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Journal of the Korean Physical Society, Vol. 59, No. 6, December 2011, pp. 3356∼3362
Athermal Lens Mount with Ring Flexures
Hagyong Kihm,∗Ho-Soon Yang and Yun-Woo Lee
Center for Space Optics, Korea Research Institute of Standards and Science, Daejeon 305-340, Korea
(Received 12 October 2011)
We present a new athermal lens mounting scheme made of cascaded ring flexures. Two circular
grooves are concentric at the adhesive injection hole and are fabricated monolithically on the lens
cell or the barrel itself. The ring flexure can accommodate six-degree-of-freedom motions by con-
trolling dimensional parameters. We evaluate thermo-elastic deformations by using interferometric
measurements and verify the results with finite element analyses. Also, we compare the athermal
performances from a simple elastomeric mount and a ring-flexured mount. This lens mounting
scheme should be a promising candidate for environmentally-challenging optical systems like those
used in space and military applications.
PACS numbers: 42.15.Eq, 07.87.+v, 95.55.Fw
Keywords: Lens mount, Optomechanics, Flexure, Space optics
DOI: 10.3938/jkps.59.3356
I. INTRODUCTION
Precision lens systems under a large temperature vari-
ation require athermal mounting structures. The mount
should minimize thermo-elastic stresses and maintain the
axial/lateral alignment of a lens element. Athermal lens
mounting methods use flexures, elastomers, or their com-
binations [1]. The flexure mounting is a semi-kinematic
method constraining all motions without using any ad-
hesive. Kvamme and Jacoby used sophisticated flexures
as low-stress mounts for space-borne optics [2]. On the
other hand, the elastomeric mounting method adjusts
the thickness of a bondline filling the gap between a lens
and a cell. Theoretical derivations of the athermal bond-
line thickness have been used as design guidelines. Bayar
used a simple equation using CTE (coefficient of thermal
expansion) differences [3]. Muench derived an equation
using CTEs and Poisson’s ratio [1]. Herbert considered
nonlinear material properties, especially of the adhesive,
to derive an athermal equation [4]. These equations,
however, only consider radial stresses. Stresses in axial
or lateral directions can be evaluated using finite element
analyses (FEAs) [5,6]. Doyle et al. used a FEA to show
that discrete bondings are preferred for nearly incom-
pressible adhesives where Poisson’s ratio approaches 0.5
[7]. According to Miller, the thermo-elastic stress is rel-
atively insensitive to the adhesive thickness as the bond-
line becomes thicker [8]. However, a thick bondline is not
desirable for adhesive strength. Combining elastomers
and flexures can secure optics with a maximum adhesive
strength and minimize thermo-elastic stresses. For in-
∗E-mail: hkihm@kriss.re.kr
stance, Saggin et al. presented tangential edge flexures
with thermal adapters for a space-borne infrared optic
[9]. Froud et al. introduced radial flexures in cryogenic
mounts for large fused-silica lenses [10]. So far, most
lens mounting flexures have been made independent of
other lens mounts due to manufacturing difficulties. Ma-
chined flexures are assembled into a lens barrel, making
the whole system bulky and heavy. Also, the fabrication
cost is high due to the frequent use of electrical-discharge
machining.
In this paper, we present a new type of radial flex-
ure for an athermal lens mounting. Flexures are made
monolithically on a lens cell or a barrel itself. Two cir-
cular grooves are concentric at the adhesive injection
hole. They are implemented easily with a generic me-
chanical machining. Each flexure can accommodate six
degree-of-freedom (dof) motions by controlling dimen-
sional parameters. Stability and flexibility of the flex-
ure are compromised to meet the performance require-
ments. We used a FEA for optomechanical simulations
and verified optical performances of a batch of pilot sam-
ples by using a commercial optical interferometer. Opti-
cal displacements and birefringence induced by thermo-
elastic stresses were measured under temperature varia-
tions. Section II explains the design and the configura-
tion. Section III presents simulation results from a FEA.
Section IV shows the experimental results from interfer-
ometric measurements. Conclusions follow in Sec. V.
