Title: Extreme Contrast Adaptive Optics with Extremely Large Telescopes
1Extreme Contrast Adaptive Optics withExtremely
Large Telescopes
- Richard Dekany
- Caltech Optical Observatories
- 23 July 2004
- 2004 Michelson Summer School
- Frontiers of High Contrast Imaging in Astrophysics
2Outline
- Extremely large telescopes
- AO Scaling Laws
- Thirty Meter Telescope
- Current and near-term ExAO state-of-the-art
- Palomar AO Coronagraph
- ELT AO Technical Challenge
- ELT ExAO
- Architectural Elements
- Performance Model
- Menagerie of Worrisome Phenomena (10-6, 10-8,
10-10) - High-leverage Component Technologies
- Potential Science Reach
- Reaching the Fundamental Limits
- Strategies for Low-Q Operation (e.g. IFUs)
- Passive v. Active Speckle Suppression
- Ground / space ExAO comparison summary
3Extremely Large Telescopes
4Lessons of History
- Plot of largest optical/IR telescope size vs.
time reveals exponential growth - Remarkable given various social, economic, and
technical factors - Extrapolating from Keck 10 m
- 10 m 1993
- 25 m 2034
- 50 m 2065
- 100 m 2097
- History does not explain how future gains will be
made
Log10 collecting area (meters2)
Courtesy J. Nelson
5Large telescope projects 1950-2020
1949 1990 1995 2000 2005 2010 201
5 2020
Hale Keck1 Keck2 MMT HET Gemini (x2) VLT
(x4) Magellan .others LBT (x2) GTC TMT
HST SIRTF NGST TPF
OWL
6Adaptive Optics (AO) Scaling Laws
- AO significantly extends the science gain of
large telescopes - Signal-to-noise
- AO off D
- AO on D (D/r0) D2 r0-1, for unresolved
background limited target - The AO gain, (D/r0) is typically 30 - 60 in the
near-IR - With such promising return, it must be hard,
right? - Required number of degrees of freedom D2 l-12/5
- Required closed-loop bandwidth l-6/5
- Required wavefront measurement photon flux
l-18/5 - Required level of control of systematics l
- Note, scaling laws to reduce residual wavefront
error (l) are typically steeper than for
increasing aperture diameter
7Thirty-Meter Telescope
- Public / private collaboration of ACURA, AURA,
Caltech, and UC - First light 2015 w/ general-purpose AO
- ExAO is currently a top priority 2nd generation
instrument
8ExAO contrast metric
- Approximate smooth-halo contrast estimate
- Collected planet flux grows ? S D2 where S is
the Strehl ratio - Halo flux per AO diffraction-limited resolution
element ? (1-S) - Contrast within a resolutions element ? Q ? S D2
/ (1-S) - Practical contrast limits within todays small
working angles are usually dominated by speckle
noise from quasi-static errors - Sources are typically non-common-path errors
- Thermal induced telescope/instrument changes
- Gravity gradients
- Chromatic errors
- Local turbulence effects
9Photon-noise-limited ExAO contrast metric
TMT/MCAO 248 nm
TMT ExAO
Keck / XAOPI
Keck 248 nm
Gemini ExAOC
PALAO 165 nm
PALM-3000 85 nm
Adapted from J. Graham
10TMT draft science capabilities
- Field Mode Spatial Spectral
Wavelength (µm) - AO 10 FoV n-IFU l/D R 4,000 0.6 - 5
- (---) 20 FoR N-Slit r0/D(/2) 150 lt R lt
6,000 0.3 - 1.3 - AO 10 FoV 1-Slit l/D 5,000 lt R lt 100,000 5 -
28 - AO 5 FoR n-IFU l/D 2,000 lt R lt 10,000 0.8 -
2.5 - AO 2 FoV C 108 - 2x1010 l/D 50 lt R lt
300 0.8 - 2.5 - AO 2 FoV 1-Slit l/D 20,000 lt R lt 100,000 1
- 5 - ---- 5 FoV 1-Slit r0/D 50,000 lt R lt
100,000 0.3 -1.3 - AO 30 FoV Imaging l/D 5 lt R lt 100 0.6 - 5
- Notes
- FoV Field of View, FoR Field of Regard
(fields quoted by diameter) - N gtgt n gtgt 1
- (/2) Indicates GLAO option - to be evaluated
11Adaptive Optics Modes
