behind the coronagraphic mask
DESCRIPTION
Slides of a talk I gave at the second Lyot conference held in Paris in 2010. Presentation slides are the only conference proceedings for this meeting. This is the first talk I gave on the new high angular resolution technique I proposed, called Kernel-phase: the presentation shows that new information can be extracted from readily available archive data from the Hubble Space Telescope.TRANSCRIPT
Behind the coronagraphic mask
Frantz MartinacheCEAO Research FellowSubaru Telescope Paris, 10/10/29, Spirit of Lyot 2010
A new approach to look for companions in the so-called “super resolution” regime
Take care of an ill-posed problem
I = O ⊗ PSF Eliminate the PSF out of the equation
the ADI way... the exAO way...
Thalman et al, 2009, ApJ, 707, 123 Guyon et al, 2009, PASP, 122, 71
... or use interferometry!
Interferometry produces good observable quantities
1
Φ2-1
Φ3-2
Φ1-3
2
3
Not about producing the best image possible, but
about extractingobservable quantities
(closure-phase) that do not depend on
phase residuals
Φ(2-1) = Φ(2-1)0 + (φ2-φ1)
Φ(3-2) = Φ(3-2)0 + (φ3-φ2)
Φ(1-3) = Φ(1-3)0 + (φ1-φ3)
measured = intrinsic + atmospheric
Σ
Jennison, R. C. 1958, MNRAS, 118, 276
Ditch these dirty images, keep clean information only!
Example of Palomar closure-phase data
40 % strehl0.3 deg scatter
stability ~ λ/1000all passive !
The best “picture” you can give of one or more companions around a star is a series of astrometric data:
separation, PA, contrast with associated uncertainties
A new regime of angular separations
50 100 150 200 250Projected separation (mas)
5.0
5.5
6.0
6.5
L co
ntra
st li
mit
GJ 517
GJ 559.1GJ 617B
HD 108767B
HD 187748
V383 Lac
NIRC2 L’interferogram
powerspectrum
HD 187748
2 3 4 5 6 7Projected separation (AU)
0
20
40
60
80
Com
pani
on m
ass
dete
ctio
n lim
it (M
J)
50 Myr
150 Myr
V383 Lac
2 3 4 5 6Projected separation (AU)
0
20
40
60
80
Com
pani
on m
ass
dete
ctio
n lim
it (M
J) 50 Myr 150 Myr
HD 108767B
2 3 4 5 6Projected separation (AU)
0
20
40
60
80
Com
pani
on m
ass
dete
ctio
n lim
it (M
J)
40 Myr
260 Myr
GJ 617B
0.5 1.0 1.5 2.0 2.5Projected separation (AU)
0
20
40
60
80
Com
pani
on m
ass
dete
ctio
n lim
it (M
J)
100 Myr
1000 Myr
GJ 559.1
2 4 6 8Projected separation (AU)
0
20
40
60
80
Com
pani
on m
ass
dete
ctio
n lim
it (M
J)
20 Myr
120 Myr
GJ 517
1 2 3 4Projected separation (AU)
0
20
40
60
80
Com
pani
on m
ass
dete
ctio
n lim
it (M
J)
50 Myr 50 Myr
Martinache et al, in prep
examples of NRM detection limits:
Strengths and limitations of NRM
Self-calibration properties of closure phase make NRM “bullet-proof”
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NRM onboard JWST in the TGS-TFI.
If anything goes wrong with the primary, this might be the only instrument that
will still work
But: it requires a non-redundant pupil.Is there anything comparable we could do
without masking at all?
Sivaramakrishnan et al, Astro2010T, 40
Φ(2-1) = Φ(2-1)0 + (φ2-φ1)Φ(3-2) = Φ(3-2)0 + (φ3-φ2)Φ(1-3) = Φ(1-3)0 + (φ1-φ3)
... ... ... ... ... ...Φ(k-l) = Φ(k-l)0 + (φk-φl)
... ... ... ... ... ...
Matrix form anyone?
A more “general” formalism
Φ Φ0= + φA ×
measured Fourierphase
“true” Fourierphase
transfermatrix
pupilphaseerrors
For a non-redundant array:The transfer matrix is essentially filled with zeroesExcept: per line, one +1, one -1
Closure phase relations are one example of a left-hand operator K, so that KxA produces rows of zeros.
