The opto-mechanical performance prediction of thin mirror segments
for E-ELT.
Jan Nijenhuis, Roger Hamelinck, Ben Braam, TNO Technical Science, Stieltjesweg 1, 2623 CK
Delft, The Netherlands.
ABSTRACT
The mirror segments for the E-ELT and TLT are nearly equal in size and shape (hexagonal, 1.2 m over flat sides). They
are very thin (about 50 mm) compared to their size. Supporting these mirrors and obtaining high optical performance is a
challenge from design and manufacturing point of view. TNO has designed and build (together with VDL-ETG) three
identical prototypes for supporting the mirror segments of the E-ELT. These mirror segments vary in size. Hence the
gravity induced deformation of the mirror segments will vary from mirror to mirror segment when no measures are
taken. The paper will concentrate on the design and analysis of the design features within the support structure to
minimize the mirror deformation due to gravity. These features concern passive and active means to influence the mirror
segment shape and to compensate for deformation differences.
Keywords: Opto-mechanics, Warping harness, adaptive optics, ELT, M1 support structure.
1. INTRODUCTION
The E-ELT is going to be the biggest ground based optical telescope in the world in the coming decades. It will have a
primary mirror of 39m (hexagonal shape) which consists of 798 hexagonal shaped segments (figure 1) with a nominal
width of 1.2m. The mirror will get a parabolic shape which causes that the individual mirror plan shape will slightly
deviate from the perfect hexagon.
The support structure for each segment will be identical for economic
reasons. Inevitably this will result in mirror deformations due to gravity that
will be different for each segment. Therefore compensation is needed to
minimize the deformation differences. In principle two options exist being
active and passive compensation. Both have their (dis)advantages and both
will be applied. The clear benefit of passive compensation is that it does not
need for electronics, sensors, control etc.
Other sources of static surface form deformations are e.g. manufacturing
errors and tolerances of the support structure or the manufacturing errors
that are made during manufacturing of the mirror segment. Although the
mirror segments will be polished in assembly, still some error will remain
that can be compensated for. All these kind of surface form deformation can
be compensated by static means. However because they are not known by
design they have to be compensated by so called warping harnesses which is
a form of active surface control.
Furthermore error sources exist which are related to temperature or the wind
speed. These have a dynamic nature and are therefore not predictable and
have to be compensated after measurement by active means.
2. DESIGN DESCRIPTION SEGMENT SUPPORT STRUCTURE.
A short description of the segment support structure is given below. Only those elements of this structure are described
that are needed to understand this paper. Additional information can be found in [1] and [2].
figure 1: Segmentation of mirror M1.
Modern Technologies in Space- and Ground-based Telescopes and Instrumentation II,
edited by Ramón Navarro, Colin R. Cunningham, Eric Prieto, Proc. of SPIE Vol. 8450, 84500A
© 2012 SPIE · CCC code: 0277-786X/12/$18 · doi: 10.1117/12.926263
Proc. of SPIE Vol. 8450 84500A-1
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2.1 The axial mirror segment support
Each mirror segment is axially supported at 27 support points. These points are grouped into 9 tripods with three support
points each. Three tripods are again supported by the Top Level Tripod. Together they form a whiffletree. This is
illustrated in figure 2. Such support structure is statically determined which means that the support reaction loads depend
only on the whiffletree geometry. The same statement applies to the loads of the segment support struts and the struts
connecting the various tripods. The stiffness of the tripods do not influence these loads as long as their deformations are
negligible compared to their geometry. The three upper tripods of each whiffletree carry loads of about one third of the
lower tripod. Therefore they are also smaller causing that they have much lower mass as the lower tripod.
The 27 support points have been selected by ESO such that the gravity induced deformation has been minimized for the
average segment shape. The three support points provide three parallel reaction loads normal to the segment surface
thereby constraining three Degrees Of Freedom (DOF) of the mirror segment. These are piston and tip/tilt.
figure 2: The whiffletree support structure of a mirror
segment
figure 3: Lateral support of the a mirror segment.
