ao - ForOT Optical Turbulence Forecasts

TURBULENCE IN
HIGH ANGULAR RESOLUTION
TECHNIQUES IN ASTRONOMY
Invited Lecture by:
JACQUES MAURICE BECKERS
EMERITUS ASTRONOMER
US NATIONAL SOLAR OBSERVATORY

WHY DO I LIKE THIS CONFERENCE
The study of temperature fluctuations on a small scale
(~ 5 cm) in the Earth’ atmosphere is of great importance
for astronomical observations. More interest by
Meteorologists for such research would be most welcome.

DETRIMENTAL EFFECTS BY THE ATMOSPHERE
ON ASTRONOMICAL OBSERVATIONS
(1) ABSORPTION & SCATTERING
⇒ (a) most of the electro-magnetic
spectrum can only be observed from space
(b) at optical wavelengths extinction limits photometry
(c) scattering limits solar corona observations
(2) REFRACTION
⇒ (a) atmospheric dispersion/refraction
(b) atmospheric turbulence “seeing” limits resolution
(c) atmospheric turbulence “scintillation/twinkling”
limits photometry
ESO
(3) POLLUTION
⇒ (a) contrails limit photometry
(b) mirror coating deterioration
(c) thermal emissivity by dust etc.

DETRIMENTAL EFFECTS BY THE ATMOSPHERE
ON ASTRONOMICAL OBSERVATIONS
“SPECKLE IMAGE” OF STAR
NOTICE: (i) speckle size = size of Airy disk of telescope
(ii) speckles colored (diffraction phenomena)
(iii) number of Speckles N sp
≈ (D/r o
) 2 . D = Telescope Diameter
r 0
= “Fried Parameter” = 10 cm for 1” seeing @ 500nm
D = 10m N sp
≈ 10000
(iv) speckle image changes rapidly (≥ 10 Hz)
(v) for D ≤ r 0
Airy disk N = 1
(one speckle) which “dances”
(2) REFRACTION
(a) atmospheric dispersion/refraction
(b) atmospheric turbulence “seeing” limits resolution
(c) atmospheric turbulence “scintillation/twinkling”
limits photometry
ESO/Paranal
MOON
NOTICE: (i) image motions
(ii) “Iso-Kinetic Patch”
[(iii) “Iso-Planatic Patch”]

SO: WHY BOTHER WITH GROUND-BASED TELESCOPES
SPACE OBSERVATORIES HAVE:
‣ NO ATMOSPHERIC ABSORPTION : RESULTS IN FULL WAVELENGTH ACCESS
⇒ BROAD COVERAGE OF PHYSICAL PROCESSES (many space observatories)
‣ NO ATMOSPHERIC SEEING : RESULTS IN HIGH RESOLUTION IMAGING
⇒ RESOLVE STARS, GALAXIES PLANETS, EXOPLANETARY SYSTEMS etc. (HST)
‣ NO SCINTILLATION : RESULTS IN PRECISION PHOTOMETRY
⇒ EXOPLANET TRANSITS; ASTROSEISMOLOGY (COROT)
‣ LOW THERMAL BACKGROUND : VASTLY IMPROVES INFRARED OBSERVATIONS
⇒ COLD MATTER, STAR FORMATION, etc. (JWST)
‣ LOW ATMOSPHERIC SCATTERED LIGHT : HELPS CORONAGRAPHY (SOHO-LASCO)
⇒ EXOPLANET IMAGING; OTHER HIGH CONTRAST OBJECTS
BUT:
SPACE-BASED FACILITIES ARE MANY ORDERS-OF-MAGNITUDE (100x to
1000x; more) MORE COSTLY THAN GROUND-BASED FACILITIES
⇒ COST IS THE MAIN DRIVER FOR PURSUING HIGH-RESOLUTION
TECHNIQUES FOR GROUND-BASED TELESCOPES AND INTERFEROMETERS

