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Introduction to
exoplanetology
Lesson #6: Direct exoplanet detection methods (1/2)
Olivier Absil
[email protected]
Outline
I. Direct detection: why and how?
II. High contrast imaging from the ground
III. High contrast imaging from space
IV. Main results from high-contrast imaging
V. Stellar interferometry
I. Direct detection
Why and how?
Why direct detection?
•
Characterization of
planetary atmospheres
•
Needs spectroscopy on
actual planetary photons
→ isolate planet from star
Why direct detection?
Transits
mostly
here
•
Access non-transiting
planets
•
Opens up a wide range of
separations (beyond a few
0.1 AU)
•
Complementary with
transit spectroscopy
Why direct detection?
•
Get full orbital solution
•
3D orbit —> direct,
model-independent
access to the planet mass
•
Study dynamics of
planetary systems,
interactions with dust
disks, etc.
Challenge #1:
contrast
•
•
Visible: reflected light
Infrared: thermal
(blackbody-type) emission
Challenge #2:
angular
separation
•
•
•
1 AU @ 10 pc = 0.1 arcsec
Theoretically within reach
of 10-m class telescope
But … watch out for
turbulence!
Challenge summary
A firefly close to a lighthouse … 1000 miles away!
(note: the star never turns off)
Technique #1: imaging
•
•
Diffraction in circular
aperture → Airy pattern
Angular resolution = size
of Airy disk: θ = 1.22 λ/D
•
λ = 2 µm, D = 10 m → θ = 0.05" (50 mas)
= 1 AU at 20 pc
•
Extended pattern ≡ noise!
Rayleigh
criterion
The Airy pattern
: aperture radius
θ = 1.22 λ/D
Technique #2: interferometry
•
Two separated
telescopes → fringes
•
Angular resolution set
by baseline (B):
θ = 0.5 λ/B
•
Crests of 1st packet fall on
troughs of 2nd packet
•
λ = 2 µm, B = 100 m → θ = 2 mas
B
ang58
m.
an
d a
ime
tion
8–30
The fringe pattern
unresolved binary
resolved binary
nnel
ð19Þ
(fringe packets offset for clarity)
Fig. 5 An illustration of the optical Ramsey method. A
wave packet oscillates between the Rydberg states, n, an
II. High contrast imaging
from the ground
Atmospheric windows
V IJ HK
L
M
N
Imaging through the Earth atmosphere
•
Temperature variations
Short exposure
•
Distorted wavefront
•
Short exposure: speckles
•
Long exposure: wide PSF
Long exposure
Loss of angular resolution
La Palma
•
Fried parameter r0: diameter of a circular
area over which the rms wavefront
aberration due to passage through the
atmosphere is equal to 1 radian
•
r0 ~ 10 cm at good astronomy site
•
Same resolution as 10 cm telescope!
D = 5 cm
10 cm
60 cm
1.2 m
Atmospheric turbulence
•
•
Wavelength dependence: r0 ∝ λ6/5
•
10 cm @ 500 nm
•
50 cm @ 2 µm
•
4 m @ 10 µm
Seeing = FWHM of long
exposure image
•
Equal to 0.98 λ / r0
•
1" seeing for r0 = 10 cm @ 500 nm
•
Varies slowly with wavelength (λ−1/5)
Atmospheric turbulence
•
•
Coherence time: t0 = 0.31 r0 / ⟨vwind⟩
•
Valid under Taylor’s « frozen
turbulence » hypothesis
•
t0 ≃ 3 msec for r0 = 10 cm and ⟨vwind⟩ =
10 m/s
Isoplanatic angle: θ0 = 0.31 r0 / ⟨h⟩
•
θ0 ≃ 1.3" for r0 = 10 cm and ⟨h⟩ = 5 km
•
Stars separated by θ0 have different
short-exposure PSFs
Correction
needed!