2.2 The lateral mirror segment support
To control the other three DOF of the mirror segment as well (translation in X- and Y-direction together with rotation
around the Z-axis) a membrane is installed in a pocket in the center of the segment (
figure 4). The membrane center is
fixed to the moving frame that acts as “fixed world”. To enhance its torsion load capability a clocking strut is added at
the edge of the segment (
figure 3). The other end is connected to the intermediate solid body called moving frame which
itself is fixed to “ground”. Further details can e.g. be found in [1].
2.3 Lateral support for the whiffletree tripods.
Tilting the telescope will cause that the gravity induced loads of the tripods can be decomposed into components parallel
and normal to the segment surface (
figure 5). By providing lateral struts for the tripods this lateral load is transferred to
the moving frame. The figure also illustrates that the center of gravity of each tripod should coincide with the plane that
is defined by the lateral support struts. This way no gravity induced bending moments to the segment are created.
figure 5: Lateral support for whiffletree tripods.
figure 4: Segment membrane.
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3. GRAVITY INDUCED MIRROR DEFORMATIONS AND COMPENSATION
A common way to describe surface form deviation is by use of Zernike coefficients. This allows decomposing the
surface from deformation into individual deformation shapes that can be linked to the mechanical support structure.
Hence it can be used to optimize the mechanical structure [2]. Piston and tip/tilt are the first Zernike modes and usually
the biggest. These are not important for the mirror deformation because they concern rigid body modes that are
compensated using the three actuators that support each mirror segment. Higher order deformations like focus,
astigmatism, coma etc. are important because these represent actual mirror segment deformations. These can be
compensated for by applying moments to the tripods. This will cause out of plane deformations of the mirror segment.
There are two option to apply the moments i.e. either by applying a direct torque or by applying a force at certain
distance from the tripod.
The way to calculate the best possible surface form compensation is by calculating the deformation caused by individual
unit moments applied to the tripod. Because each whiffletree has four tripods this results in eight influence function per
whiffletree (
figure 6). Hence a total of 3x8=24 influence functions result. In figure 7 the influence functions are presented
for one of the whiffletrees. The influence functions for the other two whiffletrees are identical but 120° and 240° rotated.
From
figure 7 it becomes clear that moments 2 and 20 cause a deformation pattern that is dominated by focus. For
moments 1, 7, 9 and 20 this is astigmatism. For each subset of the 24
moments the best fit of the actual deformation is obtained with a linear
combination of the influence functions. A set of moments results for each
subset and always a small residual error remains.
One option to correct for focus error has not been mentioned yet. It was found that a mass mounted at the center of the
segment is very efficient in compensation for focus error i.e. with less mass the same focus compensating effect can be
achieved.
4. MINIMIZING GRAVITY INDUCED DEFORMATION WITH PASSIVE MEANS.
Segment deformation will be dominated by gravity because of the small thickness of the segment (50mm) compared to
its hexagonal shape of 1.4m (corner to corner).. It was required by ESO that this segment deformation should be limited
to 30 nm rms. Only passive means were allowed to realize this. The reason for this requirement is that the telescope will
have good optical performance without having to use the active compensation system. During the commissioning phase
of the telescope this may prove to be a valuable feature.
The segment deformation decreases when the telescope rotates from zenith to the horizon. Calculating the mirror
segment deformation due to gravity and analyzing the results reveals that the segment deformation is dominated by focus
and astigmatism. This can be understood when one realizes that the corners of the hexagon have the tendency to hang
down (center goes up) when the mirror is bigger than the average (inner mirror segments). The opposite happens for the
figure 6: Moments applied to the tripods.
figure 7: The influence function of one of the three whiffletrees.
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outer mirrors segments because these are relatively small. Clearly this can be recognized as a focus error. Astigmatism
occurs because radial and tangential oriented bending of the mirror segment is in general not equal.
From
figure 7 it can be concluded that focus is best compensated by applying moments at input locations 2, 4 and 6
(figure 6). Moments 20, 22 and 24 can do the same but are less efficient because moments 2, 4 and 6 act on all four small
tripods of the whiffletree while moments 20, 22 and 24 are only applied to one small tripod. Note that the indicated
moments not only compensate for mirror segment focus error but also cause higher order deformations. Fortunately the
higher order deformations are much smaller in magnitude than the focus error and therefore the total wavefront error of
the mirror segment is still reduced.
