2011
Wednesday, 28 September 11
2

NCPA initial approach
for GeMS
Multiple (typ. 9) 24x24 SHWFS
measurements spanning the
85”x85” FoV
Feed to Tomographic
reconstructor (synthetic)
➜ phase @ multiple altitude
Project on LGS WFS slopes
Typical performance, average
over field of view:
from SH ~ 5 to 50% (inc. astigs)
to SH ~ 95%
OSA, AO Session, Toronto, July 10-14, 2011
Wednesday, 28 September 11
3

Example of preliminary SHWFS + tomography
AO4ELTs2, Victoria/Canada, September 26-30, 2011
Wednesday, 28 September 11
4

NCPA issues for wide field systems
Impossibility to compensate for anything that’s not
occuring close to the DM altitude !
Beware optical designers
Need to multiplex for efficient/quick convergence
MCAO: funky effects induced by WFSs differential
aberrations (finite range, off-axis LGS sources). Lead to
non tomographic error. Funny reconstruction
MCAO tips and tricks: Filtering of quadratics
General note: Zernikes are well known, but bad when
considering N>~80 due to extreme edge slopes.
A good replacement are KL or Disk Harmonic
OSA, AO Session, Toronto, July 10-14, 2011
Wednesday, 28 September 11
5

Two new ideas (as far as I know ?)
Tomographic phase diversity:
The classical PD approach can be extended to process data over
an extended field of view.
Instead of solving for a 2D phase, solve for a 3D phase (discrete
or continuous). E.g 2-3 phase planes + a tomographic projector
Naturally more overconstrained/robust than PD in individual
direction + tomographic reconstruction (assuming # of field
positions/images is larger than the # of phase planes).
The PD minimisation criterion can be expressed in the
Fourier plane (OTF-based phase diversity)
(Potentially) saves one Fourier transform
Allow weighting per spatial frequencies
✚ I will present 2 packages developed by D.Gratadour
(PRAy, image based) and F.Rigaut (OPRA, OTF-based)
OSA, AO Session, Toronto, July 10-14, 2011
Wednesday, 28 September 11
6

“Classical” PD
2D-phase
PSF
Vib Kernel
Object
Minimization
method
Model
Data
Criterion
Single focal
plane point
OSA, AO Session, Toronto, July 10-14, 2011
Wednesday, 28 September 11
7

“Tomographic” PD
3D-phase
PSF
Vib Kernel
Object
Minimization
method
Model
Data
Many focal
Criterion
plane points
OSA, AO Session, Toronto, July 10-14, 2011
Wednesday, 28 September 11
8

Tomographic PD ≠ PD + Tomography
In tomographic phase diversity, data = all focal plane
images and the free parameters include the 3D phase
volume. The Tomography is solved naturally by the
minimization process.
avoids an intermediate step, lower noise propagation (?)
overconstrained problem, reduce risk of being trapped in local
minima, lower noise propagation (?)
iterative, thus slower
Opposite, the PD + tomography does PD for each focal
plane image independently, then uses the retrieved
phases to feed a more conventional linear tomographic
reconstruction.
Slightly faster (PD speed ^ faster than #par)
Easier to tune tomography (add virtual layers, etc)
OSA, AO Session, Toronto, July 10-14, 2011
Wednesday, 28 September 11
9

Pray
PRAy = Phase Retrieval Algorithm in yorick
Classical or tomographic. Can use zonal or modal
(Zernike/DH/KL) “influence functions”.
2D Gaussian kernel/object (for vibration modelling)
Can fit focus scale, differential TT between stars
Uses optimpack (yorick pluging from E.Thiebaut, main
algorithm is VMLM-B: a variable metric method with
limited memory requirements with optional bound
constraints on the parameters)
Fast. Typically 1 it/s for a GeMS case; 920 actuators /
19x3 images on 64x64 arrays (typically reach a solution
within a minute).
OSA, AO Session, Toronto, July 10-14, 2011
Wednesday, 28 September 11
10

Pray GUI
OSA, AO Session, Toronto, July 10-14, 2011
Wednesday, 28 September 11
11

Wednesday, 28 September 11
12

OPRA
OPRA = Otf-based Phase Retrieval Analysis
OTF-based (duh); the data and model are expressed in
the Fourier plane
Use Levenberg-Marquardt minimisation
The following quantities can be free parameters
phase (modal, Zernikes/DH/KL or can use yao machinery in 3D)
image pixel size/lambda
defocus scale
2D gaussian kernel (vibrations)
differential image positions and intensity in 3D mode
Uses numerical finite difference. Slow, but arbitrary
recipes/parameters can be easily introduced (testing
tool for now). Speed is an issue for use w/ CANOPUS.
OSA, AO Session, Toronto, July 10-14, 2011
Wednesday, 28 September 11
13

OPRA GUI
OSA, AO Session, Toronto, July 10-14, 2011
Wednesday, 28 September 11
14

Wednesday, 28 September 11
15

Loop closed, one it.
Loop closed, no NCPA
of TomoPD NCPA.
SH 5% to 50%
SH ~ 72%
Wednesday, 28 September 11
16

Some quantitative results on sim. data
OSA, AO Session, Toronto, July 10-14, 2011
Wednesday, 28 September 11
17

Some quantitative results on sim. data
OSA, AO Session, Toronto, July 10-14, 2011
Wednesday, 28 September 11
18