Cone-effect-free Adaptive-optics Laser-guide-star Development for the
ELTs
Domenico Bonaccini Caliaa, Richard M. Myersb, Franco Zappac, Gordon D. Loveb,
Timothy J. Morrisb, W. Hackenberga, Richard Wilsonb, David F. Buscherd
a
ESO, Garching bei Munchen, Germany
b
Univ. of Durham, UK
c
Politecnico di Milano, Italy
d
Univ. of Cambridge, UK
ABSTRACT
The goal of the CALDO experiments is to demonstrate Laser Guide Star technologies which can scale directly to a 100m
diameter primary aperture, and which are not compromised by the cone-effect at very large telescope diameters. The
laser guide star group at ESO and the adaptive optics group at Durham have proposed two different laser wavefront
sensing methods designed to meet this goal. Though based on quite different physical principles, the two methods
achieve their scalability through the use of a parallel sensing beam projected from the whole of the telescope primary
mirror. They can therefore both be demonstrated by performing a scaled-down projection and sensing experiment on a
smaller telescope. The CALDO experiments evaluate the ESO and Durham methods concurrently and provide a
comparison with Natural Guide Star wavefront sensing, and with each other, without the uncertainty introduced into a
separate evaluation by changing atmospheric conditions.
The location for CALDO is the 4.2m William Herschel Telescope, which has the advantage of the GHRIL Nasmyth
facility for adaptive optics experiments and which has already been used by the Durham group for shared-optics launch
experiments with a laser guide star.
We describe the ESO and Durham methods, the current progress on the experimental subsystems, and the projected
timescales for the experiments.
Keywords: Adaptive Optics, OWL, Laser Guide Stars, Cone Effect.
1. INTRODUCTION
Although research is ongoing, past trends show it is likely that in the timeframe of 10 years LGS Multiconjugate AO will
become a mature, advanced, deployable technology enabling AO to overcome or make negligible the current limitations
of Adaptive Optics: guide star brightness and anisoplanatic field of view. By the use of multiple laser guide stars current
and future adaptive optics (AO) systems will be capable of providing imaging at the diffraction limit of resolution over a
wider field of view and at shorter wavelengths than currently possible. This is because laser guide stars (LGSs) can be
projected virtually anywhere in the sky and made bright enough to fulfil the utmost flux requirements for real-time
compensation of the atmospheric turbulence. The use of laser guide stars focussed at 90 km still suffers from the cone
effect, creating an error term which becomes serious on 8m class telescopes correcting in the visible, and prohibitive for
the future extremely large telescopes AO. However we feel that there is room for new ideas and techniques for layer
oriented LGS sensing.
We introduce here two groups of preliminary concepts for cone-effect-free and ELT-scalable laser guide star wavefront
sensing. The first group, all of which use turbulence sensing on the upward-propagating path, originates at Durham
University (and D.F. Buscher, now at Cambridge University), whilst the second concept comes from ESO, and exploits
the coherence of Rayleigh scattering.
These concepts are subject to ongoing analysis and, on the basis of work so far, a joint experimental programme has been
initiated. This will be carried out on the 4.2m William Herschel Telescope, probably in 2006, and will evaluate both
experiments using a parallel-launched Rayleigh laser guide star. Specific enabling technology from the Politecnico di
Milano, namely an array of 60 avalanche photodiodes, will be employed for the evaluation of one of the Durham
concepts. The 4.2m William Herschel Telescope is operated on the island of La Palma by the Isaac Newton Group of
Telescopes in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias.
2. DURHAM PROPOSED METHODS
The coneless LGS methods proposed by the Durham/Cambridge groups are all variants of Projected Pupil Plane Patterns
(P4). The key features are that a parallel (or nearly parallel) laser beam is projected from the full primary aperture and
that sensing takes place on the upward path. The methods therefore rely on an observable modulation of the scattered
intensity by turbulence-induced phase distortions during upward propagation of the laser beam. There are three main
variants:
 ‘Pupil-plane’ Curvature Sensing
 ‘Smartt on the Sky’
 SPLASH: Sky Projected Laser Array Shack Hartman
The first two methods are dealt with in Buscher et al (2002), whilst the latter is introduced in Love et al (2003).
