Chapter 37 - Handbook of Optics

CHAPTER 37
MOUNTING OPTICAL
COMPONENTS
Paul R. Yoder, Jr.
Consultant in Optical Engineering
Norwalk , Connecticut
37.1 GLOSSARY
A
D
E
K
m
P
p
R
S
T
t
W
a
D
Dr
DT
f, w
θr
…
acceleration factor (mach number) and area (with subscript)
diameter
Young’s modulus
special factors
reciprocal of …
total preload
linear preload
radius of curvature
stress
temperature
thickness
weight
thermal expansion coefficient
decentration
radial clearance
temperature change
angle
roll angle
Poisson’s ratio
Subscripts
A
axial
c
other contact
E
lens edge
G
glass
37.1
37.2
OPTICAL DESIGN TECHNIQUES
M
R
T
t
metal
radial
toroid
tangent contact
37.2 INTRODUCTION AND SUMMARY
This chapter summarizes the most common techniques used to mount lenses, windows, and
similar rotationally symmetric optical components as well as small mirrors and prisms to
their mechanical surrounds. Typical interfaces between the optical and mechanical
components are discussed. Included are considerations of mechanical (clamped) and
elastomeric mounts for individual components and for assemblies of components,
equations for estimating stresses within certain components due to mounting forces, and
selected design methods for minimizing the adverse effects of shock, vibration, and
temperature changes. Although we refer here to optics as if they are always made of glass
and to mechanical parts (housings, cells, spacers, retainers, etc.) as if they are always made
of metal, it should be understood that many of these mounting considerations also apply to
other materials such as plastics or crystals. Examples are given to illustrate typical
mounting design configurations.
Mountings for large (i.e., astronomical-telescope-sized) optics are not considered here.
Readers interested in more general treatments of optical component mounting technology
are referred to ‘‘Selected Papers on Optomechanical Design,’’ SPIE Milestone Series , vol.
770, D. C. O’Shea, editor, (1988) and ‘‘Optomechanical Design,’’ SPIE Critical Rey iews ,
vol. CR43, Paul R. Yoder, Jr., editor, (1992).
37.3 MOUNTING INDIVIDUAL LENSES
General Considerations
Contact between a rotationally symmetric optical component and its mount can occur at
the cylindrical rim, at ground bevels, or at the polished surfaces. Any force in the axial
direction exerted by the mount onto the component within or outside the clear aperture is
called axial preload. Generally, a modest axial preload is desired at assembly since this
tends to prevent motion of the component relative to the mount. Forces exerted in the
radial direction at the rim of the component are generally referred to as ‘‘hoop’’ forces.
Both types of compressive forces tend to introduce stress into the glass, so should be kept
within acceptable limits. Stress can introduce birefringence into the component or, in
extreme cases, damage the glass. Changes in temperature, vibration, and shock are
common causes of excessive applied forces which cause stress.
A glass optical component can usually withstand compressive stress as large as
3.45 3 108 N / m2 without failure, so this value is generally accepted as a survival tolerance.1
In some designs, component surfaces can be placed in tension as a result of applied forces.
A commonly accepted tolerance for tensile stress is 6.9 3 106 N / m2. Under operating
environmental conditions, distortions of optical surfaces due to mounting stresses can
degrade performance. No simple means for predicting refracting or reflecting surface
deformations due to external forces are available; techniques such as finite element
analysis are usually employed to evaluate such deformations. Systems using polarized light
may be sensitive to stress-induced birefringence. A common tolerance for stress in such
cases is 3.45 3 106 N / m2.
MOUNTING OPTICAL COMPONENTS
37.3
(a)
(b)
FIGURE 1 Techniques for holding a lens in a cell with (a ) C-shaped ring
snapped into a groove and (b ) pressed-in continuous ring. [From Ref. 7.]
Simple, Low-Cost Designs
Two techniques sometimes used to secure lenses into housings or cells with nonthreaded
retaining rings are illustrated in Fig. 1. In Fig. 1a , the lens is constrained between a
shoulder integral to the mount and a ‘‘C’’-shaped (i.e. discontinuous) ring with circular
cross section that snaps into a groove machined into the inside diameter (ID) of the
mount. The edge thickness of the lens, the cross-sectional diameter of the ring and the
location, depth, and width of the groove all need to be controlled during manufacture if
both the shoulder and ring are to touch the lens at assembly.