WAVEFRONT DISTURBANCE BY REFRACTIVE INDEX (n) CHANGES
∆y
d
n 2
n 1
Sea Level
RH = 1
∆x = (n 2 -n 1 )*d
∆φ = ∆x/λ
∆x
NOTE: ∆x , dx/dy (tilt) and
d 2 x/dy 2 (curvature)
are achromatic if
n is λ-independent
CIRCLES: RH = 1 AIR
Cerro Paranal
RH = 0
RADIO
WAVES
R.J. Mather, 2004
ANOMALOUS DISPERSION EFFECTS
J H K L M
NOTE:
(i) in general refractive index is function of
temperature & water vapor (RH)
(ii) in optical/IR water vapor has little effect;
T (⇒ P & density) variations dominate seeing.
(iii) in radio & far-IR astronomy water vapor
variations dominate “seeing”
(iv) anomalous dispersion effects occur mostly
outside atmospheric transmission windows;
they have minor effects on n variations
(and do not “compensate seeing” as I had hoped many years ago)

HEIGHT VARIATION OF REFRACTIVE INDEX FLUCTUATIONS
Structure Function: D n (ρ) ≡ r ≡ C n2 |ρ| 2/3 for Kolmogorov turbulence
Height Variation of C n2 (h) according to “Hufnagel-Valley model”:
Roddier (1981)
day
night
Beckers (1993)
boundary layer in daytime
free
atmosphere
‣ Boundary layer control is a major issue in site selection & development
‣ Actual C n2 (h) changes with location, time & wind profile
‣ In daytime lake locations and Antarctic Dome C have very low boundary layer
‣ Balloon observations show major small scale height structure in C n2 (h)

SEEING CONDITIONS AT DOME C
Annual Variation at Different Heights
2835 m
FRENCH-ITALIAN
CONCORDIA STATION AT DOME C
3810 m
4100 m
3250 m
WINTER
SUMMER
Summer/Daytime Seeing at 8.5m Height
1.3
Winter Seeing at 8.5
m
Winter Seeing at 30 m
AGABI et al. 2006 ARNAUD et al. 2007

Height (meters)
WINTER
SUMMER
SEEING ABOVE INDICATED HEIGHT
CALCULATED FROM BALLOON C n2 (h)
OBSERVATIONS
BEST SUMMER/DAYTIME SEEING AT
8.5 m HEIGHT (0.3”) IS CLOSE TO
FREE ATMOSPHERE SEEING (0.25”)
AVERAGE MID-SUMMER/DAYTIME
SEEING (0.7”) IS ABOUT 50% OF
WINTER SEEING AT 8.5 m HEIGHT
ROUGH SURFACE ENERGY BALANCE:
ASSUME STEADY STATE & LOCAL
CONDITIONS EXTEND EVERYWHERE
IN WINTER SURFACE COLDER THAN
THE AIR
IN SUMMER SOLAR RADIATION EQUALIZES
SURFACE AND AIR TEMPERATURES
REAL SITUATION IS NON-STEADY & NON-LOCAL

SPATIAL POWER SPECTRUM OF WAVEFRONT DISTURBANCES
L 0
l 0
Κ (m -1 )
NOTE: A LOW OUTER SCALE
COMBINED WITH VERY
GOOD SEEING IS A GOOD
THING ESPECIALLY FOR
INTERFEROMETRY
‣ inner scale of turbulence (l 0 ≈ 1 cm)
is of little interest for astronomy
(in contrast to laser propagation)
‣ outer scale of turbulence (L 0 ) is of
major interest for astronomy since:
(i) it has dimensions comparable to
the diameters of Large Telescopes
(D ≈ 8 m for VLTs to 42 m for ELTs)
(ii) it is small compared to the baselines
of Optical Interferometers
(e.g. VLTI 200 m ; CHARA 330 m )
‣ L 0 depends on number of factors (like
dome size, landscape, vegetation,
height, telescope structure, radiation
cooling, height)
‣ measured L 0 : La Palma/Hershell 2 m
Sydney/SUSI 5 m
Palomar/PTI 16 m
Paranal 22 m
Mauna Kea 27 - 50 m
OHP/France 14 m
‣ it is quite possible for a site to have
multiple outer scales !!!