Adaptive optics
Adaptive optics
Wavefront sensing
Shack-Hartmann wave front sensor
Strehl ratio
•
•
S = |⟨exp(iφ)⟩|2 ≃ exp(−σφ2)
•
φ = wavefront phase
•
σφ = rms phase on pupil
Quantifies image quality
•
≃ peak intensity ratio wrt
perfect image
•
Perfect image → S = 1
•
D = r0 → S = 0.36
AO correction
MACAO on VLT
50%
20%
Detection in speckle noise?
ESO-3.6m/ComeOn+ (1994)
S=0.21
Planet
Speckles
Getting rid of
speckles
1. Observing strategies
Solution: PSF subtraction
•
•
aka Reference-star Differential
Imaging (RDI)
β Pic
Observe a reference star
•
Similar to science target
•
Scale its PSF (flux)
•
Subtract it from science
observation
α Pic
β Pic − α Pic
Limitations of RDI
•
No perfect reference star
•
Should be of same magnitude, color and position as science target
•
Time spent on reference star is « lost » (no planetary photon)
•
Atmospheric conditions change with time
•
Telescope/instrument aberrations also change with time
•
Quasi-static speckles, can mimic planetary signal
Four differential solutions
•
Keep observing the same target (no reference star)
•
Tune an observing parameter to discriminate
between stellar PSF and planet
•
Spectral differential imaging (SDI)
•
Spectral deconvolution (SD)
•
Angular differential imaging (ADI)
•
Polarimetric differential imaging (PDI)
Spectral differential imaging
SDI in practice
λ1
λ2
λ1−λ2
λ3
(λ1−λ2) − k(λ1−λ3)
Pros and cons of SDI
+
Detection down to diffraction limit (1 λ/D)
−
Companion needs strong molecular absorption
(e.g., methane)
−
Differential aberrations between the three
wavelength optical paths
−
Narrow filters → lower sensitivity
Spectral deconvolution
•
Integral Field Spectrograph
(IFS)
•
•
Diffraction and speckle pattern
scale as function of wavelength
•
•
Provides field image as function of
wavelength (« image cube »)
Pattern moves out from star with
increasing wavelength
Exoplanet position is fixed
•
Can be distinguished from
speckles
SD in practice
Similar principle as SDI, on much wider wavelength band
Observed (x,λ) slice
Rescaled (x,λ) slice
Pros and cons of SD
+
Works with any type of planet (no specific feature)
+
No differential aberrations / simultaneous observations
+
Does not rely on specific feature in planet spectrum
+
End product = spectrum of the planet!
•
Detect and characterize planet at the same time
−
Speckle pattern not perfectly constant over wavelength
−
Limited inner and outer working angles (depend on
wavelength range and spectral resolution)
Angular differential imaging
•
Use field rotation while
keeping telescope fixed
•
Usually done by switching
off derotator
•
Planet moves around
star as a function of
parallactic angle
•
Quasi-static speckles
stay at fixed position
ADI in practice
Pros and cons of ADI
+
Works with any type of planet (no specific feature)
+
Does not require specific hardware
−
Does not work well for stars far from zenith (small variation of the
parallactic angle)
−
Limited inner working angle (planet must move by more than 1 λ/D
in the field for ADI to work)
−
Speckle pattern evolves with time
Speckle decorrelation
t0
t0 + 10 min
(t0 + 10 min) − t0
t0 + 100 min
(t0 + 100 min) − t0
Polarimetric differential
imaging
•
Reflected light from planet is partially polarized
•
Typically 10% polarisation
•
Star produces unpolarized light
•
Can be exploited by polarimetric imager
8
PDI in practice
Chapter 1
H. Canovas et al.: Near-infrared imaging polarimetry of HD 142527
Figure 1.4: Schematic view of the polarization measurement process using temporal and spatial modulation used by ExPo. The modulator switches between orthogonal directions of the polarisation to be
measured, defining states A and B. The polarising beamsplitter then separates the two orthogonal polarisation states into left (L) and right (R) beams. Double subtraction of (AL-AR)-(BL-BR) minimises
(systematic) spatial and temporal differences (Canovas et al. 2012a). Image credit: M. Rodenhuis
way of modulating but one can design, and optimise, many different modulation schemes
depending on what Stokes component (or cobination of them) one is interested in measuring.