AO Mode (w/ corresponding science capability ) Wavelength range Enabled science Components/ Instrument feed Priority
MOAO a.Small-Field (1, 6) b.Multi-Objects on wide-field (4) a)0.65- 5m b)1-2.5 m Galaxy chemistry Star forming chemistry Multi Lasers Deployable AO MEMS a) 0.005 IFU b) 0.025-0.040 IFU 1st light, if successfully demonstrated
MIRAO Mid IR (3) 7-28m Star forming regions, protoplanetary disks Characterize planetary systems AGNs Cryogenic DM or Adaptive Secondary NGS or multi-lasers MidIR Echelle Spectrometer MidIR Imager 1st light
GLAO Wide Field (2) (Ground Layer) 0.31-1.0m Large sample galaxy spectra Optical multiobject spectrograph Option on 1st light wide-field instrument
ExAO Extreme (5) 0.8-2.5m Exo planet imaging Protoplanetary disks MEMS Coronagraph or Nulling Interferometer Planet Imager Not yet known
MCAO Multiconjugate (8) 0.8-5m Dark ages Early galaxies, AGNs Nearby galaxies resolved star pop. and nuclei Galactic Center Star forming regions Multi Lasers Tomography Single or multi- DM IFU (with imaging) 2nd light, assuming MOAO validation
12TMT focal plane
13ExAO state-of-the-art
14ExAO state-of-the-art
Palomar occulting spot
Gemini ExAOC outer working angle N64 (2009)
PALM-3000 outer working angle N64 (2007)
AEOS outer working angle N32 (2004)
Keck outer working angle N18
Palomar outer working angle N16
Courtesy B. Macintosh and S. Metchev
15ExAO today
- ExAO today is saddled with the heavy yoke of
general-use AO systems - Todays AO
- Is designed to optimize faint guide star Strehl
ratio over wide FoV - Relies on non-common-path and non-common-wavelengt
h wavefront sensing - Uses 70 yr-old coronagraph technology
- Tolerates hysteretic and temperature dependent
deformable mirrors - Is devoid of any real-time metrology
- And Nyquist samples the focal plane
- One can hardly imagine setting out to design a
worse ExAO system - ELT ExAO systems are likely to
- Be highly specialized to the specific scientific
requirements (ie, search young systems for hot
exo-Jupiters in emission find water on
exo-Earths at Eps Eri etc.) - Pursue brand new architectures
- Require successive generations of prototypes and
demonstrations - Require large amounts of telescope time
16Palomar Adaptive Optics
Closed Loop FWHM 0.090 arcsec Strehl 80 at
K 165nm Wavefront Error
Open Loop FWHM 0.70 arcsec Strehl 2 at K Log
Stretch
- Facility instrument at Palomar observatory for
last 4 years - The most requested instrument at Palomar
- Natural guide star AO system
- 16x16 subapertures
- Bright guide star Strehls as high as 80 at 2.2
mm - Maximum frame rate 2000Hz (lt7e- read noise)
- Limiting magnitude 13.5mV, 10-15 Strehl at 2.2
mm - Read noise 3.5e- at lt 500 fps
- Science Camera
- J, H, and K imaging and 0.025 and 0.040
arcseconds/pixel - Coronagraph 0.41 and 0.91 arcsecond spot
- J, H and K spectra at R1500
17PALAO High Strehl Images
- Ten 5 sec images
- Ks (2.145 mm)
- r0(0.5 mm) 11 cm
- Strehl (Mean/sample Stdev) 75 /- 2
- RMS Wavefront error 185 /- 10 nm
- Wavefront error Max/Min 198/168 nm
- Strehl estimates are a lower estimate of truth
- Ignore 2 Strehl loss to reflection
- Ignore spiders an 3 effect
- ? Mean Wavefront 165 nm!
18Palomar AO Comparison
Log Stretch
3 arcseconds
Simulated AO Image RMS wavefront
130nm Strehl0.86 (using Caltechs Arroyo C
library)
Measured image on sky RMS wavefront165nm Strehl
0.80
Perfect Image (simulated wave diffractionw/
spiders and 1.5 ghost)
- Simulations performed using Arroyo (Caltech)
- Wavelength Ks (2.145 mm, width0.3mm)
- 5 second exposures
- Excellent agreement with simulations!
