For polishing the ultra-thin TMT M3MP, a polishing support system with 18 hydraulic supports (HS) is introduced. This work focuses on the designing and testing of these HSs. Firstly the design concept of HS system is discussed; then mechanical implementation of the HS structure is carried out, with special consideration of fluid cycling, work pressurization and the weight component. Afterward the piping installation and the de-gas process for the working fluid are implemented. Pressurization and stiffness are well checked before system integration for the single HS unit. Finally the support system is integrated for the polishing process

Cole, Glen

Ford, Virginia

Hu, Haifei

Hu, Haixiang

Luo, Xiao

Qi, Erhui

Zhang, Xuejun

Caltech Authors - Main

Hydraulic supports for polishing TMT M3MP 
Haifei Hu*a, Erhui Qia, Glen Coleb, Haixiang Hua, c, Xiao Luoa, Virginia Fordb, Xuejun Zhanga 
aChangchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, 
Changchun 130033, Jilin, China 
bThirty Meter Telescope Observatory Corporation, Pasadena, CA 91105, USA 
cUniversity of Chinese Academy of Sciences, Beijing 100049, China 
ABSTRACT 
For polishing the ultra-thin TMT M3MP, a polishing support system with 18 hydraulic supports (HS) is introduced. This 
work focuses on the designing and testing of these HSs. Firstly the design concept of HS system is discussed; then 
mechanical implementation of the HS structure is carried out, with special consideration of fluid cycling, work 
pressurization and the weight component. Afterward the piping installation and the de-gas process for the working fluid 
are implemented. Pressurization and stiffness are well checked before system integration for the single HS unit. Finally 
the support system is integrated for the polishing process. 
Keywords: Ultra-thin mirror, hydraulic support, de-gas process, pressurization, stiffness 
1. INTRODUCTION
TMT is one of the world’s largest telescopes and has attracted staff from over five countries to join in. CIOMP has been 
involved in TMT project since 2012, and is responsible to fabricate the tertiary mirror system, keeping the mirror 
surface’s root mean square of slope values (SlopeRMS) bellow 0.89 micro-radians (μrad).1 The M3 Mirror (M3M) is 
made of Zerodur and is an elliptical flat mirror with dimensions 3594×2536×100 mm3 having an aspect ratio of 35. The 
required SlopeRMS is rather hard to obtain. In addition, the requirement for the SlopeRMS value was assumed to apply 
with the mirror set upon its axial support system facing upwards in a 1 gravity environment, so that support print-through 
is polished out. For feasibility study and reducing the risk, a prototype (M3P) scaled by 25% has been fabricated. 
For fabricating large mirrors, people usually use a polishing support system, different from the structural support system, 
to restrain the magnitude of “Print-through effect” and gravity off-loading deflection.2-6 For the prototype mirror (M3P), 
a custom polishing support to achieve polishing out print-through was developed and used. 
2. CONCEPTUAL DESIGN
1.1. Scaling mirror dimensions 
This thin mirror’s deflection could be roughly decided by analytical solution from theory of thin plates. According to 
Timoshenko’s theory, for circular plate with clamped edges and bearing uniform load, the maximum deflection is at the 
center of the plate and could be expressed as 7 
D
qaw 64
4
= , (1)
where w is the deflection, q is the uniform load, a is the radius of the circular plate, and D is the Flexural rigidity. D 
could be expressed as ( )2
3
112 v
EhD −= , where E is Young’s modulus, v is Poisson’s ratio and h is the plate thickness.
When the mirror is loaded by gravity, q=ρgh, where ρ is the material density and g is the gravity acceleration. So 
equation (1) could be rewritten as 
* E-mail: huhf@ciomp.ac.cn, Tel: +86 431 8670 8687
AOMATT 2016: Large Mirrors and Telescopes, edited by Myung Kyu Cho, Bin Fan, Proc. of SPIE Vol. 9682,
968208 · © 2016 SPIE · CCC code: 0277-786X/16/$18 · doi: 10.1117/12.2245642
Proc. of SPIE Vol. 9682  968208-1
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X.26 6 2667 Ú c 246
( )
2
42
16
13
Eh
gavw ρ−= . (2)
And the corresponding slope could be derived by ( )
2
32
4
13
Eh
gav
a
ws ρ−=∂
∂= . (3)
It’s seen from equation (3), for keeping s almost the same, if the aperture a is scaled by 1/4, the thickness h should be 
scaled by 1/8. As M3’s dimensions are a=3594 mm, b=2536 mm and h=100 mm, the prototype’s dimensions are scaled 
to a′=898.5 mm, b′=634 mm and h′=12.5 mm respectively.  
For deciding the number of support points N needed to limit the mirror surface deflection between discrete supports to 
some tolerable value δ, there’s a simplified equation in SI unit system written as following8 
δ
ρ
E
g
h
LN 8
3 2= , (4) 
where N is the minimum number of support points, L stands for the largest dimension of the aperture; other parameters 
are as previously defined. For M3P, L= a′=898.5 mm, h= h′=12.5 mm, ρ=2.53e-9 t/mm3, E=9.03e4 MPa, δ=6.33e-5 mm, 
the corresponding N could be calculated as N=51. For whiffle-tree implementation, a number of 54 for N is chosen. 
1.2. Layout optimization 
The FEA model of M3P for the polishing support system is shown in Fig 1. Due to symmetry, a quadrant of the mirror 
was developed, and a polishing pressure of 1 kPa, whose total action force is assumed to be equally born by the 18 
polishing supports, is applied to the reflecting surface. In the model, there are 19 hard points, shown in green triangles, 
which include 14 points representing polishing support points and the remaining 5 points representing mirror axial 
support points. When polishing the mirror, the polishing supports rise to contact the back side of the mirror for balancing 
polishing pressure.  The gravity sag of the glass between the axial supports is maintained. Symmetric displacement 
