Transcript PSF reconstruction - Caltech Optical Observatories

PSF reconstruction:
a review of the quests
D. Le Mignant & R. Flicker
Outline
•
•
•
•
•
The challenge of PSF variability
Science requirements
Approaches to reconstructing the PSF
Telemetry based PSF reconstruction
The many challenges yet ahead
PSF reconstruction: a review
2/25
The challenge of PSF variability
Atmospheric variations during
observations of the Galactic
Center.
The red points indicate measurements
at zenith while the green data points
are from Galactic Center images
(courtesy M. Britton, Caltech).
PSF reconstruction: a review
3/25
The challenge of PSF variability
•
Atmospheric turbulence profile and wind
profile vary with time.
1. Temporal variation of wf phase: r0, t0, 0, L0, d0
2. Temporal variation of wf amplitude: scintillation
•
•
E.g., Kenyon 2006
Na profile vary with time as well
•
•
E.g., Drummond 2004, d’Orgeville 2003, Chueca 2004
AO correction is only partial
•
•
AO PSF displays a core/halo structure
Energy fraction in core/halo vary with time, field
location and wavelength
PSF reconstruction: a review
4/25
The challenge of PSF variability
Keck AO
Gemini/Hokupa’a GC data
4 nights - 30sec itime - 4.8”x4.8” fov
(from Christou et al. 2004)
PSF SR=1
SR=0.65
QuickTime™ and a
decompressor
are needed to see this picture.
Kp, NGS,
R mag. = 7
SR=0.15
QuickTime™ and a
decompressor
are needed to see this picture.
Kp, NGS,
R mag. = 15.3
PSF reconstruction: a review
5/25
Science-based requirements:
towards quantitative AO science
The astronomers define:
1. Photometry precision (and accuracy)
2. Astrometry precision (and accuracy)
3. Sensitivity for high-contrast and low-brightness regimes
4. Morphology (spatially resolved 1 & 2)
5. Completeness fraction (need to observe x objects)
The instrument team derive requirements for the AO facility:
1. Residual wavefront error over the science field (OPD, SR, EE)
2. Residual tip-tilt error, differential atmospheric refraction residual,
non-common path calibrations
3. Efficiency: acquisition time, duty cycle during observing sequence
4. Etc..
5. PSF calibrations requirements
PSF reconstruction: a review
6/25
The science requirements
e.g., TMT
• Differential photometric precision
– Systematic errors in differential photometry should
under 2% (10 mn integ. @ 1m over the 30”
FOV).
– Absolute photometry accuracy should be of 2%
• Differential astrometry
– Residual time dependent distortions should be
less than 10  arcsec or limited by the intrinsic
variations caused byt the atmosphere (over 30”
FOV).
PSF reconstruction: a review
7/25
The challenge of calibrating the PSF
• In many cases, the science
field does not include a “good”
PSF calibrator
– SNR, distance from GS,
background object/emission,
occulting mask, etc
QuickTime™ and a
decompressor
are needed to see this picture.
• Dedicated PSF observations is
unlikely to match the science
observations
– Atmospheric turbulence
variations, GS flux, centroid gain,
pupil angle, etc
– Setup & SNR on the science
instrument
– Difficulty to reproduce the GS /
science field geometry
(anisoplanatism)
– Time consuming
PSF reconstruction: a review
Melbourne et al. 2007
QuickTime™ and a
decompressor
are needed to see this picture.
8/25
The wavefront error residuals
• The wavefront error residuals on each
sensor (TT, LOWFS, HOWFS):
– Fitting error
– Detection noise, spatial aliasing, DM/WFS
calibrations
– Centroid gain (spot size), loop delay, nonlinearity for DM and WFS
• The atmospheric dependent aberrations:
– Isokinetic, isoplanatic effects
– Focal anisoplanatism
• The telescope, AO and science
instrument optics:
– The telescope optics wavefront error
– Static and varying non-common path
aberrations
PSF reconstruction: a review
9/25
The knowledge of the PSF
Science
Isoplanatic (NGS)
Field dependent
LGS-assisted
Method
Auto-calibration
Differential imaging
Image selection?
PSF per iso. field
PSF per iso. field
PSF observations
On-axis
GS
Field stars or cluster
GS
Field stars or cluster
Ancillary data
WFC data
WFC data
Cn2
PSF cam monitoring
WFC data
Cn2
Na profile?
PSF monitoring
Model-based PSF
Fitting error
Speckle density
Aniso. TF
Aniso. FWHM kernel
Aniso. TF
Aniso. FWHM kernel
Numerical
(Myopic)
deconvolution
Adaptive kernel
Adaptive kernel
Methodology used depends on science field, science requirements, observing
facility, skills, etc.