- Difference of 100nm is consistent with AO
calibration errors
19Palomar Performance
- Excellent agreement with simulation
- High-Contrast imaging
- AO corrected image is only a factor of 3 worse
then perfect case for field angles greater then
0.5 arcseconds - Spectra (and optical communication)
- A factor of 2.4 improvement in 80 enclosed energy
20?Ks 11.3 at 2.6? (3.010-5)
HD 166435
6 x 60 sec on-source exposure with
coronagraph Ks band (2.16µm) V 6.9 Strehl ?
65.
Slide courtesy of Stan Metchev
21AO challenge for ELTs
AO experience
ELT LGS Trajectory
22AO development
ELT LGS Trajectory
AO experience
23ExAO architecture elements
- A respectable first stage AO system
- Typically gt 85 Strehl ratio (enables
linearization of the residual phase errors) - Excellent diffraction suppression
- Many techniques exist (e.g., occulting or
phase-mask coronagraph, nulling beamcombiner,
Gaussian pupil apodization, cats-eye apodization) - Dedicated system for nanometer wavefront control
- Second stage high-order AO
- Dark hole (Malbet), dark speckle (Layberie),
black speckle (Dekany), ripple sensor (Angel,
Traub) - New detection architectures
- Polarization, multi-wavelength backends have make
it to the telescope - IFUs, interferometers, statistics engines et al.
have not yet - Calibration, calibration, calibration
- Data analysis pipeline and algorithms directly
drive the hardware architecture (integrated
experiment design)
24ExAO performance model
25Key ExAO concepts
- Working region
- Area of focal plane between inner and outer
working angle, where wavefront corrector exhibits
beneficial control (a function of wavelength) - Phase ripple
- A single frequency component of a two-dimensional
wavefront phase power spectrum - Phase ripple variance, sk2, is integral of power
spectrum from k to kdk - Q value
- Planet photoflux photons/m2/sec divided by
stellar photoflux within a single focal plane
resolution element - Q 4 Cplanet/sk2
- Unpublished Palomar AO results (Boccaletti, 2002)
hint thatQ 1/60 detections possible with
existing systems and careful calibration
26Small phase error PSF
- Using a 2nd order complex wave expansion, the
halo can be described as the sum of individual
haloes for independent error processes having
unique spatio-temporal behavior - Example power spectra (following Rigaut et al.
1998)
27PSF halo widths
- The high-contrast point spread function (PSF) can
be modeled as the superposition of haloes due to
various error processes - Each halo has its own envelope, width (w), and
speckle lifetime - For frozen wind and boiling wind, w l/r0
- For scintillation, w Sqrt(lz) the Fresnel
length - For photon noise, WFS read noise, w l/dx dx
actuator spacing (assumed same as WFS sensor
spacing for pupil sensor) - Interference effects average away over many
speckle lifetimes - Each halo contributes to reduce the SNR of planet
detection - The contribution of the total wavefront variance
attributable to a single phase ripple of spatial
frequency k is - s2k s2 / Nspeck in halo s2 (l/w)2/(l/D)2
s2 (w/D)2
28Minimizing integration time
- Optimize AO system design for subaperture
diameter, dx, and sensor sample time, dt, for
different observation cases
where S is Strehl ratio, Fp is planet flux, A is
telescope area, Fsky is sky background flux,
Fssci is parent star flux at science wavelength,
s2i is wavefront variance from ith error process,
w is ith halo width, ti is the coherence time of
the ith process, and T is total integration time
29Speckle noise
- Speckle noise (e.g. Racine, et al. 1999)
- Fundamentally different than photon noise
- Speckle noise variance based upon the square of
speckle photoflux - Smooth-halo photon noise variance based upon
speckle photoflux
- PALAO PSF stability (Apr 04) over 1 minute
- 15 five-second K-band images taken on a 6th
magnitude star in 0.9 (visible) seeing. The
images are log stretched and 3 arcsec on a side. - The average Strehl is 80 - 2, equivalent
to165 nm - 9nm of RMS wavefront error - Coronagraph contrast ( 5 x 10-4) dominated by
speckle noise
30ExAO issues I
Effect (10-6, 10-8, 10-10) Potential mitigation Mitigation maturity
