Title: Outline
1Outline
- AO Imaging
- Constrained Blind Deconvolution
- Algorithm
- Application
- - Quantitative measurements
- Future Directions
2References
- S.M. Jefferies J.C. Christou, Restoration of
astronomical images by iterative blind
deconvolution, Astrophys. J., 415, 862-874,
1993. - E. Thiébaut J.-M. Conan, Strict a priori
constraints for maximum-likelihood blind
deconvolution, J. Opt. Soc. Am., A, 12, 485-492,
1995. - J.-M. Conan, L.M. Mugnier, T. Fusco,, V. Micheau
G. Rousset, Myopic deconvolution of adaptive
optics images by use of object and
point-spread-function power spectra, App.
Optics, 37, 4614-4622, 1998. - B.D. Jeffs J.C. Christou, Blind Baysian
Restoration of Adaptive Optics images using
generalized Gaussian Markov random field models,
Adaptive Optical System Technologies, D.
Bonacinni R.K. Tyson, Ed., Proc. SPIE, 3353,
1998. - E.K. Hege, J.C. Christou, S.M. Jefferies M.
Chesalka, Technique for combining
interferometric images, J. Opt. Soc. Am. A, 16,
1745-1750, 1999. - T. Fusco, J.-P. Véran, J.-M. Conan, L.M.
Mugnier, Myopic deconvolution method for
adaptive optics images of stellar fields,
Astron. Astrophys. Suppl. Ser., 134, 193-200,
1999. - J.C. Christou, D. Bonaccini, N. Ageorges, F.
Marchis, Myopic Deconvolution of Adaptive Optics
Images, ESO Messenger, 1999. - T. Fusco, J.-M. Conan, L.M. Mugnier, V. Micheau,
G. Rousset, Characterization of adaptive
optics point spread function for anisoplanatic
imaging. Application to stellar field
deconvolution., Astron. Astrophys. Suppl. Ser.,
142, 149-156, 2000. - E. Diolaiti, O. Bendinelli, D. Bonaccini, L.
Close, D. Currie, G. Parmeggiani, Analysis of
isoplanatic high resolution stellar fields by the
StarFinder code, Astron. Astrophys. Suppl. Ser.,
147, 335-346 , 2000. - S.M. Jefferies, M. Lloyd-Hart, E.K. Hege J.
Georges, Sensing wave-front amplitude and phase
with phase diversity, Appl. Optics, 41,
2095-2102, 2002.
3Adaptive Optics Imaging
Adaptive Optics systems do NOT produce perfect
images (poor compensation)
Seeing disc
Without AO
4Adaptive Optics Imaging
- Quality of compensation depends upon
- Wavefront sensor
- Signal strength signal stability
- Speckle noise - d / r0
- Duty cycle - t / t0
- Sensing observing - ?
- Wavefront reconstructor geometry
- Object extent
- Anisoplanatism (off-axis)
5Adaptive Optics PSF Variability
- Science Target and Reference Star typically
observed at different times and under different
conditions. - Differences in Target Reference compensation
due to - - Temporal variability of atmosphere(changing r0
t0). - - Object dependency (extent and brightness)
affecting centroid measurements on the
wavefront sensor (SNR). - - Full sub-aperture tilt measurements
- - Spatial variability (anisoplanatism)
- In general Adaptive Optics PSFs are poorly
determined.
6Why Deconvolution and PSF Calibration?
- Better looking image
- Improved identification
- Reduces overlap of image structure to more
easily identify features in the image (needs high
SNR) - PSF calibration
- Removes artifacts in the image due to the point
spread function (PSF) of the system, i.e.
extended halos, lumpy Airy rings etc. - Improved Quantitative Analysis
- e.g. PSF fitting in crowded fields.
- Higher resolution
- In specific cases depending upon algorithms and
SNR
7The Imaging Equation
- Shift invariant imaging equation
- (Image Domain)
- (Fourier Domain)
g(r) f(r) h(r) n(r)
G(f) F(f) H(f) N(f)
g(r) Measurement h(r) Point Spread Function
(PSF) f(r) Target n(r) Contamination - Noise
8Deconvolution
- Invert the shift invariant imaging equation
- i.e. solve for f(r) INVERSE PROBLEM
- given both g(r) and h(r).
- - But h(r) is generally poorly determined.
- - Need to solve for f(r) and improve the h(r)
estimate simultaneously. - Unknown PSF information
- Some PSF information
- Blind (Myopic) Deconvolution
9Blind Deconvolution
Solve for both object PSF
contamination
Measurement
unknown object irradiance
unknown or poorly known PSF
Single measurement Under determined - 1
measurement, 2 unknowns Never really blind
10Blind Deconvolution Physical Constraints
- How to minimize the search space for a solution?