More generally, instead of using a rotating polariser, the modulation is achieved by means of
a retarding element (i.e. modulator) and a fixed polariser (i.e. analyser). A retarding element
imparts a phase lag to one of the orthognal components of the electric field, thus, modifying
the polarisation state of the wave passing through. by carefully orienting the retarder in the
required direction we can transform the polarisation state we want to measure in the direction
fixed polariser
filter
the
Fig.the
1. Processed
images of HDwould
142527 (top
row)toand
HDdetector.
161743 (bottom row) in H band. From left to right: intensity image (I) in logarithmic
Pros and cons of PDI
+
Speckle subtraction can be very good
+
No limitation in inner or outer working angle
−
Small fraction of planet light is polarized → low sensitivity
−
Works only in reflected light (best in visible range)
−
Requires specific, non-standard hardware
Getting rid of
speckles
2. Image processing
The LOCI algorithm
coefficients to be determined
•
Locally Optimized
Combination of Images
•
Goal: make best use of a
set of reference images
•
Can be used with
various observing
techniques
•
Solve a linear system to
minimize residuals
ref PSF
to be minimized
pixels
target PSF
individual
frames
LOCI working with ADI
Practical use of LOCI
•
To be applied locally because correlation between
frames expected to depend on position
•
Optimize LOCI coefficient on « optimization » zone
•
Perform PSF subtraction on « subtraction » zone
•
Optim. zone > subtr. zone to avoid planet signal subtraction
Pros and cons of LOCI
•
−
−
Several free parameters
+
Can be fine tuned to any particular data set
−
Not very straightforward to use
Strong self-subtraction of planetary signal
•
LOCI tries to remove everything → bias on photometry
•
Can be evaluated with fake companions, or mitigated by
introducing even more parameters (masking)
CPU intensive
Principal Component
Analysis (PCA)
•
Method to reduce the
number of variables
needed to describe a
data set
•
Build an orthogonal
basis on which to
decompose the images
•
Truncated basis to
perform PSF
subtraction
How PCA works
•
Subtract mean (M) from data set (D): A = D − M
•
Calculate covariance matrix: C = AAT
•
Calculate eigenvectors (Q) and eigenvalues
•
CQ = QΛ, with Λ a diagonal matrix of eigenvalues
•
Choose first K components in Q → QK
•
Project data onto these components
•
F = QKA → new data set of reduced dimensions
PCA with a stack of images
•
Use the women’s face to compute orthogonal basis
•
Project man’s face on first 50 coefficients and add
•
a stack
of images
Describe PCA
man’s with
face with
50 coefficient
instead of
(same method, but every pixel is a dimension)
thousands of pixels
8 new components per image
Take the best N PCA eigenfaces and dot product a real face with
Practical use of PCA
Pros and cons of PCA
+
−
Can be applied to whole image at once
+
CPU time can be drastically reduced!
−
In practice, annulus-wise version is generally better
Self-subtraction reduced, but still present
+
Reduced bias wrt LOCI, generally more linear
•
Fake companion injection still used in most cases
+
Forward modeling also possible
A « real-life »
example
HR 8799
2008: ADI detection
Contrast ~ 14 mag
(~10−6)
th
4
planet with ADI+LOCI
2010: long slit spectroscopy
Figure 2. Image with the HR 8799 c spectrum before extraction. The spatial
direction along the star–planet axis is vertical. The spectral direction is
horizontal, with wavelength increasing from left to right.
ANSON ET AL.