II. DESIGN AND CONFIGURATION
An elastomeric lens mounting is the simplest way of
athermalizing a lens element, and finding the optimum
-3356-
Athermal Lens Mount with Ring Flexures – Hagyong Kihm et al. -3357-
bondline thickness has been an issue especially in mili-
tary and space applications. Equation (1) is the so-called
Bayar’s equation, where αG,αM, and αeare the CTEs
of the lens, the mount, and the elastomer respectively
[3].
te Bayar =DG
2(αM−αG)
(αe−αM).(1)
Equation (2) includes the Poisson’s ratio νeand is
called the Muench equation [1].
te Muench =DG
2(1 −νe) (αM−αG)
[αe−αM−νe(αG−αe)].(2)
From these equations, athermal bondline thicknesses
are proportional to the lens diameter DG. For small
lenses, athermal bondlines are thin, comparable to
the recommended thickness for the maximum adhe-
sive strength. As the lens becomes larger, the ather-
mal bondline becomes thicker, which is not desirable
for the adhesive strength. Kihm et al. showed the
experimental results using a titanium cell (Ti6Al4V,
αM= 8.8×10−6/◦C) and an optical flat (SchottrSF6,
αG= 8.1×10−6/◦C) with a 3MrEC2216 adhesive
(αe= 102 ×10−6/◦C) [6]. The difference between αM
and αGis so small that the athermal bondline thick-
ness temainly depends on the lens diameter DG. If the
CTE difference between a cell and a lens is large, which
is the usual case using a metallic cell and a glass lens,
the athermal bondline is too thick to apply in real cases.
A flexured cell mount can overcome this limitation, and
the adhesive strength can be fully utilized with a recom-
mended adhesive thickness.
In this research, we used a set of pilot samples made of
aluminum cells (Al6061, αM= 23 ×10−6/◦C) and op-
tical flats (fused silica, αG= 0.52 ×10−6/◦C) for exper-
imental verification. Aluminum is the most commonly
used material for support structures. It has a low den-
sity with a high specific stiffness and good thermal, vac-
uum, and manufacturing properties. However, the CTE
is quite high compared with the glass materials’. Fused
silica is also a widely used optical material due to its good
optical quality and high availability. We prepared two
sets of pilot samples for comparison: one is configured as
a simple elastomeric mount, and the other is made with a
new flexure mount. Also, we used two kinds of adhesives
to compare their athermal performances: 3MrEC2216
[11] and HysolrEA9394 [12]. Both adhesives are used
frequently in space applications. 3M r
EC2216 B/A is
used for coupling optical elements with metallic mounts
[1,13,14]. Hysol r
EA9394 is used for fixing mechanical
structures like CFRP (carbon fiber-reinforced polymer)
[15, 16]. Their strengths are almost the same at room
temperature, but the CTEs and elastic moduli Eare
quite different. EA9394 (αe= 55.6×10−6/◦C, E = 4237
MPa) is more rigid even though its CTE is just half that
of EC2216’s (αe= 102 ×10−6/◦C, E = 978 MPa). Soft
adhesives are preferred for optical applications, but we
Fig. 1. Elastomeric lens mount: (a) section view and (b)
disassembled view
experimented with EA9394 to amplify the thermo-elastic
distortions of the elastomeric mounts.
Figure 1 shows the configuration of a pilot sample of
an elastomeric lens mount. An optical flat is used to rep-
resent a lens element. The optical flat is made of a fused
silica (Corning r
HPFS code 7980), and it is 50.8 mm
in diameter and 8 mm in thickness. The front and the
back surfaces are anti-reflection (AR) coated. They are
slightly wedged by a 30 arcmin to reduce unwanted inter-
ference effects caused by multiple reflections. Thermo-
elastic distortions and birefringence inside the optical flat
can be observed at once with a single interferometric
measurement. The bondline thickness is 0.2 mm, which
is the vendor’s recommendation for the maximum shear
strength. Even though the athermal bondline thickness
is 2.66 mm from Eq. (2), it is too thick to apply in actual
cases.
Figure 2 shows the ring-flexured lens mount configu-
ration. Six ring-flexures are made monolithically on a
lens cell. Two circular grooves are concentric at the ad-
hesive injection holes. The diameter of the central ring
is 8 mm, which is the thickness of the optical flat. The
ring and its annular space is 1.5 mm in thickness. Each
ring-flexure can accommodate six dof motions by adjust-
ing dimensional parameters. The stiffness of the flexure
should be sufficiently high to keep the optical element
from sagging, but also low enough to avoid deformation,
birefringence, and even breakage of the optic. The ring
flexures are sized to survive handling, transportation,
and launch loads. The bondline thickness is 0.2 mm as
in the elastomeric case. The next section discusses the
athermal performances of the elastomeric mount and the
ring-flexured mount from FEA results.