“Fried Parameter” r 0 definition:
For Telescope Diameter D and r 0 = D the
RMS Wavefront Distortion Equals 1/6 Wave
Diffraction limited Image
For Larger D/r o RMS Wavefront Disturbances
Increase as (D/r 0 ) 5/6 Imaging Deteriorates

A FEW MORE EXPRESSIONS (for Zenith Angle = 0)
Fried Parameter r 0 (:) λ 6/5 (∫C n2 dh) -3/5
Image Size (FWHM) = λ/r 0 (radians) (:) λ -1/5 (∫C n2 dh) 3/5
RMS Image Motion (:) D -1/3 ∫C n2 dh
Scintillation Index Stars= (∆I RMS /I) 2 (:) λ -7/6 ∫h 5/6 *C n2 dh
Scintillation Index Sun/Moon= (∆I RMS /I) 2 (:) ∫h -1/3 *C n2 dh
Time Constant τ ≈ r 0 / Cn2 (uses Taylor approximation)
Radius of “Isoplanatic Patch” φ 0 ≈ 0.3 r 0 / Cn2
Number of Speckles ≈ (D/r o ) 2
Speckle Size = λ/D (radians)
For more detail see:
F. Roddier, “The Effects of Atmospheric Turbulence in Optical Astronomy”
in Progress in Optics 19, 281, 1981.

REMOVING SEEING EFFECTS IN TELESCOPE IMAGING
THROUGH ADAPTIVE OPTICS (“AO”): CONCEPT
‣ Originally proposed by H. Babcock (1953)
‣ Is complex servo system involving 3 parts:
(1) measurement of Atmospheric Wavefront
distortion on “Reference Star or Beacon”
(2) uses a “Deformable Mirror” to flatten the
wavefront
(3) uses a Processor to couple the wavefront
sensor and the deformable mirror
for 0.75 arcsec seeing & 10m/s wind:
λ
(μm)
r 0
(cm)
τ 0
(sec)
φ 0
( “ )
Sky
Coverage
0.55 15 .015 1.9 .0003%
1.25 40 .040 5.1 .05%
2.2 80 .079 10.1 1.3%
‣ Servo loop has to correct the wavefront
with spatial resolution of ≤ r 0 and temporal
resolution ≤ τ 0 (see table on the left)
‣ Reference object has to be within Isoplanatic
Patch φ 0 and could be object/star itself
‣ Since r 0 , τ and φ 0 increase with wavelength
AO is being implemented first in the IR
‣ All major Solar Telescopes now have adaptive
optics. Some Nighttime Telescopes have
‣ To provide all sky coverage at night many
efforts are focused on artificial stars
(Laser Beacons or Laser Guide Stars=LGSs)

OF SPECIAL INTEREST FOR THE TOPIC OF THIS CONFERENCE:
WAVEFRONT SENSING = ATMOSPHERIC TURBULENCE SENSING!
Three methods are used to sense the wavefront:
(A) Wavefront Tilt sensing using Shack-Hartman Sensor
image of telescope pupil
• For longer wavelengths (> 500 nm) wavefront tilts
are close to achromatic
• So wavefront sensing at visible wavelengths using
CCD arrays can be used for IR astronomy
• Number of lenslets = (D/r 0 ) 2 ≈ 5000 for D = 10 m
BMC
• Algorithm needed for wavefront reconstruction
from wavefront tilts (e.g. Zernike expansion)
(B) Wavefront Curvature Sensing using Roddier-Beckers Sensor
• Out-of-Focus images of original MMT mirrors
showed ring- and other structure.
• Interpreted by JMB to correspond to wavefront
curvature.
• F. Roddier then incorporated Out-of-Focus images
as the sensor for his “Curvature Adaptive Optics”
(C) Faucoult Knife Edge Test ⇔ Ragazzoni Pyramid Wavefront Sensor

SOME EXAMPLES OF IMAGES RESTORED BY ADAPTIVE OPTICS
STAR IMAGE
NGC 1097 (ESO-VLT)
no AO
with AO
no AO
NEPTUNE (KECK TELESCOPE)
SUNSPOT (NSO DUNN TELESCOPE)
with AO
with AO
HUMAN RETINA (A. ROORDA)
with AO
no AO
no AO
with AO

SODIUM (& RAYLEIGH) “LASER GUIDE STARS” (or “Laser Beacons”)
Keck Observatory
Uses Na-lasers at 589 nm wavelength
Scattered radiation on 95 km high atomic Sodium
layer creates artificial star of about 1 arcsec size
This “Laser Guide Star”, or LGS, is not at infinity.
Therefore (i) its focus is behind the nominal focus
of the telescope and (ii) the light received is a
cone rather than as cylinder (“Cone Effect”)
The Cone Effect requires multiple LGSs to infer
the wavefront coming from the actual star
Laser power limits (~ 10W) the LGS brightness to
V ~ 9 (depends strongly on laser properties and
on Mesospheric Na density)
Laser is best transmitted from
the telescope center to minimize
the elongation of the LGS due
to the 10 km Na-layer thickness
Rayleigh Scattering
laser location
LGS perspective elongation
Keck

