Multiconjugate Adaptive Optics for the Swedish ELT
Alexander Gontcharov and Mette Owner-Petersen
Lund Observatory, Box 43, s-22100 Lund, Sweden
The Swedish ELT is intended to be a 50 m telescope with multiconjugate adaptive optics (MACO) integrated directly as a
crucial part of the optical design. In this paper we discuss the effects of the distributed atmospheric turbulence with regard to
the choice of optimal geometry of the telescope. Originally the basic system was foreseen to be a Gregorian with an adaptive
secondary correcting adequately for nearby turbulences in both the infrared and visual regions, but if the performance
degradation expected from changing the basic system to a Cassegrain keeping the adaptive secondary could be accepted, the
constructional costs would be significantly reduced. In order to clarify this question, a simple analytical model describing the
performance employing a single deformable mirror (DM) for adaptive correction has been developed and used for analysis.
The quantitative results shown here relates to a wavelength of 2.2 µm and are based on the seven layer atmospheric model for
the Cerro Pachon site, which is believed to be a good representative of most good astronomical sites. As a consequence of the
analysis no performance degradation is expected from changing the core telescope to a Cassegrain (Ritchey-Chrétien). The
paper presents the layout and optical performance of the new design.
Keywords: telescope, adaptive mirror, atmospheric turbulence compensation
Related to large aperture telescopes (ELT’s) the cost of the mirrors and the mechanical construction must be kept as low as
possible. Since the size of the adaptive mirrors scales with the aperture, it will therefore be an advantage to integrate them in
the optical design if possible, instead of having post focal correction. Also it will be an advantage to keep the telescope as
short as possible (in order to make a cost-effective mechanical design for telescope and its enclosure, Ref. ), which will
favor a basic Cassegrain design over a Gregorian design. In Section 2 of this paper we describe a simple analytical model for
what to be expected from adaptive correction of turbulence using one DM and one wavefront sensor focussed on the
telescope primary pupil. The wavefront sensor probes a certain number of guide stars. The model applies to big aperture
small field telescopes in the sense that the pupil projected back to the upper atmosphere for maximum guide star angle does
only shift insignificantly from the axial projection when compared to the pupil diameter. Since the shift corresponding to 1
arcmin FOV is 4 m at 15 km altitudes, this assumption is reasonable for a 50 m aperture telescope. The model takes into
account as many turbulent layers with appropriate altitudes and r0’s as is adequate, the geometry of the guide stars used for
correction and the fitting error for the DM. The guide stars are assumed to be infinitely distant. The quality of the correction
is estimated from the ensemble averaged squared residual error, also averaged over the guide stars, which is expected after
correction. This error will depend on the position of the mirror and may be used for evaluating the performance loss when
changing from the Gregorian to the Cassegrain. Based on the results from the model, it was concluded that changing the core
telescope from a Gregorian with adaptive secondary to a Cassegrain with adaptive secondary would result in no significant
performance loss averaged over a certain field in the prime focus. For small field applications in the infrared, the resulting
residual error may be adequate, but if larger fields or visual correction are wanted, more DM’s must be implemented in the
design Refs. [2,3,4]. Since the gain obtained by going from two to three DM’s should be proportional to the field and
inversely proportional to the pupil diameter Ref. , we believe that one extra DM may be adequate for a large aperture
telescope. As can be seen from Table 1 in Section 2, the worst high altitude turbulence are localized around 13 km. Assuming
that some of the intermediate turbulence may be corrected by the second DM, we choose the conjugation altitude for this
mirror to be around 8 m. The precise altitude is however not a crucial design parameter, since the second DM can easily be
moved within reasonable limits without affecting the image quality. Establishing the optimal localization must await the, at
the present stage, still unclear problem of MCAO for large aperture telescopes to be clarified. In Section 3 the modified
optical design is presented and commented upon (original design, see Ref. ). Using raytracing through the atmospheric
sheets, it has been verified that the sequence of correction on more than one DM is of no importance for the infrared region. It
may however be important in the visual region at daytime seeing Ref. , which is not relevant to this telescope.