Vol. 710
15%
400 s,
taken
nt. A
plied
799 c
re 1).
re an
on of
c and
his is
tions.
ound
ation
were
l sky.
dures
ected
ringe
e flat
Since
on on
to be
aging
speco this
ectrorame
on of
Figure 4.
into three
(circles, d
dash-dotte
No. 1, 2010
SPECTROSCOPY OF HR 8799 c
Figure 2. Image with the HR 8799 c spectrum before extraction. The spatial
direction along the star–planet axis is vertical. The spectral direction is
horizontal, with wavelength increasing from left to right.
L37
Figure 3. Upper panel: spectrum of HR 8799 c. The dashed lines and faintly
shaded area (light blue in the online version) denote the errors. Lower panel:
log g =
detailed
that non
Non-equ
large dif
particula
presence
4 µm fo
Fortney
(2008) t
being pr
behavio
of whet
thereby
The r
planet de
ing purp
narrowe
since it
models.
true also
in the sp
8.66 ma
9.50 ma
and is ex
In the
2011: HK band IFS
The Astrophysical Journal, 733:65 (18pp), 2011 May 20
Ba
The Astrophysical Journal, 733:65 (18pp), 2011 May 20
Barman et al.
Table 1
OSIRIS Observations
Target
HR8799b
HD210501
BD+14 4774
#exp
9
5
4
Exp. Time (s)
900
30
30
Band Pass
K
UT Date
2009 Jul 22
HR8799b
HD 210501
BD+14 4774
6
7
5
900
30
30
H
2009 Jul 23
HR8799b
BD+14 4774
7
7
900
30
H
2009 Jul 30
HR8799b
HD210501
9
3
900
30
K
2010 Jul 11
HR8799b
HD210501
8
3
900
30
H
2010 Jul 13
and no artificial wavelength shifts were discovered; a potential
concern given the temperature variations encountered during the
observations.4
While the planet is easily detected in all of the BCD cubes,
contamination by scattered starlight remains a concern. Figure 1
shows the FOV and orientation for the OSIRIS observations
Figure 1. Unprocessed NIRC2 image (20 s exposure) of HR8799. The rectangle
and the extent of speckle contamination in the observed region.
shows the orientation and size of the OSIRIS spectrograph FOV (0.′′ 02 scale).
Since the spatial scaling of the speckles, radially from the star,
HR8799b is barely visible in the center of this rectangle and comparable in
proportional
toofλ,HR8799b
speckles(scaled
can intersect
spatial
of
Figure 3. OSIRIS H -isand
K-band fluxes
to 10 pc)the
plotted
withlocation
1σ uncertainties.
The location of prominent water, CH4 , and CO abs
brightness to the speckle contamination. Dithering was done along the long axis
are
indicated.
The
fluxes
extracted
without
the
speckle-suppression
algorithm
are
shown
as
dotted
lines.
The bottom two curves are the mean residuals o
the
planet
in
a
wavelength-dependent
manner.
To
suppress
the
of the FOV.
with flat spectra extracted
from
the
same
data
cubes
(see
the
text
for
details).
The
Kn3
spectrum
of
Bowler
et al. (2010) is shown as green pluses (sca
speckle pattern, each BCD cube was processed with custom IDL
down) overplotted with
the broadband
spectrum
(black
points) interpolated
the Bowler
et al. Kn3 wavelength points. The mean 1σ uncertainties a
routines
that first
subtracts
a (spatially)
low-passonto
filtered
version
range
are
shown
at
either
end
for
each
data
set.
The
larger
red
filled
symbols
are
the
NICI
CH
short/long (boxes), NIRC2 narrow (circles), and NIRC
wavelength and dispersion solutions, sky subtraction, cosmic
of the
image
slice
in
each wavelength
channelphotometry
and rebins
the 4from
(stars)
photometry
taken
from
Table
3.