Figure.1. Scheme showing a P4 LGS wavefront sensing system. The system is essentially a curvature sensor
projected onto the sky. This will be one of the two set-ups for the CALDO experiment
The Curvature Sensing variant is illustrated in figure 1. A single parallel beam is projected into the sky and the evolution
of scattered intensity is monitored from at least two distinct altitudes, using a temporally range-gated pulsed Rayleigh
beacon. Given sufficient propagation length, phase variations induced by atmospheric turbulence at lower altitudes cause
intensity variations higher up. This corresponds to the near-pupil variant of curvature sensing. There are a number of
potential difficulties which are immediately apparent: (1) the variations in scattered intensity must be observed through
the inducing turbulence, giving rise to a danger of partial geometrical reciprocity of lower-order (slowest varying
spatially) modes (Ragazzoni, 2003); (2) variations in atmospheric density will give rise to false signal and must be
continuously calibrated out; (3) there may be insufficient propagation length available within the atmosphere to give a
signal which is both unambiguous in terms of wavefront phase and detectable against background noise for reasonable
laser power. Although this is the simplest case and has several difficulties to address, the current simulations described
below show that a complex zernike prescription for the aberating phase is indeed recoverable. It is also easy to conceive
of the technique being extended to more than 2 intensity sampling altitudes and this is indeed proposed for CALDO.
Figure 2. An alternative P4 approach based on point diffraction, or Smartt, interferometry. (a) In the left hand figure a
parallel beam the size of the telescope (the test beam) is simultaneously launched with a smaller beam (the reference
beam) which diffracts to produce an interference pattern projected onto the sky. (b) The right hand scheme shows a
modified arrangement involving a number of beams to reduce the focal anisoplanatism further, at the expense of
complexity.
The “Smartt on the sky” method, illustrated in figure 2a, involves creating an overlaying reference beam and producing
an interferometric pattern in the scattered intensity. This appears to dispose of the propagation length problem, but the
reference beam must be produced in some way, and in fact this relies on achieving a certain propagation length. An
initially narrow second beam is produced with a fixed phase relationship to the first beam, and allowed to broaden to the
telescope diameter by diffraction. The majority of the broadening must take place above the dominant turbulent layer in
order to provide an unaberated beam. Given a reasonable laser wavelength, the only other free parameter that can be
adjusted to achieve this is the initial beam diameter. Therefore in order to obtain an expansion at some reasonable
altitude to the full telescope diameter of an ELT, several such reference beams are necessary, as illustrated in figure 2b.
Figure 3. Concept of SPLASH, showing the upward passage of the beams. We show a possible optical implementation
whereby the laser is launched from a hole in the secondary mirror (in the space corresponding to the secondary mirrors
own shadow) via a lenslet array. This only a conceptual diagram and not a formal optical design. The size of each of the
converging beams is ~r0 although we have only shown 4 here for clarity. Furthermore, we have shown the beams as
converging to a spot, whereas in reality they would be diffracted.
SPLASH is illustrated in figure 3. In this concept several beams are focussed on to the sky to produce a Shack-Hartman
pattern at some altitude. As the pattern is observed by the whole telescope, the effect of tilt reciprocity is simply to
remove the common mode tilt (the normal situation for a single beacon). The cone effect, however, is only applied to
individual subapertures and therefore greatly reduced. There are clearly constraints on the minimum size of subapertures
which can be employed without diffraction and seeing effects causing the spots to overlap, and in fact it may well be
worth accepting some divergence in the overall projected beam to reduce this effect. Another alternative is temporal
multiplexing of spot illumination in order to reduce cross-talk. In the absence of this approach SPLASH does not require
a pulsed laser and it is also usable with a sodium laser.