III. SIMULATION
We modeled four pilot samples in a FEA. They are
(a) an elastomeric mount with EC2216 adhesive, (b) a
ring-flexured mount with EC2216 adhesive, (c) an elas-
tomeric mount with EA9394 adhesive, and (d) a ring-
flexured mount with EA9394. An isothermal load with
-3358- Journal of the Korean Physical Society, Vol. 59, No. 6, December 2011
Fig. 2. Ring-flexured lens mount: (a) front view and (b)
disassembled view
unit temperature is applied as a load. Surface displace-
ments of the front and the back surfaces are recorded
and processed with Zernike polynomial fitting for qual-
itative analysis [17]. The birefringence effect inside the
optical flat is also considered using stress optic coeffi-
cients [18]. The mechanical properties of the adhesives
are nonlinear and hysteretic, depending on the temper-
ature [19], and their strengths change according to the
adherent materials [11,12]. Even though modelling the
nonlinear properties of adhesives is possible in a FEA,
the results are doubtful when compared with real exper-
imental results. In this paper, we apply a unit tempera-
ture load, assuming the adhesive properties to be linear
at the room temperature. Also, we use FEA results just
as a qualitative reference. Quantitative athermal per-
formances from experiments are presented in the next
section.
We used CATIArfor the FEA and MATLABrfor
the optical analysis with Zernike polynomials. The ad-
hesive pads were modelled using parabolic hexahedron
elements with at least 5 elements through the thickness
of the pads. Adaptive meshing is used to model the small
features and the critical regions of stress concentration.
The numbers of finite elements are about 8.1×105for
the elastomeric mount and 7.7×105for the ring-flexured
mount. The distributions of displacements and stresses
are interpolated over rectangular grids for pixelated sum-
mation through the optical axis.
Thermo-elastic stress induces surface distortions and
birefringence of a lens element. In our experiment, the
optical flat is AR-coated on both surfaces to measure dis-
tortions and birefringence simultaneously by transmis-
sive testing with an optical interferometer. The OPD
(optical path difference) for a single pass is then a sum-
mation of the thickness variation of an optical flat and
the birefringence effect, as expressed in
OP D =A−B+KSZσdt, (3)
where Aand Bare the front and the back surface dis-
placements. As the sign conventions of Band OP D are
opposite, the back surface distortion is −B.KSis the
Fig. 3. (Color online) Thermo-elastic deformation of the
optical flat (φ50.8 mm) with an elastomeric mount and the
adhesive EC2216 under unit temperature rise. Only the re-
sults from half the cross section are shown due to symmetry.
(a) Displacement Aof the front surface (nm), (b) displace-
ment Bof the back surface (nm), (c) Von Mises stress σ
(MPa), and (d) OPD due to the stress σinside the optical
flat
stress optic coefficient, which is 3.5×10−6mm2/N for
Corningrfused silica. The OPD due to the birefrin-
gence is obtained by integrating stresses over the beam
path, which is normal to the optical flat. Von Mises
stress σis used to calculate the birefringence [18].
Figure 3 shows an example of the FEA results from
an elastomeric mount with EC2216. Figure 3(a) is the
displacement Aof the front surface. Figure 3(b) is the
displacement Bof the back surface. Figures 3(c) and
(d) are the Von Mises stress inside the optical flat and its
OPD, respectively. Only the results from a half the cross-
section are shown due to symmetry. As the CTE of the
adhesive EC2216 is over two orders of magnitude higher
than the optical flat’s, the edges of the flat receive tensile
shear stresses upon temperature rise. The expansions of
the edges are shown in Figs. 3(a) and (b). Displacements
Aand Bdecay from the edges, but there are overshoots
at a radial position of −22 mm, where the thickness of
the optical flat becomes minimum. This is due to the
radial tensile stress from the elastomeric mount. Adhe-
sives filling the injection holes bulge out with increasing
temperature and causes additional stresses, as shown in
Fig. 3(c). In Fig. 3(d), significant thermo-elastic birefrin-
gence is observed up to −10 mm from the edge, affecting
60% of the optic’s aperture
The thermo-elastic deformation of the optical flat with
Athermal Lens Mount with Ring Flexures – Hagyong Kihm et al. -3359-
Fig. 4. (Color online) Thermo-elastic deformation of the
optical flat (φ50.8 mm) with a ring-flexure mount and the ad-
hesive EC2216 under unit temperature rise. Only the results
from half the cross section are shown due to symmetry. (a)
Displacement Aof the front surface (nm), (b) displacement
Bof the back surface (nm). (c) Von Mises stress σ(MPa),
and (d) OPD due to the stress σinside the optical flat
a ring-flexured mount and the adhesive EC2216 is shown
in Fig. 4. The edges receive tensile shear stress from
the adhesive pads and become thicker as in the previous
case, but the displacements Aand Bconverge to zero
monotonically with no overshoots being present in Fig. 3.