Blue
symbols
are
the
corresponding
derived
the OSIRIS spectra.
ray rejection, and so forth (Krabbe et al. 2004). On all three
data cube (by taking the median in the λ dimension) to 25
(A color
version of this figure is available in the online journal.)
nights in 2009, OSIRIS was operating above its normal
detector
wavelength channels (R ∼ 60). Each monochromatic image
2013: full IFS study with SD
The Astrophysical Journal, 768:24 (16pp), 2013 May 1
Oppenheimer et al.
Figure 4. Spectra of the b, c, d, and e components using the S4 algorithm. 1σ error bars are indicated on either side of each point. Spectra are shown for comparative
purposes in normalized fλ . The dotted spectrum of component c is extracted from the 2012 October data and shows poorer detection in the J band due to seeing
conditions. All other spectra are from the 2012 June epoch. The black dashed lines are spectra of the background extracted at the same radial distance from A for each
component. They consist of the average of six different randomly-selected locations in the azimuthal direction; they represent comparative “noise level” estimates.
Tentative identification of some molecular features (excluding water) are indicated at the top of the plot. CO2 is listed with a question mark as explained in Section 8.3
and could also be attributable to HCN.
Getting rid of
speckles
3. Hardware solutions
Coronagraphy
Coronagraphy
With central obscuration
Phase mask coronagraph
•
Proposed by
Roddier (1997)
•
Apply 180° phase
shift to PSF center
•
Ideal mask size =
43% of 1st Airy
ring
•
Very chromatic
design
Four Quadrant Phase Mask
Beyond the FQPM
•
Quadrants → octants → continuous phase ramp
Vortex phase mask
•
Continuous phase ramp from 0 to 4π
•
Main problem:
chromaticity
of
the
phase
ramp
December 15, 2005
/
Vol.
30,
No.
24
/
OPTICS
LETTERS
3309
The Astrophysical Journal Supplement Series, 209:7 (8pp),
2013 November
y profile, 'U!x! , y!"'2 of a beam containx. (b) Surface profile of a VPM.
in Fig. 3(a). Images for vortex coronagraphs having
topological charges m= 0, 1, 2, and 3 are shown in
Figs. 3(b)–3(d), respectively. The m = 2 case provides a
bright image of the weak off-axis source, while eliminating light from the on-axis image.
The superior performance of the m = 2 case is attributed to zero intensity values for the starlight extending over the entire exit pupil of radius REP. This
remarkable result may be found analytically by computing a second-order Hankel transform of the Airy
disk.13 Assuming paraxial rays, we find19
'U1!u!,v!"' =
(
2
2
A1REP /%! , %! ) REP
0,
%! & REP
)
.
!5"
Its
(o
tra
ax
th
W
de
fin
in
to
a
be
ca
Je
Achromatic phase mask?
•
1194
Sub-wavelength gratings → achromatic half wave plate
MAWET ET AL.
Fig. 6.—Pancharatnam
phase
ramp of the AGPM
"p ¼ complex
2!.
Fig. 3. 4QZOG
implementation:
s and coronagraph:
p are the vectorial
2. Within
one light
revolution
around
thek. In
The associatedamplitude
topologicalcomponents
charge is lp of¼ the
incoming
of wave
vector
meters
of
the
2(2!).polarization states
optical axis, i.e.,
! of
¼ the
2!, one
confirms
"p p¼global
each
four easily
quadrants,
the that
s and
r to the grath h, and the
are decomposed in the corresponding TEi and TMi vectorial com-
Vol. 633
Fig. 7.—AGPM scheme and analogy with the FQ-PM coronagraph. The
AGPM can be seen as a polarization FQ-PM. The parallel potentially interfering
polarization states are out of phase according to the FQ-PM focal plane phase
shift distribution. Here " TE and " TM are the output phases of the polarization
components TE and TM such that !" TE"TM ¼ j" TE " " TM j ¼ !.