- Uses Physical Constraints.
- f(r) h(r) are positive, real have finite
support. - h(r) is band-limited symmetry breaking
- prevents the simple solution of h(r) ?(r)
- a priori information - further symmetry breaking
(a b b a) - Prior knowledge (Physical Constraints)
- PSF knowledge band-limit, known pupil,
statistical derived PSF - Object PSF parameterization multiple star
systems - Noise statistics
- Multiple Frames (MFBD)
- Same object, different PSFs.
- N measurements, N1 unknowns.
11Multiple Frame Constraints
Multiple Observations of a common object
- Reduces the ratio of unknown to measurements from
21 to n1n - The greater the diversity of h(r),the easier the
separation of the PSF and object.
12An MFBD Algorithm
- Uses a Conjugate Gradient Error Metric
Minimization scheme - - Least squares fit.
- Error Metric minimizing the residuals
(convolution error) - Alternative error metric minimizing the
residual autocorrelation - Autocorrelation of residuals
- Reduces correlation in the residuals
- (minimizes print through)
- So not sum over the 0 location.
-
13An MFBD Algorithm
- Object non-negativity
- Reparameterize the object as the square of
another variable HARD - or penalize the object against negativity.
- SOFT
- PSF Constraints (when pupil is not known)
- - Non-negativity
- Reparameterize - or penalize
- - Band-limit
14PSF Constraints
- Use as much prior knowledge of the PSF as
possible. - Transfer function is band-limited
- PSF is positive and real
MTF
fc D/?
15An MFBD Algorithm
- PSF Constraints (Using the Pupil)
- - Parameterize the PSF as the power spectrum of
the complex wavefront at the pupil, i.e. - where
-
PSF
Pupil
16PSF Constraints
- PSF Constraints (Using the Pupil)
- - Modally - express the phases as either a
set of Zernike modes of order M - - or zonally as
where which - enforces spatial correlation of the
phases. - Phases can also be constrained by statistical
knowledge of the AO system performance. - Wavefront amplitudes can be set to unity or can
be solved for as an unknown especially in the
presence of scintillation.
17Object Constraints
- In an incoherent imaging system, the object is
also real and positive. - The object is not band-limited and can be
reconstructed on a pixel-by-pixel basis leads
to super-resolution (recovery of power beyond
spatial frequency cut-off). - Limit resolution (and pixel-by-pixel variation)
by applying a smoothing operator in the
reconstruction. - Parametric information about the object structure
can be used (Model Fitting) - - Multiple point source
- - Planetary type-object (elliptical uniform
disk)
18Object Constraints
- Local Gradient across the object defines the
object texture (Generalized Gauss-Markov Random
Field Model), i.e. fi fj p where p is the
shape parameter.
19Object Constraints
20Object Prior Information
- Planetary/hard-edged objects (avoids ringing)
-
- Use of the finite-difference gradients ?f(r) to
generate an extra error term which preserves hard
edges in f(r). - ? ? are adjustable parameters.
21An MFBD Algorithm
- Myopic Deconvolution (using known PSF
information) - - Penalize PSFs for departure from a typical
PSF or model (good for multi-frame
measurements) - - Penalize PSF on power spectral density (PSD)
- where the PSD is based upon the atmospheric
conditions and AO correction.
22An MFBD Algorithm
- Further Constraints
- Truncated Iterations (Tikenhov)
- Support Constraints
- In many cases, a limited field is available and
it is important to compute the error metric only
over a specific region M of the observation
space, i.e.
23idac iterative deconvolution algorithm in c
- SNR Regularization (Fourier Domain)
- Minimize in the Fourier domain rather than the
image domain, i.e. -
- where
24An MFBD Algorithm
- Forward Modeling of Imaging Process
- Compute Error Metric based on Measurement
- where data is not pre-processed
Noise terms
Measurement
Signal
Background (sky dark)
Gain (flatfield)
25idac an MFBD Algorithm
- idac is a generic physically constrained
blind-deconvolution algorithm written in C and is
platform independent on UNIX systems. - Maximum-likelihood with Gaussian statistics
error metric minimization using a conjugate
gradient algorithm. - It can handle single or multiple observations of
the same source. - It allows masking of the observation (convolution
image) permitting the saturated regions to make
no contribution to the final results for both the
target and the PSF. - It has the option to fit a the strength of a bias
term in the image (skydark) asik - The algorithm can be run as with either a fixed
PSF or a fixed object or both unknown. - idac was written by Keith Hege Matt Chesalka
(as part of a collaborative effort with Stuart
Jefferies and Julian Christou) and is made
available via Steward Observatory and the CfAO.