PSF reconstruction: a review
10/25
Designing the observations for the PSF
• On-axis: simultaneous (or a-posteriori) differential techniques used primarily
for detection of stellar companion or disk in high-contrast regimes
– In imaging mode, different flavor of the roll subtraction techniques: e.g, Liu
2004, Marois et al. 2006, Biller et al. 2007, Fitzgerald et al. 2007
– In imaging spectroscopy: e.g, McElwain et al. 2007, Janson et al. 2008
– IFS in preparation for the extreme-AO: Mugnier et al. 2008, Fitzgerald et al.
2008 (see Saturday’s session)
AU Mic observations and roll subtraction technique - Fitzgerald et al. 2007
PSF reconstruction: a review
11/25
Field-dependent PSF estimation methods
• Voitsetkhovich et al. 1998, computed the structure function due to residual
phase aberrations resulting from anisoplanatism, and predicted SR as a
function of distance from guide star.
• Fusco et al. 2000: analytical expression for the off-axis OTF as the product of
the on-axis OTF x an anisoplanatic transfer function (ATF). Demonstrated
method using Cn2 data.
• Weiss et al. 2002, demonstrated similar method with ALFA + Cn2 data
• Britton (PASP, 2006) uses similar principles to predict and reconstruct field
dependent PSF, based on DIMM/MASS Cn2 data at Palomar.
Anisoplanatic structure function estimated from Cn2 data
PSF reconstruction: a review
12/25
Field-dependent PSF estimation methods
in the absence of Cn2
• Simultaneous (or a-posteriori) observations of a calibration field to estimate
and parameterize anisoplanatism effect from “wide” field PSF s(e.g., Larkin et
al. 2000, Steinbring et al. 2005, Minowa et al. 2005, Cresci et al. 2006)
• Cresci et al. 2006, 2007 in study of Survey of Wide Area with Naco (SWAN
- 15 sq. arcmin) described the PSF as convolution between on-axis and a
spatially varying kernel (an elliptical Gaussian elongated towards the AO
guide star).
26.8” off-axis star in NGC 6752
PSF, model PSF and residuals
PSF reconstruction: a review
13/25
Isoplanatic PSF calibration methods
On-axis and isoplanatic PSF:
Extract PSF from data over an isoplanatic field (PSF is field independent) and
use estimated PSF with (myopic) deconvolution or PSF fitting techniques
•
Direct model fitting or blind deconvolution techniques (e.g., Jefferies et al. 1993,
Fusco et al. 1999, Diolaiti et al. 2000, Barnaby et al. 2000, Christou et al. 2004,
Marchis et al. 2006)
– See Christou et al. 2004 for a comparison of photometry and astrometry on crowded fields
(and low SR) with IDAC, StarFinder and parametric deconvolution.
•
Modeling the modulation transfer function, combined with OTF of the AO system to
derive the corrections for the photometry (e.g., Sheehy et al. 2006) . Photometry
accuracy within a few % compared to HST.
•
PSF reconstruction from wavefront controller data at the CFHT using the Veran
method (e.g., Beuzit et al. 2004)
PSF reconstruction: a review
14/25
WFC telemetry-based PSF reconstruction
Veran et al. 1997, JOSA A, v14, 11
• PSF related to other quantities “easier” to model and
reconstruct:
• Total OTF as the product of component OTFs
PSF reconstruction: a review
15/25
WFC telemetry-based PSF reconstruction
Veran et al. 1997, JOSA A, v14, 11
Diffraction limited
static OTF
Reconstructed
long exposure OTF
Corrected mirror
modes residual OTF
High-order component of
the turbulent phase OTF
Measured PSF
(high SNR or artificial source)
Estimate phase
structure function
from WFC data / model
Atmospheric turbulence
model scaled by D/r0
(Kolmogorov, van Karman)
Assuming:
1. No scintillation
2. Gaussian statistics for the residual phase error
3. Parallel and orthogonal phase components are statistically uncorrelated
4. Structure function of the residual phase is homogeneous
5. “infinite bandwidth” approximation
PSF reconstruction: a review
16/25
WFC telemetry-based PSF reconstruction
Veran et al. 1997, JOSA A, v14, 11
• The parallel component can be estimated from the mean
residual phase structure function
<T>: residual mode covariance matrix measured by averaging
cross-products of modal coordinates during an exposure.
• Uij functions computed for mirror modes M over the aperture P
Nx(N+1)/2 Uij functions that are computed once
PSF reconstruction: a review
17/25
WFC telemetry-based PSF reconstruction
Gendron et al. 2006, A&A, 457, 359
• Uij functions with 100-1000 actuators (and corrected modes)
produces Gb of data to store and load for each calculations (heavy
and slow).