Annular Groove Phase Mask
(AGPM)
The AGPM performance
Peak%rejec)on%
1000"
100"
10"
1"
août(10" nov.(10" févr.(11" juin(11" sept.(11" déc.(11" avr.(12" juil.(12" oct.(12"
Fig. 8. Azimuthally averaged coronagraphic profile (CP) obtained with the OVVC2 u
LCP, measured at 1550 nm and with a virtual defect size 10% of the beam size F λ .
PSF is also shown in dashed line. The camera noise floor (dotted straight line) of a
3 × 10−5 is quickly reached at 3.5 λ /d.
On-sky example
Raw image
Post-processed (ADI+PCA)
Sensitivity to planets
β Pic b
Apodization
•
« Pupil plane coronagraphy »
•
Act on amplitude or phase of wavefront in pupil
•
Redistribute the intensity in the focal plane to make
it more compact or create a dark region
Amplitude apodization
•
Goal: reduce PSF side lobes
•
Degraded angular resolution
Apodized coronagraph
•
Apodization
makes PSF
more compact
on the focal
plane mask
Shaped pupils
How it’s done
P. Martinez et al.: Design, analysis, and testing of a microdot apodizer for the Apodized Pupil Lyot Coronagraph
•
Microdot mask
5. Left: simulation map of the binary apodizer with 5 × 5 µm dots. Right: shadowgraph inspection of the manufactured microdots apodizer
0). For the sake of clarity, only a quarter of the apodizer is shown.
Phase apodization
•
Act on wavefront phase
instead of amplitude
•
Can produce
asymmetric PSF
APP: Apodizing Phase Plate
On-sky example
L50
QUANZ ET AL.
Vol. 722
Figure 1. Left: median combination of one cube of unsaturated exposures of β Pictoris used to determine the photometry. The effect of the APP can be seen in the
left side of the PSF where the diffraction rings are effectively suppressed increasing the contrast between 2 and 7 λ/D. Middle: median combination of one cube of
saturated exposures of the PSF reference star HR2435. Right: median combination of all PSF-subtracted science exposures. β Pictoris b is indicated by the arrow. The
right side suffers from subtraction residuals as does the central region of the PSF, which has been masked out.
Table 1
Summary of Observations on 2010 April 3
emission, we subtracted from each individual frame the cor-
Phase-induced amplitude
apodization
Other hardware solutions
•
Low-order wavefront sensing
Adaptive Optics for Extremely Large Telescopes II
•
•
•
Performed at instrument level (science camera, unexploited
suggesting that we are not in a Fraunhofer case. Hence, in the current configuration, the bench
is not ready for the demonstration of the Fresnel effects we plan to do.
stellar light, etc)
The presence of very bright off-axis ghosts (carrying each its speckle structure) seems to have
a significant contribution to the non–symetry of the speckle structure. These ghosts are due to
the coating of the DM that is not optimized for NIR. Another source of errors may come from
amplitude errors of the apodizer itself. Finally, the source being highly coherent, even faint
unwanted light may interfere with the speckle field.
Corrects for non-common path errors between AO and
instrument
Speckle nulling
•
Fig. 5. Preliminary results of speckle nulling with the FFREE bench. Left: Coronagraphic image without
Measure the complex
amplitude
quasi
and
correction.
Speckle intensity isof
between
10 and 10static
in the probespeckles
zones.. Middle: correction
on both
sides: speckle rejection factor (rms intensity) = 5×. Right: correction on one side only: speckle rejection
factor = 30×
(rms intensity).
correct with deformable
mirror
-4
7. Conclusion
-3
Tree of life
All steps in one picture
Telescope pointed
(i)
(i)
(i)
(i)(i)
AO turned on
(ii)
(ii)
(ii)
Speckle calibration
Centered on mask
(ii)(ii)
(iii)
(iii)
(iii)
(iii)
(iii)
ADI + postprocessing
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