INCREASING THE CORRECTED AREA ON THE SKY
BY MULTI-CONJUGATE ADAPTIVE OPTICS
CONCEPT:
Place N Deformable Mirrors (DM)
at N Images of Conjugated
Layers of the Atmosphere
Example: Ground Layer and
Tropopause (here: N = 2)
Deform each Mirror to Correct
Wavefront at that Layer
Measure Wavefront of M (≥ N)
Stars with M Wavefront
Sensors (here: M = 2)
Using Tomography Techniques
Estimate the Wavefront
Distortion at Different Layers.
Technique is referred to as
“Atmospheric Tomography” or AT
=TOMOGRAPH (“CAT”)

“TRADITIONAL TOMOGRAPHY” IN MEDICINE
MOVING X-RAY SOURCE
STATIONARY OBJECT/SUBJECT (HUMAN BODY)
IMAGE PLANE
MOVING PHOTOGRAPHIC FILM
“DEFOCUSSED” BODY CAUSES “BACKGROUND”
“TOMOGRAPHIC ANGLE” IS LARGE
ASTRONOMY VERSION OF TRADITIONAL TOMOGRAPHY
Using Natural Guide Stars. Problem:
Only works in clusters of stars
Using Laser Guide Stars. Problem:
Need to also correct Cone Effect
For N = 4 Patch
Diameter increases
by 2N x or 8 x
SCAO
MCAO

SOLAR S-H
WAVEFRONT
SENSOR FOR
ATMOSPHERIC
TOMOGRAPHY
127”
725 mm
73 mm
Configuration:
NSO Dunn Solar
Telescope
D = 76.2 cm
Wavelength = 411 nm
Bandwidth = 2.5 nm
CCD: 2078 x 2108
pixel size 13.8 μm
= 0.623 arcsec
FOV=127” x 127”
Exp. Time = 10 ms

COMPUTER AIDED TOMOGRAPHY
(“CAT”) IN MEDICINE USES
LINEAR X-RAY SOURCE/DETECTOR
ARRAYS & COMPUTER 2D IMAGE
RECONSTRUCTION.
ADD 1D SCANNING ⇒ 3D IMAGES.
NOTE: LARGE TOMOGRAPHIC ANGLE
IN ATMOSPHERIC TOMOGRAPHY ASTRONOMERS USE:
2D NATURAL OR LASER GUIDE STAR ARRAYS
2D DETECTOR ARRAYS, ONE FOR EACH GUIDE STAR
VERY SMALL TOMOGRAPHIC ANGLES (~ 1 arcmin)
COMPUTER AIDED RECONSTRUCTION
‣ BALLOON, SCIDAR AND OTHER C n2 (h) PROFILING
TOOLS GENERALLY SHOWS A NUMBER OF
DOMINANT THIN OPTICAL TURBULENT LAYERS
‣ EVENTUALLY (I SUSPECT) AT & MCAO WILL
INCLUDE REAL-TIME C n2 (h) KNOWLEDGE TO
OPTIMIZE THE 3D TOMOGRAPHY AND THE
CHOICE OF THE DM CONJUGATE HEIGHTS.
10% best seeing
median seeing
Mauna Kea
SCIDAR

NAME
Balloons
SCIDAR
G-SCIDAR
S-S S SCIDAR
LOLAS
DASS
PlaSci
MOSP
SODAR
SNODAR
A LARGE NUMBER OF C n2 (h) RANGE PROFILING TOOLS EXIST
h-RANGE
∆h FULL NAME & COMMENTS
All h
greater h
all h
greater h
low h
HVR-GS
all h
all h
low h
low h
~ 1 m Direct C 2 T (h) C 2 n (h); ; only occasionally available
~ 200 m SCIntillation
Detection
And
Ranging
requires ~ 1 to 3 m telescope & binary star
~ 200 m Generalized
SCIDAR
requires ~ 1 to 3 m telescope & binary star
modest
Single
Star
SCIDAR
LOw LAyer
Scidar
needs small telescope and wide binary angle
~ 25 m High
Velocity
Resolution
G Scidar
needs small scale velocity structure with height
Double-Aperture
Scintillation
Sensor
MASS greater h ~ 400 m Multi-Aperture
Scintillation
Sensor
SHABAR
low h
SHABAR-P all h
LuSci
SLODAR
low h
~ 400 m SHAdow
BAnd
Ranger
uses scintillometer array on Sun or Moon
~ 400 m SHABAR Planet version
Planetary
Scintillometer (Planet version of SHABAR)
~ 400 m Lunar
Scintillometer (Lunar version of SHABAR)
Monitor of Wavefront Outer
Scale
Profiles
SLOpe
Detection
And
Ranging
similar to SCIDAR but uses WFS iso scintillation
SOnic
Detection
And
Ranging
uses scattering by sound waves on turbulence
1 m Surface layer NOn-Doppler
Acoustic
Radar