conditions are applied to the nodes located on axes. And the node centered on the ellipse is restrained in Z direction for 
FE solution consideration. For updating the moving boundary conditions, one just needs to change the location of these 
hard points. 
Fig 1 Conceptional model for M3MP polishing support 
Essentially here layout optimization of mirror supports mainly refers to a reverse problem for finding locations where 
forced boundary conditions should be imposed to minimize the deflection of the surface. Layout optimization model of n 
supports could be described as 
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400
300
200
E 100
E
>
E, 0
dá -100
-200
-300
Z Displacement of TMT_M3 Prototype(PV= 87nm,RMS =13nm)
-400
-500 -400 -300 -200 -100 0 100 200 300 400 500
Aperture X /mm
x 10
-5
400
300
200
E 100
E
d 0
-100
-200
-300
Slope of TMT_M3 Prototype(SlopeRMS= 0.77prad)
-400
-500 -400 -300 -200 -100 0 100 200 300 400 500
Aperture X /mm
2.5
1.5
0.5
( )
( )
G
Find            , ,  1,  2,  ,  
Minimize    RMS(d ), 1,  2,  ,  
         and  SlopeRMS(d )
Subject to    ,
         and  ,  
i i i
k
k
i i
i j
P x y i n
z k N
z
P x y
PP D i j
=
=
∈Ω
> ≠
K
K
, (5) 
where Pi(xi, yi) represents the location of support i, dzk is the difference between the actual position and the ideal position 
of grid k, NG is the number of surface grids, Ω is the aperture of the mirror, and |PiPj|>D implies the fact that the distance 
between two supports should be larger than a certain distance of D, e.g., the largest diameter of the support structure. 
The PV and RMS are calculated by Zernike polynomials fitting, and SlopeRMS is calculated using equation: 
( ) ( )
2 21 1
1, , , 1 ,
1 1
1SlopeRMS
1 1 d d
N M
i j i j i j i j
i j
S S S S
N M x y
− − + +
= =
⎡ ⎤⎛ ⎞ − −⎛ ⎞ ⎛ ⎞= +⎢ ⎥⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟− − ⎢ ⎥⎝ ⎠ ⎝ ⎠⎝ ⎠ ⎣ ⎦
∑∑ , (6)
where N is the number of sample grids in x direction, M is the number of sample grids in y direction, Sij is the figure 
difference of grid (i, j), dx and dy are the sample distances.  
Optimized indexes δPV, δRMS and δSlopeRMS are shown in Tab 1. From Tab 1, it’s seen that through layout optimization of 
support points, δPV is reduced from to 1756 nm to 80.6 nm, scaled by 4.6%; δRMS is reduced from to 417 nm to 12.7 nm, 
scaled by 3.0%; δSlopeRMS is reduced from to 4.56 μrad to 0.71 μrad, scaled by 15.6%. The optimized δRMS is about λ/50, 
and the optimized δSlopeRMS is within allowed 0.8 μrad. 
Tab 1 Results summary of initial scheme and optimized scheme 
Initial layout Optimized layout 
δPV /nm δRMS /nm δSlopeRMS /μrad δPV /nm δRMS /nm δSlopeRMS /μrad 
1756 417 4.56 80.6 12.7 0.71 
The distribution of surface grids’ displacements and slopes are shown in Fig 2. 
(a) Displacement distribution of optimized scheme (b) Slope distribution of optimized scheme
Fig 2 Figure accuracy comparison of initial scheme and optimized scheme 
From Fig 2 it’s seen that the optimized layout makes the mirror’s deformation much more uniform and makes the 
magnitude of displacements much smaller. Layout optimization brings a significant improvement for the mirror’s rigidity. 
Proc. of SPIE Vol. 9682  968208-3
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cover
diaphragm holder
axial limit board
ut pipe
A
TA
®
.
Q
o
The impleme
hydraulic uni
3.1. Design o
The mechani
system is also
6 equal-force
mirror’s rear 
For each sing
linked to a sp
pipe forms a 
the floating c
bolt acts as th
the manufact
modulus. 
Fig 3 M
(2) Stiffn
(a) 
Stiffness test
testing, show
force F and t
straight enoug
was tested lea
To achieve h
ntation of the
t; (2) stiffness
f the support
cal implemen
 illustrated. T
 hydraulic su
side. The 3 pa
le hydraulic 
here valve. So
narrow space
omponents. A
e lateral limi
uring support
echanical impl
ess test of th
Cross-section
s of the hydr
n in Fig 4(b)
he correspond
h, we use k=
st 3 times to 
igher support
 hydraulic su
 test of the un
 system and 
tation for the
here are 54 h
pports. Each
ds are design
support unit, 
 it could be s
 for the work 
 plastic seal 
t when not w
 system. The
(a) 2D view
ementation for
e units 
 of the suppo
Fig 4 Mechanic
aulic support
. We load the
ing displacem
dF/du for a s
improve the te
 stiffness, the
pport are div
its; and (3) th
the single hy
 manufacturin
ydraulic polis
 hydraulic su
ed to average
the mechanic
een that the i
fluid to fill in
cushion faste
orking, so it 
 fluid used fo
 manufacturing
rt  
al design and s
s were perfor
 support tow
ent u of the
pecific region
st accuracy.
 volume of a
ided into 3 s
e system inte
draulic unit
g support sy
hing support
pport contro
 the force of e
al design is s
nput pipe, the
. The lateral
ned by the se
could holding
r working fl
 TMTM3P, 54
(b) Stiffne
tiffness test of 
med using a
ard 200 N, a
 support; and
. Most F-u c
ir bubbles mu
teps: (1) desi
gration. 
stem is illust
s divided into
ls a load spr
ach hydraulic
hown in Fig 4
 static piston,
limit board p
al bolt produ
 the mirror at
ow is glyceri
(b) 
 support points
ss testf
a single hydrau
 Chinese Nat
pproximating
 compute the 
urves are ver
st be minimi
gn of the sup
rated in Fig 3
 3 groups, eac
eader that lin
 support. 
 (a). The inp
 the diaphrag
rovides a free
ces a good p
 a high preci
n, as it is vis
3D view
for polishing a
  (c
lic support uni
ional Standar
 the polishing
stiffness k by
y close to line
zed, so a buff
port system a
, where the l
h of which is
ks 3 pads at
ut and the ou
m, the cover 
 motion of ab
ressurization.
sion after the 
cous and .ha
nd 18 points fo
)Air buffer bo
t 
d Machine fo
 load of 20 k
 k=F/u. If th
ar. Each hyd
er bottle is u
nd the single
ateral suppor
 supported by
tached on the
tput pipes are
and the outpu
out 8 mm fo
 Also the sea
integration o
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ttle 
r mechanica
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e curve is no
raulic suppor
sed, shown in
 