Figure 4. Initial simulation of the P4 concept. A Fresnel propagation code was used to calculate projected pupil-plane
intensity patterns for an input phase map comprising a summed set of Zernike aberrations. A solution phase map was
recovered from the projected intensities via the amoeba downhill simplex method. The figure shows the simulation
diagnostic display at convergence - Top left: Input and recovered Zernike coefficients versus mode number. Top right:
Residual (input - recovered) phase variance versus iteration number. Bottom left: Projected intensity distributions
(upper conjugate) for the input and recovered phase maps. Bottom right (left to right): The input and recovered phase
maps, and their difference.
The programme of evaluation for all three of the above concepts consists of a detailed modelling phase and, given a
successful outcome, an on-sky evaluation using Durham’s Rayleigh laser system. The modelling phase, including
evaluation of SNR limitations and requirements for ELT implementation, is expected to take ~18months. The current
status is that simple simulations have been conducted for the curvature sensor concept and detailed modelling of SPLAS
has begun. The results for the curvature sensor are illustrated in figure 4 and show that a phase prescription can indeed be
recovered from the projected phase, at least under some circumstances. Given the lead-time for experimental
verification, the requirements for advanced equipment, and the need to secure the availability of telescope facilities, we
believe that the formation of the CALDO collaboration and the planning for experimental verification is both timely and
justified by the currently available results. The details of the proposed experiments are amplified below.
3. ESO PROPOSED METHOD
ESO proposed method is based on the fact that projecting a pulsed laser beam collimated from the full aperture D, the
mesospheric area which is backscattering has spatially coherent patches of the order of ro when reaching the ground.
Figure 5: Simplified coneless sensig scheme with Pulsed laser, and a Shearing WFS. This scheme will be tested
within the CALDO experiment, with a parallel beam projection and a Rayleigh pulsed laser at 532nm.
In the experiment the highest conjugate layer will not be on the mesosphere, but at 6km.
We demonstrate it using the Van Cittert-Zernike theorem below. This is because the field from a noncoherent source
acquires coherence by the very process of propagation. The design we show is applicable to any size telescope, and it is
cone-effect-free. The design is made to correct at the same wavelength of the pulsed laser, i.e. it is also suitable for
corrections in the visible with ELTs.
If at the infinity focal plane of the telescope an apodized field stop selects the returned beam angular extent, equal or
smaller than the isoplanatic patch (Fig 5), then the wavefront spatial coherence is sufficient to have e.g. a shearing
interferometer wavefront sensor, with shear s ~r o(λlas), with λlas the emitted laser wavelength. For Multiconjugate
operations, multiple apertures may be placed at the infinity focal plane, isolating isoplanatic wavefronts coming from
different directions and feeding correspondingly Wavefront Sensors.
The advantages of a shearing wavefront sensor with monochromatic light are similar to those reported for curvature and
pyramid sensors: gain tunability in closed loop, full aperture advantage. The latter means that if the WFS senses a
diffraction limited wavefront at its operating wavelength, these type of sensors have an advantage coming from the full
aperture imaging.
Moreover the Shearing wavefront sensor is self referencing, i.e. it uses the warfront itself to
reference relative tilts across the shearing distance s, and does not need an image of the source. We can thus use the pupil
interference. The Shearing Wavefront sensor works at best with monochromatic wavefronts, such as those provided by
Laser Guide Stars. It has been already successfully used with Rayleigh lasers (532nm) guide star systems by Dave
Sandler et al. at Thermotrex Co. for the US Navy [6].
3.1 The Shearing Wavefront Sensor
We want to use the four-bucket scheme [7], whereby the shear is s=0.2 r o(λlas), and d=0.8 ro(λlas) corresponds to a
sampled subaperture of the deformable mirror. The shear value will be variable in the experimental setup to optimize
fringe contrast. Fringe contrasts between 0.6 and 0.9 have been reported experimentally, with a 532nm Rayleigh pulsed
laser beam [6].