STATUS OF MCAO DEVELOPMENTS
N=2 only (“Dual Conjugate Adaptive Optics”)
Solar Observatories (KIS; NSO) using “Guide-
Fields” and visible wavelengths (0.5 μm).
Nighttime Observatories in NIR (2.2 μm)
using either:
(i) Natural Guide Stars (ESO-MAD/VLT) or
(ii) Laser Guide Stars (GEMINI-S; being
commissioned)
Laboratory trials ( CfAO/Santa Cruz; Lund
(Observatory)
NSO-DST
(0.8 m ;0.5 μm)
ESO-MAD/VLT (8 m ;2.2 μm)
no AO
MCAO
20”
Guide Fields
44”

THE MANY FLAVORS OF ADAPTIVE OPTICS
AT only
MOAO
Multi-
Object
LTAO
Laser
Tomography
SCAO
Single
Conjugate
MCAO
&
AT
GLAO
Ground
Layer
DCAO
Dual
Conjugate
LOAO a
Layer
Oriented
“Full”
MCAO
LOAO b
Low
Order
ExAO
Extreme
PSAO
Pupil
Slicing
MCAO & AT

THE MANY FORMS OF ASTRONOMICAL ADAPTIVE OPTICS
AO
MCAO
AT
SCAO
DCAO
GLAO
Adaptive Optics Original concept proposed by Babcock (’1959)
Multi-Conjugate AO
Atmospheric Tomography
Single Conjugate AO
Uses multiple DMs conjugated at different heights to
increase FOV (Beckers, 1988)
Gives 3D refractive structure of atmosphere by
tomography using many guide stars (J. Beckers, 1988).
Removes also the cone effect for LGS.
MCAO conjugated to only one height.
Dual Conjugate AO MCAO conjugated to two heights (eg(
ground and
tropopause).
Ground-Layer AO MCAO conjugated to the ground layer (Rigaut(
Rigaut, , 2001)
LOAO a
LOAO b
MOAO
LTAO
ExAO
PSAO
Layer Oriented AO
Low Order AO
Multi-Object AO
Laser Tomography AO
Extreme AO
Pupil Slicing AO
MCAO using optical means on stars (instead of AT) to
sense wavefronts at MCAO conjugates (Ragazzoni(
Ragazzoni, , 2001)
Corrects only large scale wavefront Distortions
Uses separate SCAO for each of a number of objects
(Hubin).
Same as SCAO/AT combination to remove cone effect
for Laser Guide Stars (UofA, 2005).
AO designed to have minimal light in the wings of the
Point-Spread
Spread-Function for High Contrast Imaging.
Uses a number of DMs in segmented/sliced pupil (Beckers
et al. 2006).

MANAGING SEEING EFFECTS IN INTERFEROMETRY
There are two types of Astronomical Imaging Interferometers:
(i) “Monolithic” Interferometers (e.g. Fizeau Experiment; MMT; LBT)
‣ Optical Path Differences (OPD) are small and
constant
‣ Pupil-in = Pupil-out leads to large Field-of View
(FOV) also called “Homothetic Imaging”
‣ Without AO ⇒
“Fringed Speckles”
‣ AO badly needed!
(ii) “Non-Monolithic Interferometers (e.g. VLTI; CHARA; COAST; KECK-I ++)
‣ OPDs are very large (up to few hundred meters), vary rapidly with time and are chromatic
‣ OPD correction needs fast variable Delay Lines (DLs) with Chromatic Correction
‣ Homothetic imaging can be done but has not been implemented (yet) ⇒ currently very small FOV
‣ Dual field interferometry using unresolved object in one field allows Co-Phasing (needs 2 DLs)

