Behind the Coronagraphic Mask
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Transcript of Behind the Coronagraphic Mask
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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
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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
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... or use interferometry!
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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
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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
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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:
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Strengths and limitations of NRM
Self-calibration properties of closure phase make NRM “bullet-proof”
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9:;?3"3>-@3<-A3>+A-@B3CDEFGH*
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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
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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.
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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.
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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
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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
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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
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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
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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
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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