We use symmetric later shears of ±s/2 for the two interfering
beams, for two orthogonal axis, x-y. For each axis four
sheared beams are created with phase shift steps of 90°,
giving four images of the sheared pupils (Figure 6) on a Dalsa
DS-12-16K5H, 1282 490 fps detector camera. The
corresponding 16 μm detector pixels in the four images will
conjugate to the deformable mirror subaperture of size d.
They are used to compute the single-axis tilt in each
subaperture.
A linear combination of the four pixels intensities gives the
wavefront slope tij across the subaperture ij (Eq 1). The shear
extent s can be tuned in closed loop, thus optimizing the WFS
gain for the larger effective ro. Variable sinusoidal lateral
shearing (heterodyne) have been used in the past, to increase
the stability and the performance of the Shearing WFS. We do
not plan to use it since the closed loop tilt residuals will
automatically smooth the wavefront sensor gain response over
the different Zernike terms. Hence we will implement the test
with a dc adjustable-shear interferometer.
Eq 1
 I ij ( 2)  I ij ( 4) 
d
1
t ij   tan  (3)

(1)
s
 I ij  I ij 
3.2 The photon budget
The arctan term in Eq 1 gives the phase difference measurement. Differentiating it we get the expression for the
subaperture wavefront sensor tilt variance (x and y summed)
Eq 2
 pd 2 
8
2
 2 ccd2
2
 N  N
where σccd is the sensor rms readout noise, N is the total number of photon counts per subaperture summed over the four
pixels of the sheared beam images, α is the fringe visibility. The computation of the latter is dealt with in the next
section.
Similarly to other wavefront sensors, the contribution of
the detector read-out noise to the phase measurement
error is very significant. This and the use of pulsed laser
favour significantly, in future systems, the nanosecondgated photon-counting parallel detectors, such as the
Single Photon Avalanche Diode Arrays presented at this
conference [9].
Solving Eq 2 for N, targeting σpd= λ/30, α=0.6, λ
=589nm, we get e.g. N=127/frame for read-out noise
free detectors, and N=182 for a 20e - rms read-out noise
detector. The dependence of N from the fringe visibility
is indicated in the plot Figure 7. Now we want to check
the return photon budget with the foreseen CALDO
Rayleigh laser.
By projecting a 12W equivalent power, 532nm pulsed
laser from the full WHT aperture, during the experiment,
we will gate the return flux from 10% of the pulsed
wavefront altitude. This can be done using a membrane
mirror re-imaging, in a similar fashion to what is done
with curvature AO systems, as will be explained in
section 4. The membrane mirror allows to keep fixed the
image size of the propagating beam, and always
conjugated to the CCD sensor. We can thus sum over
larger propagation ranges compared to focused Rayleigh
beam geometries, clearly an advantage for this scheme.
We will thus accumulate the Rayleigh scattered returned
photons over several hundred meters. The photon return
cumulated over a range of 10% of the beam altitude is
shown in Figure 8. Comparing this result with that of
Figure 7, it is shown that in the CALDO experiment we
can have high precision (λlas/30, i.e.18nm rms) wavefront
sensing with 20x20 subapertures, up to 6500 meters.
Figure 7 top: number of counts/subap/frame necessary to make
a subaperture tilt estimate rms error of λ/30 (17nm), vs Fringe
Visibility. Bottom: for a fringe visibility of 0.6, dependence of
the subaperture rms tilt error from the number of counts per
subaperture (bottom).