Aliasing in the wavefront sensor Spatial filtering Focal-plane WFSing Moderate (simulations)Moderate (concepts)
Aliasing in the science array Spatial filtering Moderate (simulations)
Boiling wind (e.g. non-predictable phase errors) Higher correction bandwidth Moderate
Complex occulter index of refraction Better understand and/or materials Poor
Chromatism Meteorological monitoring Common-band WFSing Moderate Moderate (concepts)
Deformable mirror fitting error Higher spatial bandwidth Moderate
Detector charge diffusion and amplifier glow (science and/or WFS) Improved detectors Moderate
Direct scintillation halo Active amplitude correctionTwo-conjugate correction PoorModerate (simulations)
31ExAO issues II
Effect (10-6, 10-8, 10-10) Potential mitigation Mitigation maturity
Dispersion displacement Lateral dispersion correctorOptimized spectralwidth of WFS Moderate (concepts)Moderate (concepts)
Flat-field stability Improved detectors Moderate
Fourth-order terms in the wavefront expansion Higher Strehl Contrast-optimizing amplitude and phase control laws Poor Poor
Frozen wind lag (e.g. predictable phase errors) Predictive phase correction of multilayer atmosphere Moderate (concepts)
Index of refraction inhomogeneities More uniform materials, better pointing control Poor
Multispectral error Common-band WFSing Good
Non-common path phase errors Common-path WFSing Improved calibration/metrology Moderate (concepts)Poor
Non-common path polarization effects Slow F/ telescopes, polarizers Vector field AO coronagraph design Poor
32ExAO issues III
Effect (10-6, 10-8, 10-10) Potential mitigation Mitigation maturity
Residual tip/tilt jitter Better control Good
Scintillation in WFS Amplitude correctionSensing of higher moments Moderate, for clearing inner halo
Telescope pointing errors(Beam walk using a T/T mirror) Better telescope pointing Adaptive secondaries (to minimize beam walk) Moderate
Uncorrectable dynamic telescope errors Improved ACS, telescope stiffness, wind shielding Moderate
WFS calibration instability WFSs insensitive to seeing changes Active thermal control ModerateModerate
WFS star and background photon noise Optimized system design Good
WFS read and dark current noise Improved detectors Moderate
33Cases to be considered
Sensing / Science mode Comment
R-band / H-band Traditional AO (chosen for maximum sky coverage)
R-band / R-band Limited by current deformable mirrors
H-band / H-band Limited by current detectors
34Performance model example(with estimated H-band
speckle coherence times)
- Planet photon noise
- Sky photon noise (msky 16)
- Extrasolar exozodical light well-resolved for
D30 m, so not significant - WFS photon noise (tphot dt, the system update
rate) - Atmospheric phase estimate imperfect due to WFS
photon statistics - Scintillation (tscint 0.024 sec)
- Due to amplitude fluctuations arising from
high-altitude turbulence - We will assume strong high-altitude turbulence
- Frozen wind (twind 0.009 sec)
- Correction is late due to finite AO correction
bandwidth - Solution By definition, can be eliminated with
predictive controller - Boiling wind error (tboil 0.200 sec)
- Component of error not predictable
- WFS detector read noise (tphot dt)
- Includes dark current shot noise, etc.
- Solution Photon-counting detectors
35Integration time by effect (30 m
Sun-Jupiter-analogue)
36Tint and Q / Expanded error terms
37Tint and Q / Fundamental error terms
38Scope of target list
Integration time vs. guide star magnitude for R/H
expanded and H/H fundamental error cases, using
optimized dx and dt pairs. We again consider a
Sun-Jupiter analogue at 10 pc, Cplanet 10-9, D
30m, 45 degree zenith angle. For most cases,
systems optimized for solar analogue good to mv
6.
39Better NIR detectors?
Integration time as a function of WFS read noise
for H/H operation and the expanded error list.
For each value of read noise, an optimal dx and
dt were determined. For zero read noise, the
optimal dx 0.20 m and dt 0.075 msec, growing
for read noise 50 e- rms to dx 1.7 m and dt
0.290 msec. Note, for large values of dx, the
Strehl ratio in practice falls due to wavefront
fitting error, violating the assumption that the
quadratic phase used here.