2. OPTIMAL CONJUGATION FOR ONE MIRROR CORRECTION
The results presented in this section relate to the Cerro Pachon atmosphere Ref.  quoted below in Table 1, which describes
the distributed atmosphere as lumped into seven layers with different r0. The values of r0 correspond to a wavelength of λ0 =
2.2 µm. Changing to the wavelength λ, the r0’s should be multiplied by (λ/λ0)6/5.
Table 1. The Cerro Pachon. Atmospheric Profile at 2.2 µm
Layer Number n Altitude hn (Km) ron (m)
1 0.0 1.14
2 1.8 3.99
3 3.3 3.14
4 5.8 6.55
5 7.4 8.01
6 13.1 3.99
7 15.8 10.89
In our model for the residual error we have assumed fitting to be dominant and given by Ref.  a mean square error σe2
σ e2 = 0.3( p roeff )5 / 3
where p is the actuator pitch projected back on the pupil and the effective Frieds parameter r0eff is given by
(1/ r )
= (1 ron )
It should be noticed that since the adaptive secondary is intended for correction of nearby turbulence in the visual range, the
fitting error will be low at 2.2 µm, that is around 0.02. The residual squared error ε2 averaged over the Q guide stars and the
pupil is given by
ε2 = P(r )ε q (r )dr + σ e2
Q q =1 Ap
ε q (r ) = Φ q (r ) − ϕ (r − hM α q )
Here P is the pupil function of the telescope, Ap is the pupil area, Φq is the measured wavefront for the star q at the angle αq,
hM is the conjugated altitude of the mirror (negative for the Cassegrain and positive for the Gregorian system) and ϕ is the
phase deformation of the adaptive mirror. For the big pupil approximation minimizing ε2 with respect to the choice of ϕ leads
to the following expression for the optimal phase.
ϕ (r ) = Φ q (r + hM α q )
Q q =1
Assuming the statistical model of the measured phase Φq which is given below
Φ q (r ) = ϕ n (r − hn α q )
and performing an ensemble average (denoted by < > ) of ε2 over the atmospheric fluctuations, the averaged squared error
could be expressed as
< ε 2 >= 2
Dn (hM − hn )(α q − α q ' ) + σ e2
n =1 2Q q =1 q '=1
where Dn is the structure function for the fluctuations in the layer n. It is assumed that the fluctuations in the atmospheric
layers are independent. In the case of Kolmogorov statistics the structure functions are given by
Dn [r ] = 6.88(r r0 n )
which leads to=
7 Q Q 5/ 3
< ε 2 >= 3.44 (hM − hn ) / r0 n (α q − α q ' ) + σ e2
n =1 Q2 q =1 q '=1
In the case of a (not realistic!) “continuous” distribution of the guide stars over a circular field of radius αm , the averaged
squared error becomes
< ε 2 >= 1.03( 2α m )5 / 3 ( hM − hn ) / r0 n + σ e2
Note that <ε > is independent of the pupil diameter. For both the discrete and continuous approach <ε2> or the corresponding
Strehl ratio SR=exp(-<ε2>) will show the same behavior as function of hM. An increase in <ε2> (or decrease in SR) will
reflect a decrease in the isoplanatic angle. Figure 1 depicts SR as function of hM calculated for 5 guide stars chosen in a cross
with an arm length of 0.5 arcmin.
-1000 0 1000 2000 3000 4000
Efficiency of wavefront correction with one adaptive mirror conjugated to different atmospheric heights. The vertical axis
shows the Strehl Ratio and the horizontal axis shows the conjugate position of the mirror in Km relative to the pupil.
Calculations were performed for a maximum field angle of 20 arcsec. The Strehl ratio is calculated from the field and
ensemble averaged squared residual error.
It is seen that SR has a quite shallow maximum at hM =1.56 km. Since SR decreases only a few percent when moving the
adaptive mirror to the conjugate position at 670 m height above the pupil for our Gregorian secondary and to the conjugate
position at 590 m behind the pupil for our Cassegrain secondary (see Section 3), we conclude that the basic Gregorian
telescope may be replaced by the shorter equivalent Cassegrain having the same diameter of the secondary without
significant loss of performance for one DM operation. Comparison of the numerical values of SR provided by the summation
over the five guide stars to the values provided by the continuos expression evaluated for αm = 0.5 arcmin shows a quite good
agreement. For this guide star geometry we therefore believe that SR also corresponds to the value which could be evaluated
from the mean squared error averaged over intermediate field points which do not participate in the estimation of the adaptive
mirror deformation. Figure 2 shows SR for the five guide star configuration as a function of field angle αm , calculated for
both the Cassegrain and the Gregorian configurations.