The CTE mismatch between the mount and the optic is
compensated for by radial motions of the ring-flexures,
resulting in fast settlements. The maximum Von Mises
stress in Fig. 4(c) is about half that in Fig. 3(c) and is
more localized at the adhesive interface. Stresses from
the adhesive filling an injection hole contribute mainly
to the birefringence effect. The OPD due to the stress in
Fig. 4(d) drops to zero, accordingly affecting only 20% of
the optic’s aperture. Compared with the results from the
elastomeric mount in Fig. 3, the clear aperture without
any birefringence distortion extends two times wider in
the radial direction.
The adhesive properties are nonlinear, depending on
the temperature. In a cryogenic temperature, Eof
EC2216 is almost three times more rigid than it is at
room temperature [11]. In this paper, we use EA9394
to represent a rigid adhesive at low temperature and to
amplify the comparative athermal advantage of a ring-
flexured mount over an elastomeric mount. Figs. 5 and
6 show the FEA results from an elastomeric mount and
a ring-flexured mount using the adhesive EA9394. Al-
though the CTE of EA9394 is half EC2216’s, the edge
Fig. 5. (Color online) Thermo-elastic deformation of the
optical flat (φ50.8 mm) with an elastomeric mount and the
adhesive EA9394 under unit temperature rise. Only the re-
sults from half the cross section are shown due to symmetry.
(a) Displacement Aof the front surface (nm), (b) displace-
ment Bof the back surface (nm), (c) Von Mises stress σ
(MPa), and (d) OPD due to the stress σinside the optical
flat
expansion of the optical flat, as shown in Fig. 5, which
is due to the CTE mismatch between the optic and the
adhesive, is almost 10 times larger than that when using
EC2216, as shown in Fig. 3. This result shows the adhe-
sive property Eis a more dominant property than CTE
for athermal performance. In Figs. 5(a) and (b), the
thickness of the optical flat is also minimum at −22 mm,
and its value is similar to that in Fig. 3. The maximum
Von Mises stress in Fig. 5(c) is almost two times higher
than that in Fig. 3(c). Considering Eof EA9394 is over
four times higher than Eof EC2216, the thermo-elastic
stress within the optic is not linear in the adhesive E.
The OPD from the birefringence in Fig. 5(d) decreases
up to −10 mm from the edge, which is similar to the re-
sult in Fig. 3(d) except the peak value. We can conclude
from this result that the size of the aperture free from
thermo-elastic birefringence does not change significantly
with the adhesive property.
Figure 6 shows the thermo-elastic deformation of the
optical flat with a ring-flexure mount and the adhesive
EA9394 under unit temperature rise. Displacements at
the edges in Figs. 6(a) and (b) are smaller than those in
Figs. 5(a) and (b). Adhesive shear stress is a dominant
factor affecting surface displacement at the edge. These
results prove the fact that soft adhesives are preferred
for less thermo-elastic deformation at the adhesive inter-
-3360- Journal of the Korean Physical Society, Vol. 59, No. 6, December 2011
Fig. 6. (Color online) Thermo-elastic deformation of the
optical flat (φ50.8 mm) with a ring-flexure mount and the ad-
hesive EA9394 under unit temperature rise. Only the results
from half the cross section are shown due to symmetry. (a)
Displacement Aof the front surface (nm), (b) displacement
Bof the back surface (nm), (c) Von Mises stress σ(MPa),
and (d) OPD due to the stress σinside the optical flat
face. However, the stress within the optic and the OPD
thereof depend on the mounting method. In Figs. 6(c)
and (d), the ring-flexure mount mitigates thermo-elastic
birefringence effectively compared with the elastomeric
mount in Fig. 5.
IV. EXPERIMENTAL RESULTS
We made four different pilot samples as explained in
the previous section. Mating surfaces of optical flats and
mounting cells, where epoxies adhere, were pretreated
for reliable adhesive strength, as in our space applica-
tion. Optical flats were polished at the rim to remove
microcracks, and 3MrEC3901 primer was applied. The
interior of the cell mount was sandblasted to produce a
ground surface. Then, 3MrEC1945 primer was applied
on the cell’s ground surface. After aligning an optical flat
into a cell, we injected the adhesive (EC2216 or EA9394)
into the cell. We used a dispenser (EFD Inc., Ultimusr)
to regulate the adhesive amount. The pilot samples were
cured at room temperature (21 ◦C) for seven days, fol-
lowing the vendor’s direction.