t 
 
 
 
t 
r 
l 
f 
 
l 
 
t 
t 
 
3. MECHANICAL IMPLEMENTATION
Proc. of SPIE Vol. 9682  968208-4
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1LU
Force sensor
V_D6 Glycerin
bottle
 
Fig 4 (c). Most of the air bubbles that are formed during piping will stored in this bottle, which contributes a volume of 
purer glycerin to the support. 
  
 
Fig 5 Piping cycle for testing the stiffness 
Piping cycle for testing the support unit’s stiffness is shown in Fig 5. During the test, we found that the pipe length 
affects the stiffness significantly, so in the piping cycle the length expressed by L, of the input pipe was changed to 
equalize all stiffness values of the supports. 
The stiffness values at certain input pipe length for the used 18 supports are listed in Tab 2 in ascending order. The 
minimum stiffness is 800 N/mm for the support numbered 20, and the maximum is 1188 N/mm for the support 
numbered 11.  
Tab 2 Stiffness summary of the 18 supports used 
Rank No. SP No L(cm) S(N/mm) 
1 20 77 800 
2 1 60 804 
3 12 56 807 
4 5 120 821 
5 8 70 826 
6 7 60 837 
7 4 60 850 
8 2 60 881 
9 14 60 893 
10 13 85 896 
11 17 60 906 
12 6 60 921 
13 10 60 974 
14 9 60 1027 
15 16 63 1071 
16 15 70 1092 
17 18 72 1135 
18 11 60 1188 
3.2. Hydraulic system integration 
According to their stiffness, all 18 supports are integrated into 3 groups, surrounded by 3 bold dark curves shown in Fig 
6(a). Group division is also shown in Tab 2 by different color. In detail, the support tick numbers for group 1 are 12, 7, 8, 
2, 14 and 6; the support tick numbers for group 2 are 1, 20, 5, 4, 13 and 17; the support tick numbers for group 3 are 16, 
9, 10, 11, 15 and 18. 
Proc. of SPIE Vol. 9682  968208-5
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/
o
 