• Two new algorithms which take advantage of the eigen
decomposition of the residual parallel phase covariance matrix :
Vii algorithm:
The residual parallel phase covariance matrix is diagonal in this new basis
N mirror modes that needs to be computed on-the-fly
PSF reconstruction: a review
18/25
WFC telemetry-based PSF reconstruction
Gendron et al. 2006, A&A, 457, 359
• Instantaneous PSF: the eigen decomposition is used to compute
phase screens
• The phase screens follow the same statistics as the residual
parallel phase covariance matrix.
• Instantaneous OTF averaged out to produce long exposure of the
mirror space PSF.
• Does not include the uncorrected part of the phase!
• Useful to assess variability of the AO PSF
PSF reconstruction: a review
19/25
WFC telemetry-based PSF reconstruction
Gendron et al. 2006, A&A, 457, 359
• Uij and Vij methods provide identical results in simulation
• Vii implementation show faster computation time (~ 20x gain for N
=160)
Radial average of PSF for 3 stars: 7.3, 12.3 and 13.6
(bottom to top)
Residual phase only (no fitting error)
PSF reconstruction: a review
20/25
Components of the PSF reconstruction
•
Fitting error (orthogonal phase)
– Turbulence PSD based on Kolmogorov or van
Karman models (e.g. Flicker 2008)
– Model for the atmosphere (measured or reference
Cn2)
– Binary mask (spatial high-pass filter) on the
turbulence PSD (e.g., Veran, Jolissaint)
– Monte-Carlo simulation to estimate ratio of the PSD
(e.g., Flicker 2008)
– Scaled by D/r0 with r0 (and L0) estimated from the
modal variance based on the DM commands
•
Residual mode covariance matrix
–
–
–
–
–
–
Temporal modeling required
DM control law
r, spatial aliasing simulated or modeled
n, noise covariance matrix
u, y and s from telemetry (Keck)
Separable TT structure function
PSF reconstruction: a review
21/25
Estimating the PSF from the AO-system
•
Veran 1997 for CFHT-PUEO
–
•
Weiss et al. 2003 for ALFA on-axis
–
•
Developed Vii method. Demonstrated in simulation and test bench. Changes to NACO RTC done. Awaiting more
engineering data and full integration. More tests being performed on Sesame AO bench. See Talk on Saturday.
Marino et al. 2006 for the Dunn Solar Telescope
–
•
Demonstrated principle in NGS AO. Needed to improve calibrations and spot size estimation, then include TT sensor for
LGS. The effort is not pursued in the short term.
Clenet et al. 2006 &2008 for VLT/NACO
–
•
Demonstrated principle in NGS AO, developed OPERA software, awaiting more engineering data and integration for
routine operations. The effort is not pursued in the short term.
Fitzgerald et al. 2004 for Lick AO
–
•
Uses on-axis principle, plus an anisoplanatism term. Requires simultaneous Cn2 data. Principle demonstrated. The effort
is not currently being pursued for routine operations.
Jolissaint et al. 2005 for Gemini-Altair
–
•
Demonstrated principle in NGS AO. Some quantities not readily available from telemetry. Not (fully) implemented for
science operations.
Egner et al. 2004 for ALFA off-axis
–
•
designed, integrated and commissioned with AO system, PSF reconstruction data delivered with science data, used for
routine operations since 1998.
Demonstrated principle for solar AO. Integrated for routine operations? Effort pursued?
Flicker et al. 2008 for the Keck II AO
–
Started in Nov 07. Goal; NGSAO demonstrated by end of year. Development of system components.
PSF reconstruction: a review
22/25
Addendum by Ralf (7/24/2008)
PSF reconstruction: a review
23/25
Future challenges for PSF reconstruction
• Only one telemetry-based system in operation
– Designed-in and built-in for PUEO, integrated with AO
– Performance for different science areas?
• What is the required accuracy for the
reconstructed PSF with current systems?
– Jolissaint’s poster this evening
• Difficult integration with current AO systems?
– Significant effort that requires AO scientists,
development phases, test time on bench, changes to
existing systems, integration, eng. time, observatory
and users’ support!
PSF reconstruction: a review
24/25
Future challenges for PSF reconstruction
• Ancillary data such as Cn2 are critical to AO integration and
performance monitoring.
– Britton and others also demonstrated it provides an accurate solution for the
anisoplanatic PSF reconstruction.
• Missing from this review are the tomography-based algorithm
and demonstration for PSF reconstruction.
– MCAO should provide more PSF uniformity
• If telemetry-based PSF reconstruction techniques critical for
AO quantitative science with future systems, then it is
important to learn more about PSF reconstruction using
current AO systems. If so,
– Requires collaboration between astronomers and AO scientists.
– Develop an observing scenario for the PSF knowledge and calibration
for the science cases
• “Developing PSF knowledge benefit the science"
PSF reconstruction: a review
25/25
Thank you!