40Larger telescopes
Integration time vs. telescope diameter for
R-band sensing/H-band science (expanded list of
errors) and for H-band sensing/ H-band science
(fundamental errors). The target system is a
Sun-Jupiter analogue at 10 pc (Cplanet 10-9)
and the desired SNR 5. Each case has been
separately optimized (R/H has dx 0.33 m and
dt 0.083 msec, H/H has dx 0.19 m and dt
0.16 msec). Exoearth times typically 50x greater,
but use similar architectures w/ similar D
dependence. Note, 8-10ms cant reach mature 5AU
exojupiters at 10pc in reflection
41Integration time vs. telescope diameterfor solar
analogue exoearth _at_ 10 pc (l 0.85 microns, r0
0.47 m, t0 10 ms, vwind 15 m/s, sc2
0.006, tscint 20 ms, Z 20 km, tboil 90 ms,
sread 3 e-, n 4 pix, q 0.1, msky 21.5 /
asec2, R 5, SNR 5, Cplanet 1.7 x 10-10)
Total Scintillation WFS read noise WFS photon
noise Frozen wind Boiling wind Planet photon
noise Sky photon noise
dt 0.00007 sec, dx 0.16 m
dt 0.00014 sec, dx 0.20 m
30 m telescope requires 5.7 hours
30 m telescope requires 70 hours
42Exoplanet astrometry and photometryat 30 m
fundamental limits
- With repeated imaging observations, we can deduce
- From orbital characteristics
- Equilibrium temperature
- Tidal locking
- Resonances among sibling planets
- From phase function
- Presence of a cloudy atmosphere
- Albedo rotation rates
- Mean radius of habitable zone at 15 pc
- 31 l/D (R-band) and 13 l/D (H-band)
- Aggressive apodization possible due to large
collector and high angular resolution - For nearest few stars, binary exoearths or
exoearths moons of exojupiters could be
resolved (but SNR still low) - _at_ 3 pc, resolution of 0.01 AU ? 25 Rjupiter
orbital radius of Callisto - Within 15 pc, there are hundreds of plausible
candidate stars for TMT-based exoearth search at
R 5 (down to mV 6)
43ELT ExAO Potential Science Reach
44Bright stars in 15 pc
45Ground-based exoearth spectroscopyat 30 m
fundamental limits
- Photon-noise limited R 5 spectroscopy (visible
and near-IR) would enable - The presence of a clear atmosphere (e.g. Earth
via Rayleigh scatter), a deeply clouded
atmosphere (e.g. Venus via Mie scatter) - R 20 spectroscopy might be reachable
- Require long integrations and careful calibration
of Telluric effects - Notable exceptions possible in sub-classes of
exoearths - e.g. H2O steam lines (seen in brown dwarfs from
the Earths surface) - Other plausible, unearthly atmospheres can be
imagined - Biomarkers (e.g. O2, O3, CH4) are likely not
available with 30 m SNR from Earths surface - High spectral resolution (R70) implies
prohibitive integration times - Telluric confusion may not be soluble at such
small SNR - Technique using orbital Doppler shifting of
narrow lines, used to study brown dwarfs,
generally not available due to low R
46Ultimate science reach for 30m
- Fundamental limits for AO allow direct detection
of exoearths with TMT but not biomarker studies - Potential number of systems
- Thousands for hot, young exojupiters (R
10-1000) - Hundreds for mature exojupiters (R 10-100)
- Scores for exoearths (R 5)
- Each requires tens of hours of observation
- Observations favor R 2 R? planets, e.g.
waterworlds - High-resolution spectroscopy is very difficult
except for non-terrestrial atmospheres (e.g.
steam lines or severe pressure broadening)
47Reaching the Fundamental Limits
48Reaching the ground fundamental limits
- New techniques
- Speckle noise suppression
- Post-processing
- Chromatic techniques
- Photon statistical techniques
- Active
- Higher-Strehl ratio operation
- Complex amplitude optimizing control laws (not
phase conjugation) - New components
- Deformable mirrors with 104 - 105 actuators
- Stable back-end instruments
- Focal plane wavefront sensors
- Prototype systems
- Develop H/H or R/R band AO systems optimized for
high contrast - Many currently uncontrolled error processes must
be addressed by design (partial list follows) - Typical development cycle for 8-10m telescope is
5 years and 10M - Likely to need several generations to get from 2
x 10-4 to 10-8
49Speckle discrimination in post-processing
- Published techniques for PSF subtraction
- Achromatic techniques
- PSF calibrator star
- COME-ON Plus (c. 1997)
- Multiple roll angles
- Field (Keck) and pupil (Palomar) rotation (c.