Support perfo
springs with 
SlopeRMS, w
those stiffnes
The proposed
print-through
2.6μrad, whic
the space betw
powder, mate
contribute to 
to the require
But it is inten
will unburden
This work is 
program No.2
[1] TMT Gro
[2] Smith, W
[3] Martin, H
Binocula
[4] Schipani
773931 (
[5] Kaercher
77332O 
[6] Martin, H
Proc. of S
[7] Timoshe
Singapor
[8] Yoder, P
rmance evalu
the tested st
ith a mean o
s difference, d
 support sch
 is about 0.71
h is not as go
een the mirr
rial removal 
the mirror’s s
d precision.  
ded that furth
 the processin
financially s
011CB01320
up, “Tertiary
S, “Manufac
M, Allena, R
r Telescope,”
, P, Capacciol
2010). 
, HJ, Eisentra
(2010). 
M, Callahan
PIE 3352, 41
nko, S and W
e, 55 (1959). 
R, [Opto-Mec
(a) Group d
Fig 
ation is carr
iffness suppo
f 2.6 μrad/kP
uring operati
eme is obtain
 μrad, lower 
od as design
or and the po
rate could sti
urface figure
er measures s
g algorithm m
upported by 
5. 
 Mirror Surfa
turing and Te
G, Cuerdena
 Proc. of SPIE
i, M, `Orsi, S
eger, P and S
, SP, Cuerden
2-423 (1998)
oinowsky-Kri
hanical Syste
ivision 
6 System integ
ied out after 
rting the mi
a. This differ
on all input v
4. C
ed through la
than allowed 
ed, it’s very n
lishing pad is
ll be kept hig
 accuracy, so 
hould be take
uch. 
ACKN
Natural Scien
R
ce Figure Spe
sting an 8.3 m
, B, et al. “Ma
 6273, 62730
 D, et al, “The
üß, M, “Mech
, B, et al, “Ac
. 
eger, S, [The
ms Design], S
  
  
ration and perf
system integr
rror, and the
ence is mainl
alves are open
ONCLUSIO
yout optimiz
0.8 μrad. Wh
ecessary to o
 larger than 1
h enough. A
the polishing
n to get close
OWLEDGE
ce Foundatio
EFERENCE
cification,” T
eter Astronom
nufacture of t
C (2006). 
 VST active 
anical princip
tive supports 
ory of plates a
PIE Press, B
   (b) Perform
ormance evalua
ation, as sho
 polishing pr
y caused by 
ed within a g
NS 
ation of supp
ereas the perf
pen all input 
0 μm, which 
lso only the 
 support syste
r stiffness for
MENT 
n of China N
S 
MT.OPT.SPE
ical Mirror,”
he second 8.4
primary mirro
les of large m
and force opt
nd shells], M
ellingham, 50
ance of real 
tion 
wn in Fig 6(
essure is 2 
the difference
roup to get cl
ort points. Th
ormance of t
valves to get 
is usually the 
testing suppo
m serves we
 M3M becaus
o.61210015 
.12.001.CCR
 Proc. of SPI
 m primary m
r support sys
irror support
imization for 
cGraw-Hill B
5 (2006). 
support 
b). The FE m
kPa, resulting
 of stiffness.
oser stiffness
e designed S
he real stiffne
closer stiffne
minimum siz
rt and the fab
ll till the mirr
e uniform su
and Chinese 
01, 12 (2014
E 3782, 157-
irror for the L
tem,” Proc. of
s,” Proc. of S
the MMT pri
ook Compan
 
odel uses 18
 in 5.2 μrad
 To overcome
. 
lopeRMS fo
ss is worse to
ss. Actually i
e of polishing
rication erro
or is polished
pport stiffnes
National 973
). 
168 (1999). 
arge 
 SPIE 7739, 
PIE 7733, 
mary mirror,”
y Inc., 
 
 
 
r 
 
f 
 
r 
 
s 
 
 
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Hydraulic supports for polishing TMT M3MP

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Hydraulic supports for polishing TMT M3MP

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