We made a thermal shroud for the pilot sample to re-
ceive an isothermal load. Heat tape with a 0.37-Ω/cm re-
sistance covers the interior of the shroud, and the applied
Fig. 7. Interferometric measurement setup of a pilot sam-
ple and its resulting OPD.
Fig. 8. (Color online) (a) Interferogram from the elas-
tomeric mount with the adhesive EC2216 after an isothermal
load up to 40 ◦C. (b) The resultant OPD with PV value of
742 nm and RMS value of 195 nm.
Fig. 9. (Color online) (a) Interferogram from the ring-
flexured mount with the adhesive EC2216 after an isothermal
load up to 40 ◦C. (b) The resultant OPD with PV value of
453 nm and RMS value of 93.4 nm.
voltage is controlled for a target temperature. We used
3 k-type thermocouples with self-adhesive backing (SA1
series) from Omega Engineering, Inc. to monitor the
temperature distribution. The temperature is recorded
by using a 16-channel thermocouple reader from Stan-
ford Research Systems Co. (SR630), where resolution is
0.1◦C. The shroud has two openings, which are normally
closed for isothermal loads and opened temporarily for
wavefront measurements with an optical interferometer
(ZygorGPI XP). The interferometer and the flat mir-
ror shown in Fig. 7 are isolated from the shroud. We
experimented with 4 pilot samples, and each OPD after
an isothermal load is calibrated with the data at room
temperature.
Figure 8 show the interferogram and its processed
OPD from the elastomeric mount with the adhesive
EC2216 after an isothermal load up to 40 ◦C. We can
easily notice 6 bonding areas, where interference fringes
are crooked at the optic boundary and the OPD has peak
values. The OPD has a PV (peak-to-valley) value of 742
nm and a RMS (root mean square) value of 195 nm.
The results from a ring-flexured mount and the adhesive
EC2216 are shown in Fig. 9. Contrary to the results in
Athermal Lens Mount with Ring Flexures – Hagyong Kihm et al. -3361-
Fig. 10. (Color online) (a) Interferogram from the elas-
tomeric mount with the adhesive EA9394 after an isothermal
load up to 40 ◦C. (b) The resultant OPD with PV value of
961 nm and RMS value of 238 nm.
Fig. 11. (Color online) (a) Interferogram from the ring-
flexured mount with the adhesive EA9394 after an isothermal
load up to 40 ◦C. (b) The resultant OPD with PV value of
583 nm and RMS value of 131 nm.
Fig. 12. (Color online) OPD profiles across the adhesive
pads from the mounts with adhesive (a) EC2216 and (b)
EA9394.
Fig. 8, salient features due to adhesive stresses can hardly
be observed in the fringe and its OPD. Its PV value is
453 nm, and its RMS value is 93.4 nm. Compared with
Fig. 8, the PV and the RMS values are reduced by 40%.
Figure 10 show the results from an elastomeric mount
with the adhesive EA9394. Thermal stress near the ad-
hesive pads are prominent in the fringe and its OPD.
The void in the OPD is the phase unwrapping error as
the OPD gradient was too steep to sample with the CCD
camera of the optical interferometer. The PV value is 961
nm and the RMS value is 238 nm. The results from a
ring-flexured mount and the adhesive EA9394 are shown
in Fig. 11, where the OPD has a PV value of 583 nm and
a RMS value of 131 nm. Even though stresses around
the adhesive pads are still discernible, their effect is more
localized at the optic boundary. Also, the PV and RMS
value are reduced by more than 40% compared with the
result in Fig. 10.
For more quantitative comparison between the elas-
tomeric mount and the ring-flexured mount, OPD pro-
files across the adhesive pads are presented in Fig. 12.
They are selected from among the 6 adhesive pads in
Figs. 8 – 11(b), where the profiles have the largest peak
values at the optic boundary. As expected from the pre-
vious results, ring-flexured mounts effectively reduce the
optic’s distortion and the stress thereof. The stresses
within the adhesive pads will also be reduced, for better
mechanical safety.
V. CONCLUSIONS
We presented a new athermal lens mount using cas-
caded ring flexures. Thermo-elastic deformations were
evaluated with the optical interferometer and FEA. The
ring-flexured mount showed superior thermo-optical per-
formance compared with the elastomeric mount. Also,
the mechanical safety against adhesive breakage in-
creased as the adhesive pads receive lower stress. The
ring-flexured mount is unique in its appearance and fea-
tures ease of fabrication and dimensional controllability
for flexibility and stability. We applied the ring-flexured
mount for assembling our infrared lenses in a space-borne
telescope and successfully conducted environmental tests
such as vibration, shock, and thermal vacuum tests.
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