26idac iterative deconvolution algorithm in c
- Conjugate Gradient Error Metric Minimization
- Convolution Error
- Band-limit Error
- Non-negativity
-
- PSF Constraint (for multiple images)
27idac Software Page
http//cfao.ucolick.org/software/idac/ http//bach
.as.arizona.edu/hege/docs/docs/IDAC27/idac_packag
e.tar.gz
28Application of idac
- Investigation of relative photometry and
astrometry in deconvolved image. - - Gemini/Hokupaa Galactic Center data
- - PSF reconstruction
- Application to various astronomical AO images.
- - Resolved Galactic Center sources (bow-shocks)
- - Solar imaging
- - Solar system object (Io) comparison with
Mistral - Artificial satellite imaging
- Non-astronomical AO imaging.
29Application of idac
- How well does the deconvolved image retain the
photometry and astrometry of the data? - - It has been suggested that it is better to
measure the photometry especially from the raw
data. - - Investigated using dense crowded field data
from Gemini/Hokupaa commisioning data. - - Comparison of Astrometry and Photometry from
these data to that measured directly via
StarFinder. - - Comparison of both techniques to simulated
data.
30Hokupaa Galactic Center Imaging
Crowded Stellar Field with partial
compensation Difficult to do photometry and
astrometry because of overlapping PSFs - Field
Confusion Need to identify the sources for
standard data-reduction programs.
See Poster
31Observed GC Field
- Gemini /Hokupaa infrared (K?
- with texp 30s) observations of a
- sub-field near the Galactic Center.
- 4 separate exposures
- Note the density of stars in the field.
- FOV 4.6 arcseconds
- Reduced with idac StarFinder
StarFinder is a semi-analytic program in IDL
which reconstructs AO PSF and synthetic fields of
very crowded images based on relative intensity
and superposition of a few bright stars
arbitrarily selected. It extracts the PSF
numerically from the crowded field and then fits
this PSF to solve for the stars position and
intensity.
32Gemini Imaging of the Galactic Center -
Deconvolution
- Initial Estimates
- Object 4 frames co-added
- PSF K' 20 sec reference
- (FWHM 0.2")
- 4.8 arcsecond subfield
- 256 x 256 pixels
- (This is a typical start for this algorithm)
33Gemini Imaging of the Galactic Center -
Deconvolution
4 frame average for each of the sub-fields.
idac reductions. FWHM 0.07"
34Gemini Imaging of the Galactic Center PSF
Recovery
- Frame PSF recovered by isolating individual star
from f(r) and convolving with recovered PSFs,
h(r).
35Gemini Imaging of the Galactic Center
- Data Reduction Outline
- Blind Deconvolution to obtain target PSF
- Estimate PSF from isolated star and h(r)
- Fixed deconvolution using estimated PSF
- Blind Deconvolution to relax PSF estimates
36Gemini Imaging of the Galactic Center Object
Recovery
- Average observation
- initial idac
result -
fixed PSF result
37Gemini Imaging of the Galactic Center Image
Sharpening
- FWHM
- Compensated 0.20 arcsec
- Initial - 0.07 arcsec
- Final - 0.05 arcsec
- Diffraction-limit
- a 0.06 arcsec
38Observed GC Field Reconstructions
Reconstructed star field distributions from
StarFinder as applied to the four separate
observations. StarFinder is a photometric fitting
packages which solves for a numerical PSF.
39Observed GC Field Reconstructions
- The fainter the point source, the broader it
is. - Magnitude measurement depends upon measuring
area and not peak.
40Observed GC Field - Photometry
Common Stars
- Comparison of Photometry and for the 55 common
stars in the 4 frame StarFinder and IDAC
reductions. There is close agreement between the
two up to 3.5 magnitudes. Then there is a trend
for the IDAC magnitudes to be fainter than the
StarFinder ones. This can be explained by the
choice of the aperture size used for the
photometry due to the increasing size of the
fainter sources. Even so, the rms difference
between them is still ? 0.25 magnitudes. A more
sophisticated photometric fitting algorithm than
imexamine is therefore suggested.
41Observed GC Field - Astrometry
Common Stars
- Comparison of Astrometry and for the 55 common
stars in the 4 frame StarFinder and IDAC
reductions. The x and y differences are shown by
the appropriate symbols. The dispersion of ?
10-14 mas is small, less than a pixel, and a
factor of four less than the size of the
diffraction spot.
42Observed GC Field PSF Reconstructions
Blind Deconvolution
StarFinder
- Reconstructed PSFs for the four frames using IDAC
(top) and StarFinder (bottom). The PSF cores
(green and white) are essentially identical with
the StarFinder PSFs generally having larger wings.
43Simulated GC Field Comparisons
Comparison of aperture photometry from blind
deconvolution to true magnitudes for the
simulated GC field.