The Strehl ratio related to the field and ensemble averaged residual squared error is shown as a function of the maximum
field angle for the Cassegrain (C) and Gregorian(G) configuration.
It is seen that on the average a good correction for both configurations could be obtained within a field of αm = 20 arcsec
which is roughly equivalent to the isoplanatic angle calculated from
−3 / 5
θ i = ê6.88 (hn / r0 n ) 5 / 3
ë n =1
resulting in θi = 14 arcsec. It is important to notice that Figure 2 does not give the distribution of SR within the field. This
distribution may be inhomogeneous favoring the axial point. Pulling up SR at the edge of the field by increasing the weight
on the contribution of the outer guide stars in the estimate of the mirror deformation will most probably result in the sacrifice
of the axial SR (trading field for Strehl). Additional DMs must be invoked to raise the overall level without sacrifice of the
3. THE OPTICS OF THE SWEDISH ELT
The optical goals for the Swedish ELT are as follows:
- 50 m primary mirror diameter - wavelength range 0.55 to 2.2 µm
- science field of view (FOV) 1 arcmin (for IR and VIS foci) - technical FOV 12 arcmin seeing limited
- diffraction limited angular resolution - Strehl ratio after AO correction 0.2/0.3
2.5 milliarcsec in V band (VIS)
10 milliarcsec in K band (IR)
The main drivers for the design comprise a fast primary mirror, Ref. , in our system f/1.0, integrated adaptive optics with
DMs conjugated to appropriate turbulent layers, Ref. , and focal ratios matched to the camera in both V and K bands,
Ref. . The basic telescope is a Ritchey-Chrétien system with focus intended for the IR range. In order to prevent
unwanted stray IR emission from the sky to reach the image surface during observations, the aperture stop is placed at the
secondary. The low altitude seeing for both the VIS and the IR regions is corrected on the adaptive secondary (DM1) used
also for slow tilt control. From the IR focus the image is relayed to the visual focus with a magnification of two. Integrated in
the relay system is a second deformable mirror (DM2) which corrects the high altitude seeing in the visual region. The
system is shown in Figure 3. Analysis of image quality performed with Zemax confirmed that the system fulfill the
requirements for both foci, see Figure 4. The technical FOV for the IR focus exceeds 12 arcmin and the technical FOV for
the visual focus equals 2 arcmin. The reason for having a large technical field is to provide means for wavefront sensing
using natural guide stars Ref. [13, 14]. The concave elliptical mirror M3 is forming an image of the 8 km altitude atmospheric
layer on the flat M4, which acts as the second deformable mirror DM2. In this case rays coming from the layer are passing a
lower 1.6 m diameter circular zone on M3. At the same time, for the infinite object M3 is working in a double reflection at
lower and upper circular zones. The 4.9 m diameter monolith M3 can be substituted by two identical off-axis segments of 1.7
m diameter, if the monolith M3 is unwanted and the technical difficulties with off-axis segment alignment are not so
M1 IR focus M3
The optical layout of the Swedish ELT (left). The magnified image of the visual relay system (right).
The spot diagrams for IR focus 3 arcmin full field (left), VIS focus for 1 arcmin full field (right). Airy disk diameter is 80
microns for IR and 40 microns for VIS.
Since the low altitude seeing in the visual region corresponds to r0=17 cm, the number of actuators across the 4 m diameter
secondary will be around 300, approximately one actuator per projected r0, corresponding to an actuator pitch of 15 mm. The
second deformable mirror is intended for correction of the high altitude (around 8 km as shown in Ref. ) seeing that has a
typical r0 = 80 cm in the visual region (for the Cerro Pachon site). Hence 75 actuators across DM2 will ensure proper
compensation of the turbulence (actuator pitch is around 20 mm). This pitch puts requirements on image quality when
imaging the 8 km altitude layer on DM2. For adequate imaging of the 8 km layer onto DM2, the image spread should be less
than 7 mm (that is one third of the 20 mm actuator pitch). Since imaging of the 8 km layer is done through the ground layer,
it is a question whether the effect of this layer must be compensated before the image is formed on DM2. This means that the
sequence of adaptive compensation becomes important Ref. . Although the proper sequence of correction is kept in the
telescope, it might be worthwhile clarifying this issue by importing phase screens generated using the Skylight software
package into Zemax. In Figure 5 we show the image formation of the 8 km layer on M4 for both the “no-atmosphere” case
and when passing the uncompensated ground layer.