CO-PHASED AND COHERENT INTERFEROMETERS
Fringe spacing varies with
Wavelength ⇒ Colored Fringes
Coherence Length = OPD range
With high fringe contrast
Scan of Delay Line ( = OPD variation) ⇒
Zero Optical Path Difference ⇒ “White Light Fringe” (WLF)
In the “CO-PHASED MODE” the OPDs in the interferometer arms have to be very
close to zero (within fraction of a wavelength)
This requires using the WLF on an unresolved star within the Field-Of-View of the
interferometer for homothetic interferometers or a differential Delay Line on a
nearby star (at VLTI this is done with PRIMA). Fringes are tracked on that star.
Because the WLF is used a broad wavelength range can be used (wide color bands)
In the “COHERENT MODE” the OPDs in the interferometer have to be within the
coherence length (CL). CL = λ * (λ/∆λ) = λ 2 /∆λ. This requires narrow color bands.
Fringes have good contrast but cannot be tracked. They may be hidden in photon noise.
If at least 3 interferometer arms are used one can use the “Triple Correlation
Technique” for the combined image analysis.
Average Triple Correlations ⇒“Closure Phases”⇒ Images (as in Radio Interferometers)

TRIPLE CORRELATION/BISPECTRUM ANALYSIS
AND CLOSURE PHASE IMAGING
‣ How to derive phase (and amplitude) information in “Coherent” interferometry
‣ No fringe tracking ⇒ fringe positions change rapidly (< second scale)
because of atmospheric seeing and instrumental effects.
‣ The same problem was encountered in radio astronomy in radio interferometry
many years ago and solved with “CLOSURE PHASE” techniques (R. Jennison, 1958)
‣ It requires the use of at least 3 Interferometer arms ( with 3 telescopes)
• Intensity in Short Exposure Combined Image ≡ I(x,x’) (x values are vectors)
• Triple Correlation TC( x,x’) ≡ ∫ I(x”) I(x”+x) I(x”+x’) dx”
• TC(x,x’) shows 3 correlation peaks at 3 spatial frequencies with observed phases
φ, φ’ and φ” each one consisting of the true phase Φ and an atmospheric error ε
• So: φ = Φ+ε ; φ’ = Φ+ε’ and φ” = Φ”+ε” where ε” = ε+ε’
• ⇒ Φ + Φ’ -Φ” = φ + φ’ -φ”
• Two of the phases e.g. Φ and Φ’ are related to the position of the object. They
can be taken as a given like (0,0) ⇒ Φ” (“closure phase”) over distance x” .
• There have to be enough photons to allow the determination of φ, φ’ and φ” in
the amount of time during which the ε values change by a fraction of 2π .
NOTE: COHERENT IMAGING USING CLOSURE PHASES HAS YET NOT BEEN USED

CONCLUDING REMARKS
1. IMAGE RECOVERY FROM THE COMPLEX ATMOSPHERIC OPTICAL TURBULENCE
DISTORTIONS IS POSSIBLE .
2. HOWEVER DOING SO IS TECHNICALLY VERY TIME CONSUMING AND EXPENSIVE
3. FOR EXAMPLE: (i) “CLASSICAL AO” (or SCAO) PROPOSED BY BABCOCK IN 1953.
FIRST ASTRONOMICAL OPERATING SYSTEM IN 1988 (AT ESO)
4. MAJOR NEEDS NOW ARE:
(ii) “MULTICONJUGATE ADAPTIVE OPTICS (MCAO) WAS
PROPOSED IN 1988. IN ITS SIMPLEST FORM (DCAO) IT WAS
FIRST OPERATIVE IN 2004 (at NSO, Sun) & 2008 (ESO, stars).
(a) Extension of AO to shorter wavelengths
(b) Production of numerous ( ≥10 4 ) actuator, large stroke DMs as
needed for ELTs and ExAO
(c) Production of Adaptive Secondary Mirrors
(d) Development of optimum Atmospheric Tomography algorithms
(e) Construction of more powerful pulsed Sodium Lasers
(f) Removal of Perspective Elongation of Laser Guide Stars
(g) Moving from DCAO to full MCAO
(h) In Interferometric Imaging: Development of Imaging Algorithms
probably building on Radio Interferometry expertise.

THANK YOU!