Comparison of aperture photometry from blind
deconvolution to StarFinder analysis for the
simulated GC field.
44Observed GC Field PSF Reconstructions
- Reconstructed PSFs for the four frames using IDAC
(top) and StarFinder (bottom). The PSF cores
(green and white) are essentially identical with
the StarFinder PSFs generally having larger wings.
45Extended Sources near the Galactic Center
- Point sources show strong uncompensated halo
contribution.
- Bow shock structure is clearly seen in the
deconvolutions.
Data from Angelle Tanner, UCLA
46Adaptive Optics Solar Imaging
- Low-Order AO System
- Lack of PSF information.
- Sunspot and granulation features show improved
contrast, enhancing detail showing magnetic field
structure
Data from Thomas Rimmele, NSO-SP
47ADONIS AO Imaging of Io
- 3.8 ?m
- Two distinct hemispheres
- 11 frames/hemisphere
- Co-added initial object
- PSF reference as initial PSF
- Surface structure visible showing volcanoes.
- (Marchis et. al., Icarus, 148, 384-396, 2000.)
48Keck Imaging of Io
- Why is deconvolution important? This is why
(Data obtained by D. LeMignant F. Marchis et
al.)
49Keck Imaging of Io
Why is deconvolution important? This is why
(Data obtained by D. LeMignant F. Marchis et
al.)
50Io in Eclipse
- Two Different BD Algorithms
- Keck observations to identify hot-spots.
- K-Band
- 19 with IDAC
- 17 with MISTRAL
- L-Band
- 23 with IDAC
- 12 with MISTRAL
51Artificial Satellite Imaging
256 frames per apparition
52Summary
- Blind/Myopic Deconvolution is well suited to AO
imaging where the PSFs are not well known. - Incorporate as many physical constraints about
the imaging process as possible. - Building a specific algorithm to match the
application is advantageous. - This algorithm (idac) suffers from the same
problem as others in that the PSF get wider as
the dynamic range increases ( a problem of
half-wave rectification of the noise with hard
positivity constraint?) - Aperture photometry yields good relative
photometry (lt0.1m for ?m lt 4 and ? 0.2m for 4.0 lt
?m lt 7.0. - A general algorithm has limitations.Can one build
a modular algorithm to incorporate as much prior
information as possible for the data? - Deconvolution algorithms are not necessarily
user-friendly. How can we do this? - Assumption of isoplanatism is assumed, how to
incorporate anisoplanatism for wide field imaging?
53References
- S.M. Jefferies J.C. Christou, Restoration of
astronomical images by iterative blind
deconvolution, Astrophys. J., 415, 862-874,
1993. - E. Thiébaut J.-M. Conan, Strict a priori
constraints for maximum-likelihood blind
deconvolution, J. Opt. Soc. Am., A, 12, 485-492,
1995. - J.-M. Conan, L.M. Mugnier, T. Fusco,, V. Micheau
G. Rousset, Myopic deconvolution of adaptive
optics images by use of object and
point-spread-function power spectra, App.
Optics, 37, 4614-4622, 1998. - B.D. Jeffs J.C. Christou, Blind Baysian
Restoration of Adaptive Optics images using
generalized Gaussian Markov random field models,
Adaptive Optical System Technologies, D.
Bonacinni R.K. Tyson, Ed., Proc. SPIE, 3353,
1998. - E.K. Hege, J.C. Christou, S.M. Jefferies M.
Chesalka, Technique for combining
interferometric images, J. Opt. Soc. Am. A, 16,
1745-1750, 1999. - T. Fusco, J.-P. Véran, J.-M. Conan, L.M.
Mugnier, Myopic deconvolution method for
adaptive optics images of stellar fields,
Astron. Astrophys. Suppl. Ser., 134, 193-200,
1999. - J.C. Christou, D. Bonaccini, N. Ageorges, F.
Marchis, Myopic Deconvolution of Adaptive Optics
Images, ESO Messenger, 1999. - T. Fusco, J.-M. Conan, L.M. Mugnier, V. Micheau,
G. Rousset, Characterization of adaptive
optics point spread function for anisoplanatic
imaging. Application to stellar field
deconvolution., Astron. Astrophys. Suppl. Ser.,
142, 149-156, 2000. - E. Diolaiti, O. Bendinelli, D. Bonaccini, L.
Close, D. Currie, G. Parmeggiani, Analysis of
isoplanatic high resolution stellar fields by the
StarFinder code, Astron. Astrophys. Suppl. Ser.,
147, 335-346 , 2000. - S.M. Jefferies, M. Lloyd-Hart, E.K. Hege J.
Georges, Sensing wave-front amplitude and phase
with phase diversity, Appl. Optics, 41,
2095-2102, 2002.