The spot diagrams show both the no-atmosphere image quality and the effects of the non-compensated ground layer when
imaging the 8 km layer on DM2. The left image in each pair corresponds to the case of no atmosphere, and two
representative image points on DM2 have been selected. Wavelength 2.2 µm
It is seen from Figure 5 that the image blur is within the tolerance limits in all shown cases, and what is more important, that
image formation through the uncompensated ground layer does not shift the position of the centroid. We conclude that the
sequence in which the upper and lower turbulence is compensated is of no importance in the IR region.
The convex spherical M5 provides the last relay to the visual focus, and the data for the system are given in Table 2. Mirrors
M3 and M4 have a common optical axis, which is parallel to the optical axis of the Ritchey-Chrétien system and shifted from
the latter by 1500 mm in the plane of Figure 3. The distance between the IR focus and the vertex of M3 projected on the
optical axis is 18 000 mm. The center of curvature of M5 lies in the plane of Figure 3 and has the coordinates (0, 10180 mm)
in a rectangular coordinate system with origo in the vertex of M3. The tolerance analysis for the position of M2 has brought
out a quite restricted budget for misalignment and tilt errors. The errors due to lateral decenter of M2 should be less then
+0.01 mm and the tilt of M2 should not exceed +0.5 arcmin to guarantee the required image at the visual focus.
Table 2. The essential optical characteristics of the Swedish ELT design
Surface Radius Thickness Diameter Shape Conic
M1 -100000.000 -46000 50335 hyperbolic -1.000809
M2 -8581.819 59000 4020 hyperbolic -1.324546
IR image surface -4100.0 18000 428 spherical 0.0
M3 -38389.377 -19800 1610 elliptical -0.65
M4 infinity 19800 1400 flat 0.0
M3 (second reflection) -38389.377 -15400 1700 elliptical -0.65
M5 -19542.790 10180 775 spherical 0.0
VIS image surface - 4175.0 920 spherical 0.0
Based on the above considerations, the following conclusions are drawn:
Since the adaptive Cassegrain performs as good (or bad) as the adaptive Gregorian, it may replace the Gregorian without
significant loss of performance. This is expected also to be true when more DM’s are invoked. The change will decrease the
cost of the telescope and its enclosure.
Analysis of the new design shows that the specified optical goals are met.
One advantage of the Cassegrain design is that the infrared focus is moved further behind the primary, which allows moving
the conjugation altitude for DM2 downwards if needed. For 1 arcmin FOV the IR image surface could be considered as a
plane surface without risk of destroying the diffraction limited image quality.
It has been shown by raytracing that the sequence of correction is not important in the IR and probably not in the VIS as well.
No choice of guide stars, NGS or LGS has been made so far, but the rather big technical field in the IR focus leaves room for
NGS if wanted. From this focus the stars could be “folded down“ to the edge of the science field and relayed to the visual
focus without need to enlarge the mirror diameters as it has been proposed for the OWL design Ref. . Since the
wavefront sensor design is dependent on the guide star type, the choice of sensor geometry, e.g. Shack-Hartmann or
pyramidal Ref. , will be subject to future work.
At the present stage we feel that the question of which gain to be expected in an ELT by going from two to three DM’s is not
quite clear Ref. . Even the benefits from two DM correction have not yet been experimentally verified. Since
implementing an extra DM may call for significant changes in the optical design due to the fact that the optimal conjugation
altitude for DM2 will change, we have not modified the design to accommodate a DM3.
Related to the above issue we will carry out an experiment on a down-scaled version of a seven layer model of the
atmosphere documenting the expected benefits from MCAO. The experiment will address the subject of optimal use of the
wavefronts sensed by guide stars, for correction of a certain science field. The layers will be implemented as fixed phase
screens and there will be two (slow) DM’s for correction. One wavefront sensor focussed on the pupil will be adequate.