2000) - Centro-symmetric PSF subtraction (2002)
- Chromatic techniques
- Discreet multispectral discrimination
- TRIDENT 3 channel (2001)
- Several discrete channel successors (2004)
50Active speckle suppression
- The large penalty for speckle noise arises when
bright focal plane speckles are allowed to build
up (typ. 1000s photons) - This suggests one strategy avoid speckle noise
by running closed-loop correction so fast that
speckles typically contain only a few photons - Wavefront sensing in the focal plane
- Minimizes speckle noise (as well as many other
error sources) - Decoupling of wavefront sensing (into the focal
plane) allows more flexibility in DM technology
(at the pupil plane) - Phase and wavelength information are both needed
- Concepts
- An interferometric technique has been suggested
by Angel (2002) - Superconducting tunnel junctions (STJs) appear
well-suited, but remain small format - New field, open to new architectures
- While good Strehl is needed to sharpen planet
light, modest DM formats (typ. N 128) allow
exploration of habitable zones on exoearth target
list
51IFUs for exoplanet study
- The logical extension of multichannel
coronagraphic imagers - R 20-100 spectroscopic speckle discrimination
- An intermediate step toward spectroscopic
focal-plane wavefront sensors - ExAO is new application for IFUs
- Requires development of new observational
techniques and data analysis - Requires a professional group of exoplanet IFU
researchers - We need to learn how to use these things
- Near-term integral field coronagraph (IFC)
prototype options - Lab tests
- Rapid prototyping, but does not engage scientific
community - Existing AO systems
- All require new (presumably, warm) coronagraph
relay and have larger than necessary spectral
resolution - Slit spectrographs (most existing AO systems)
- AO-fed IFUs (e.g. Keck/OSIRIS, 2004)
- Gemini Extreme AO Coronagraph (ExAOC) (2009)
- Instrument call includes consideration of an
IFU-mode
52IFUs for exoplanet study (cont.)
- Demand for low-Q operation drives ground ExAO
concepts - A photon-counting IFU can be used to determine
wavefront amplitude and phase and drive the
sharp-end of an optimized ExAO system (e.g.
hierarchical control) - IFU technology in the path of TMT and other ELT
ExAO development - Ground-based experience with ExAO IFUs could be
extremely useful for TPF coronagraph mission
design - Similar sub-component requirements (Detectors,
fibers/slicers, etc.) - Similar data sets
- Similar analysis techniques (Implies similar
humans) - Difference is only bandwidth of wavefront control
loop
53Why must TPF work at Q1?
- Low-Q operation aka speckle discrimination is
fundamental to all techniques of high-contrast
direct detection, and is stock in trade for
ground systems - Ground-based observers only have just a few years
experience in PSF calibration, but no one on the
ground is planning Q1 instruments - Q 0.25 published PALAO (Boccaletti, 2002)
- Q lt 0.05 reported MMT (Close, private
communication, 2003) - Q 0.016 unpublished PALAO (Boccaletti, 2002)
- Working Q value for ground-based exoplanet study
will be lt 0.1 for next 20 years - We dont fret about about this, but seek to
develop new techniques - Significant relaxation of TPF coronagraph
requirements possible if tightest contrast (1/2
exoearth) requirements planned for Q 0.1
54Exoearth study comparison
- Space
- Pros
- Biomarkers accessible
- R gt 20
- Could work at Q 0.1 1.0
- Science in visible or mid-IR
- Whole sky accessible
- Enterprise mission top priority
- Cons
- Slow mission development
- Typically 0.02 nm rms WFE
- Highly stable
- Many new technologies required to reach
fundamental limits - Speckle suppression
- Ground 30m
- Cons
- Biomarkers not accessible
- R lt 20 (integration time limited)
- Must master Q 0.001
- One hemisphere accessible
- Not top ELT priority
- Many new technologies required to reach
fundamental limits - Speckle suppression
- Pros
- Rapid instrument development
- Smaller inner working angle
- Higher spatial resolution
- Science possible in red and near-IR
- Typically 10 nm rms WFE
55EAO key concepts
- Phase ripple
- A single frequency component of a two-dimensional
wavefront phase power spectrum - Phase ripple variance, sk2, is integral of power
spectrum from k to kdk - Q value
- Planet photoflux photons/m2/sec divided by
stellar photoflux within a single focal plane
resolution element - Q 4 Cplanet/sk2
- Unpublished Palomar AO results (Boccaletti, 2002)
hint that Q 1/60 detections possible with
careful calibration - Working region
- Area of focal plane between inner and outer
working angle, where wavefront corrector exhibits
beneficial control (a function of wavelength)