Redundant scenarios
non-redundant
full aperture
Φ = Φ0 + 1 Δφ
Φ = Φ0 + Arg(ejΣi Δφi)
Im
Re
Additionof phasors
BUT: with a reasonably well corrected aperture, this complicated (non sortable) expression can be linearized, and becomes:
Φ = Φ0 + Σi ΔφiOur linear model still holds... just need a slightly more filled transfer matrix.
Determine the HST transfer matrix
0 50 100 150 200 250
0
50
100
150
200
250
discretize the HST pupil0 50 100 150
0
50
100
150
NICMOS Image
0 50 100 150
0
50
100
150
(u,v)-plane Ker-phase histogram
-200 -100 0 100 200Ker-phases (degree)
0
10
20
30
40
50
60
70
# in
bin
CalibratorBinary (GJ164)
GJ 164 Ker-phases
-200 -100 0 100 200Kernel-phases (degrees)
-200
-100
0
100
200
Best
fit b
inar
y m
odel
(deg
ree)
corresponding UV coverage
Count the baselines contributing to each
UV pointand fill up a line of A
with -1, 0, 1
A =
... ... ... ... ... ... ... ... ...
... ... ... ... ... ... ... ... ...
... ... ... ... ... ... ... ... ...
... ... ... ... ... ... ... ... ...
... ... ... ... ... ... ... ... ...
... ... ... ... ... ... ... ... ...
... 0 +1 -1 ... 0 -1 ...
In this example,A is a rectangular 155 x 366 matrix, manageable on a
netbook
Kernel-phase
Idea: construct a new operator K so that KxA = 0, but how?By hand? Painful, but manageable if not too big...Or use a tool more versatile: Singular Value Decomposition (SVD)
Rows of K form a basis for the left null space of A
The SVD of AT= U x W x VT gives it all: the columns of V that correspond to zero singular values (Wi = 0) do the trick
These new closure-phase relations are called Ker-phases
Martinache, 2010, ApJ, 724, 464
For each frame:Read the Fourier-phase informationAssemble into Ker-phases using the relations identified earlier... Then:do some statistics (frame-to-frame variability), propagate errors... and you’re done!
NIC1 datacube
Data reduction
FT
uv-plane
0 50 100 150
0
50
100
150
NICMOS Image
0 50 100 150
0
50
100
150
(u,v)-plane Ker-phase histogram
-200 -100 0 100 200Ker-phases (degree)
0
10
20
30
40
50
60
70
# in
bin
CalibratorBinary (GJ164)
GJ 164 Ker-phases
-200 -100 0 100 200Kernel-phases (degrees)
-200
-100
0
100
200
Best
fit b
inar
y m
odel
(deg
ree)
NICMOS 1 data analysis
Martinache, 2010, ApJ, 724, 464
- 4 frame dataset on SAO 179809 (1998)- 8 frame dataset on GJ 164 (2004)
Best fit Parameters:Separation: 88.2 masP.A: 100.6 degreescontrast: 9.1
Performance of the approach
Projected probability density function
70 80 90 100Angular sep (mas)
98
100
102
104
Posi
tion
Angl
e (d
eg)
70 80 90 100
98
100
102
104
Projected probability density function
70 80 90 100Angular sep (mas)
4
6
8
10
12
Con
trast
ratio
70 80 90 100
4
6
8
10
12
Projected probability density function
98 100 102 104Position Angle (deg)
4
6
8
10
12
Con
trast
ratio
98 100 102 104
4
6
8
10
12
NICMOS data contrast detection limits
100 150 200 250 300 350Angular separation (mas)
200
400
600
Con
trast
ratio
0.900
0.900 0.900
0.990
0.990
0.999
0.999
Detection Detection limits
Parameters:Separation: 88.2 +/- 3 masP.A: 100.6 +/- 0.3 degreecontrast: 9.1 +/- 1.2
1.1 λ/D
Limits based on MC simulationsfrom errors measured on a dataset acquired on a single star.
Martinache, 2010, ApJ, 724, 464
Concluding remarks
The technique is still at an early stage but is usable today
Moderate contrast detection with good astrometric precision was demonstrated within λ/D
- dozens of NICMOS archive datasets await re-analysis:> new detections in the super-resolution regime> improved detection limits
- new ground based L- and M-band observing programs should also benefit this technique