The authors would like to thank Ralf Flicker and Torben Andersen for valuable discussions.
1. P.H. Christensen and T. Andersen, “ Is There an Upper Limit to the Size of Enclosures,” in Telescope Structures,
Enclosures and Controls vol. 4004, SPIE, March 2000, these proceedings.
2. J. Beckers, “Increasing the Size of the Isoplanatic Patch with Multiconjugate Adaptive optics,” Proc. ESO Conference
on Very Large Telescopes and their Instrumentation, no. 30, p. 693, 1988, Garching.
3. J. Beckers, “Detailed Compensation of Atmospheric Seeing Using Multi-Conjugate Adaptive Optics,” in Proc. SPIE
vol. 1114, p. 215,1989.
4. J. Beckers, “Adaptive Optics for Astronomy,” in Annual Reviews of Astronomy and Astrophysics, vol. 31, 1993.
5. T. Fusco, J.-M. Conan,V, Micheau, L. M. Mugnier, and G. Rousset, “Phase Estimation for Large Field of View:
Application to Multiconjugate Adaptive Optics,” in Propagation and Imaging through the Atmosphere III, vol. 3762
6. T. Andersen, A. Ardeberg, J. Beckers, R. Flicker, A. Gontcharov, N. Christian, E. Mannery, M. Owner-Petersen and H.
Riewaldt, “The Proposed 50 m Swedish Extremely Large Telescope,” in Proc. of the Bäckaskog Workshop on
Extremely Large Telescopes, Sweden, pp. 72-82, June 1999.
7. J.W. Hardy, “Optical Configuration for Turbulence Compensation,” in Adaptive Optics for Astronomical Telescopes,
Oxford Series in Optical and Imaging Sciences 1998.
8. J. Vernin, A. Agabi, R. Avila, M. Azouit, R. Conan, F. Martin, E. Masciadri, L. Sanchez, and A. Ziad, “Gemini CP
Site Characterization Report,” in Internal Report RPT-AO-G00094, Gemini Observatory, January 2000.
9. J.W. Hardy, “Wavefront Fitting Error,” in Adaptive Optics for Astronomical Telescopes, Oxford Series in Optical and
Imaging Sciences 1998.
10. J. Nelson and Terry Mast “Giant Optical Devices,” in Proc. of the Bäckaskog Workshop on Extremely Large
Telescopes, Sweden, pp. 1-11, June 1999.
11. R. N. Wilson, “How Far Can One Go with Active Monoliths and What Are the Parameter Choices,” in Proc. of the
Bäckaskog Workshop on Extremely Large Telescopes, Sweden, pp. 139-143, June 1999.
12. T. Andersen, A. Ardeberg, A. Gontcharov and M. Owner-Petersen, “Future Large Ground-Based Telescopes,” in press
13. R. Ragazzoni, “No Laser Guide Stars for Adaptive Optics in Giant Telescopes?” in Astronomy and Astrophysics Suppl.
Ser. 136, pp. 205-209, 1999.
14. R. Ragazzoni, E. Marchetti, and G. Valente, ”Adaptive-optics corrections available for the whole sky,” Nature 403,
pp.54-56, January 2000.
15. R. Flicker, F.J. Rigaut and B. L. Ellerbroek, “ Comparison of Multiconjugate Adaptive Optics Configuration and
Control Algorithms for Gemini-South 8-m Telescope,” in Adaptive Optical Systems Technology, vol. 4007, SPIE,
16. P. Dierickx, J. Beletic, B. Delabre, M. Ferrari, R. Gilmozzi, N. Hubin, “The Optics of the OWL 100-m Adaptive
Telescope,” in Proc. of the Bäckaskog Workshop on Extremely Large Telescopes, Sweden, pp. 97-108 June 1999.
17. R. Ragazzoni, “Pupil Plane Wavefront Sensing with an Oscillating Prism,” in Journal of Modern Optics, vol. 43, no. 2,
pp. 289-293, 1996.
18. B. L. Ellerbroek and F.J. Rigaut, “Scaling Multi-Conjugate Adaptive Optics Performance Estimates to Extremely
Large Telescopes,” in Adaptive Optical Systems Technology, vol. 4007, SPIE, March 2000.