Astigmatism can be compensated for by applying moment 1, 3 and 5 acc.
figure 6. Also moments 7, 9, 11, 13, 15, 17, 19,
21 and 23 can do this but less efficient. Again this is caused by the fact that these moments act on one small tripod only.
Using balance masses
will cause moments to the
tripods. Furthermore this moment will be
dependent on the gravity direction. This is
illustrated in
figure 8. By putting the mass
balance either at the LH- or RH-side of the
symmetry line any moment up to 2.M.L can be
created (M=mass, L=moment arm). The gravity
vectors of the mass balance can be decomposed
into components normal and parallel to the
segment surface. Only the normal component
causes a segment bending moment. This way the
reduction of the balance moment due to mirror
segment tilting is equal to the reduction in
gravity induced deformation of the mirror.
Alternatively springs can be used to create the
required balance moments. However this is not
angle dependent which is why mass balancing is
preferred.
Focus compensation is obtained by mounting the balance masses in the radial direction to the tripod thereby creating
bending moments parallel to vector 2, 4 and 6. Focus compensation is shown in
figure 9. From the figure it can be
concluded that it is more difficult to create the required moment because the required location of the balance mass is
sometimes obstructed by the tripod itself. The alternative is to mount variable balance masses at a fixed position. From
an economical and logistical point of view this is not attractive although the total mass that has to be added is minimized
provided the moment arm is as long as possible.
figure 10: Combination of focus and astigmatism
correction.
figure 9: Mass balance to compensate for focus.
figure 8: Application of mass balance to compensate for astigmatism.
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Focus and astigmatism compensation can also be combined (figure 10). This will minimize the total mass for balancing.
However it is not always possible to combine the two because the balance mass would be needed where one of the arms
of the tripod is located. This option has therefore not been selected.
Another source for mass balancing is the tripod itself. Its COG (center of gravity) is located in-plane with its lateral
support (
figure 5). By giving it an offset in the radial direction it is possible to create a bending moment that helps
minimizing the required additional balance mass for focus correction. Furthermore it proved to be possible to locate the
balance mass always to the same side of the tripod (LH-side in
figure 9). As mentioned before it proved to be more mass
efficient to use a centrally mounted balance mass instead of separate balance masses attached to the three tripods.
Shifting the COG of the tripods in the tangential direction is not possible because it breaks the symmetry in the design.
For each segment there is a mirror imaged one meaning that also the support structure should be mirror imaged which is
not allowed. The idea is to build one identical support structure for all mirror segments.
Surface form deformation after correction for focus and astigmatism.
For three segments the remaining surface form error after passive compensation has been calculated. These segments are
located at the inner edge of the M1-mirror, the middle ring and the outer edge. The results clearly demonstrate that the
passive compensation can be very effective and that the requirement of 30 nm rms can be met.
5. ACTIVE COMPENSATION FOR GRAVITY DEFORMATION
Not all surface form errors can be compensated by passive means because they are not predictable. In the introduction
already several causes were mentioned. E.g. manufacturing errors due to polishing and manufacturing tolerances of the
structure. The latter will cause elastic deformation of the structure which in turn causes small bending moment that will
disturb the ideal surface form. These error sources have to be compensated by active means. This requires that the actual
surface form of the M1 mirror has to be measured at regular intervals. Based on that result it has to be calculated which
moments have to be applied to the tripods. ESO specified that simultaneously 600nm PTV focus, 1200nm PTV
Astigmatism and 300nm PTV trefoil can be reduced by factors 7, 18 and 6 respectively. It has been evaluated for many
subsets of the 24 possible moments which one could realize the required performance improvement for the minimal
number of compensating bending moment. These moment will be applied using so called warping harnesses and it was
found that warping harnesses are needed at position 1-6, 9, 13 and 17 (
figure 6). Alternatively bending moment to the
outer tripods 7, 11 and 15 can also be applied instead because of the symmetry in the mirror segment. The predicted
surface form improvement is given in
table 1. From the table it can be concluded that a small amount of coma can be
compensated too by use of the warping harnesses.
figure 11: Surface form errors after correction.
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