Returned Photons per frame, 250Hz, 0.18m subap, 12W 7 kHz pulsed laser at 532nm, 10% alt. range gate
800.00
700.00
Nphot/frame/subap
600.00
Figure 8:
returned photons
per subaperture
in the CALDO
experiments
500.00
400.00
300.00
200.00
100.00
0.00
3500
3900
4300
4700
5100
5500
Beam height (m )
5900
6300
6700
7100
3.2 The fringe visibility in the subapertures
The detector samples the 4 sheared parallel beams, which produce coherent fringes on the subaperture pixels (4 pixels
per axis). The tilt measured in the single subaperture is used to rebuild the wavefront. In previous LGS-AO systems with
shearing interferometers [6], made for the US Navy, it has been experimentally demonstrated that by projecting a
polarized laser beam the Rayleigh beacon has a degree of spatial coherence in the subapertures well sufficient to
produces fringe visibilities between 0.6 and 0.9 at optimal shear distaces. Now this value depends on the projectionsensing geometries and the seeing. The modulation depth α,or fringe visibility, equals the value of the total optical
system MTF at spatial frequency s/ (λlas), using the same notation of section 3.1. The modulation depth α is given by a
product of factors:
   shear   samp   opt   atm where
Eq 3
αshear is given by the modulus of the complex
degree of spatial coherence [9];
αopt is the system optics MTF value at spatial
frequency s/ (λlas). We disregard this term, as it
is ~0.98 for s=0.2d;
αsamp is given by exp(-σfit2), related to the fitting
error variance of the wavefront sampling,
σfit2=0.17(d/ro)5/3.
The expected value of α for different WFS beam
shears is shown in Fig.9. The increasing distance
of the scattering layer with Zenith distance is
due to the increasing degree of wavefront spatial
coherence with distance.
Coherence modulus
αatn is given in Kolmogorov atmospheres by
exp[-3.44(s/ro)5/3]. In closed loop a larger,
effective ro(λlas) has to be used. This is typically
a factor 4 larger than ro in our case. As described
below, on the CALDO experiment WHT we will
have the WHT GHRIL closed-loop AO system,
pre-shaping the wavefront, since it is the WFS
closed-loop performance which we want to
assess. Finally
MCDSC+ closed-loop Atm + Fit_error
Shear distance, m
Figure 9: The fringe visibility α has been computed for a 21cm
subaperture on a ground telescope, a closed-loop 20x20 subap
system on a 4.2m telescope, including the WF sampling error. The
shear values are those projected on the telescope primary mirror.
Optimal shear distance values s~0.2d have been reported with LGSAO, where d=0.21m in our case, hence s~0.04 in the plot above.
4. JOINT EXPERIMENTAL VERIFICATION
Although quite different, the ESO and Durham concepts share several technical requirements. Both require a parallel
beam shared optics launch. That is, a fully expanded parallel beam must be projected from the telescope primary mirror.
This necessitates some means of multiplexing the outgoing laser beam and the returning scattered light. The outgoing
beam is, of course, far brighter than the returning Rayleigh scatter, and will produce dominant scattering from any
beamsplitter as well as from the telescope surfaces it encounters. There will also be fluorescence from these surfaces
(and any dust). In practice, therefore, a pulsed laser is employed and temporal multiplexing is used to switch in the
outgoing beam and to remove initial scatter and fluorescence from the return. A pulsed laser and electro-optic range-gate
shutter are, of course, required for many Rayleigh beacon configurations in any case. In addition to the shared laser
launch requirements; there would also be a shared benefit from being able to operate with closed-loop correction of
turbulence, using an auxiliary WFS on a bright NGS.
The large number of shared requirements for evaluation raises the possibility of a concurrent or nearly concurrent
experimental test. This introduces a little extra design complexity but yields a much more valuable comparison by
eliminating the uncertainty of variable experimental conditions (particularly Cn 2(h) and the vertical velocity
distribution).
An experimental configuration incorporating a shared laser launch, closed loop AO, and two alternative LGS WFS
prototypes will require appropriate telescope facilities, preferably with a large gravity-stable optical bench. The 4.2m
WHT has exactly this facility at the GHRIL (Ground-based High Resolution Imaging Laboratory) Nasmyth focus. This
is the rationale of the proposal for a joint experimental evaluation at WHT/GHRIL. The details of these experimental
systems are summarised below.
Figure 10. Schematic diagram illustrating proposed CALDO parallel-beam LGS evaluation experiment at WHT.
NGS wavefronts and turbulence profile information is recorded concurrently with wavefront sensing information from
the two parallel beam methods. Optionally the wavefronts may be pre-processed by a conventional NGS closed-loop
AO system. There will be an option to feed wavefront information from the parallel LGS sensors direct to the closed
loop system.
Figure 10 is a schematic of the joint experimental evaluation proposed for the WHT. The components shared by both the
ESO and Durham subsystems are the Nasmyth focus, the laser and launch demultiplexer, the NGS AO system and its
closed loop WFS, and the 2-axis SLODAR WFS for monitoring wavefront information, Cn2(h) and velocity distribution
(Wilson, 2002). This last component can be readily moved before the closed loop system if required. Note the additional
anti-LGS notch filter on the closed-loop WFS to remove residual scattered launch light. The GHRIL and the shared
subsystems are described in the Partner Contributions section below.
The Durham parallel WFS subsystem will initially be in a P 4 configuration. P4 evaluation will benefit greatly by access
to the 60-element SPADA APD-based curvature sensor, currently being developed by a collaboration led by the
Politechnico di Milano as curvature sensor. This will be equipped with a sensing option for time-sliced WFSing,
essentially forming an ideal P4 evaluation sensor that will be able to sample 10 timeslices of intensity for each pulse
without overhead. It will therefore be possible to monitor the vertical evolution of intensity through known turbulence.
The observation of the intensity evolution can also take place through optionally AO corrected turbulence (initially the
entire NGS illuminated column will be corrected).
4.1 The dynamic layer tracker
The parallel laser beam moving upward can be conjugated on the sensor, keeping its image at fixed size. This is obtained
with a pupil plane membrane mirror, of the type used in curvature systems, e.g. in the ESO MACAO systems (where it is
used at the focal plane, however). A collimated 2arcsec diameter field is incident on the membrane mirror, which is at
the telescope pupil plane conjugate acting as a variable focal length lens. The following optics collimates the pupil stop
located at the membrane and produces a telecentric image, whose f/number and size are constant for appropriate
combinations of layer altitude and membrane shape. The membrane mirror has a sinusoidal variation of curvature, which
is described by:
R(t ) 
Eq 4
Rmin
sin( t   )
where Rmin is the minimum curvature radius of the membrane mirror,
ω/2π=ν is the resonating frequency of the membrane, ф is the phase delay on the sinusoidal signal.
The following optics can produce the fixed-size pupil on the SPADA sensor (or on the Shearing Interferometer entrance
pupil stop) at its focal plane. When the membrane mirror is flat, this is an image of the system pupil. An advantage of
the telecentric set-up is that the variable-height layer, conjugated on the SPADA sensor or at the Shearing Interferometer
aperture input, remains of constant size. This is because of the telecentric beam and the large radius of curvature of the
membrane mirror.
WHT Rayleigh laser focal plane location
The sinusoidal signal of the membrane creates for one
half of the period a conjugation of the following sensor
with different atmospheric heights above the telescope
primary. It does so by acting as a gentle negative lens
which collimates the layer conjugate. Adjusting the
membrane mirror parameters to Rmin=145mm, ν=1700
Hz and ф=0.414 degrees, which are reasonable values
in practice, we obtain a perfect tracking of the pulsed
laser beam conjugate, as shown in Figure 11
Image plane shift at tel focus (mm)
800
600
400
200
5
10
15
Pulse height above telescope (km)
20
Focal Plane Shift at WHT
Membrane Mirror tracking
Figure 11: Focal plane shift at the WHT, for the uplink pulse
(solid curve) with superimposed the membrane tracking (see text)
By synchronizing the emitted laser pulse with the
membrane cycles, we can gate the SPADA sensor (for
the P4 experiment), or the range-gate electronics (for
the Shearing Interferometer WFS) to integrate over
layers of a few hundred meters. All the necessary
triggering signals have been implemented for this. The
WFS will be calibrated beforehand against possible
static aberrations introduced at the different membrane
positions of interest.
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