Another design, shown in Fig. 1b , uses a continuous ring of rectangular cross section
and outside diameter (OD) slightly smaller (typically by 5 to 15 mm) than the ID of the
mount. An interference fit will then be obtained if the ring is pressed into the cell. It is
quite difficult to impose a specific axial preload on the lens if the ring must be pressed in
place since it is hard to discern when contact just occurs. Assembly is facilitated if the ring
is cooled and / or the mount is heated so the ring slides easily into the mount until it just
touches the lens. Upon returning to thermal equilibrium, a slight axial preload will then be
exerted upon the lens.
37.4
OPTICAL DESIGN TECHNIQUES
In both designs, temperature decreases will increase axial preload on the lens, while
temperature increases will decrease that preload. In the design of Fig. 1a , the ring will tend
to squeeze from the groove if the temperature drops, thereby tending to relieve axial
stress. At some elevated temperature, the lens in either design may be free of axial
constraint so it can move about within the mount under gravitational, shock, or vibration
loadings.
In these designs, radial clearance, Dr , of the order of 0.1 to 0.3 mm is typically provided
between the lens and the mount. Decentration of either lens vertex when not constrained
may then be as large as Dr and the lens may tilt (or roll) within the mount through an
angle θ r as large as 2Dr / tE in radians, where tE is the lens edge thickness in mm.
The ring of Fig. 1a can be removed if necessary for maintenance purposes, but it is
virtually impossible to remove that of Fig. 1b without damage. Neither of these designs
should be used if precise control of lens position is needed under all environmental
conditions or if a particular preload is desired at the time of assembly. Designs using
threaded retaining rings are preferred in those cases.
Figure 2 shows a typical configuration of a lens burnished into a cell. The cell must be
made of malleable material such as brass or an aluminum alloy. Usually the cell is
mounted onto a spindle (note the integral chucking thread provided for this purpose); the
lens is inserted and held securely against the shoulder while rotating. A burnishing tool
(such as a set of three rollers inclined to the rotation axis by 458 and located at 1208
intervals about that axis) is pressed against the protruding lip of the cell causing the metal
to bend over the edge of the lens and clamping it in place. If the burnishing tool’s forces
act symmetrically, the lens may tend to center within the ID of the cell. Once again,
creation of a specific axial preload is virtually impossible. Dissassembly of a lens mounted
in this manner without damage is quite difficult. This mounting arrangement is most
frequently used in microscope objectives, eyepieces, and small camera-lens assemblies.2,3
Figure 3 illustrates a simple mounting configuration described by Hopkins4 in which a
lens is appropriately centered within a cell and then secured in place with a ring of room
temperature vulcanizing (RTV) adhesive contacting the polished surface. To prevent
movement of the lens due to shrinkage during curing of the adhesive, temporary use of
centering spacers, dabs of beeswax, or an external fixture that secures the lens to the cell is
recommended. This design has the advantage of providing a relatively stress-free
environment for the optical component.
Mounts Using Threaded Retaining Rings
Typical Configurations . Use of a threaded retaining ring to secure a lens against a
reference surface such as a shoulder or a spacer within a cell or housing offers several
advantages over the above-described lens mounts. This type mount can easily be
assembled and disassembled without damage; it automatically compensates for lens edge
thickness variations; it can provide a reasonably predictable axial preload; and it is
compatible with sealing with an injected sealant or with an O-ring.
Figures 4 through 7 illustrate concepts for interfaces between a cell shoulder, a lens, and
a threaded retainer. The simplest provides line contact at a sharp corner around the
periphery of each lens surface. The corner can be a 908 intersection between a cylindrical
hole and a plane (Fig. 4a ) or an obtuse angle such as a 1358 intersection between a conical
surface and a plane (Fig. 4b ). Acute corner angles should be avoided. A sharp corner
interface can be used with either convex or concave lens surfaces. Accuracy of the actual
intersection angle is not essential; errors of Ú28 usually are tolerable. Good machining
practice calls for the sharp corner to be burnished slightly to minimize burrs or nicks.
Typically, a radius of the order of 0.05 mm then results.5 A tendency for better (i.e.,
smoother) sharp edges to result from machining an obtuse angle intersection was reported
MOUNTING OPTICAL COMPONENTS
FIGURE 2 Lens burnished into a cell made of
malleable metal. [From Ref. 12.]
FIGURE 3 Lens secured in a cell by a ring of adhesive
contacting the polished surface. [From Ref. 4.]
FIGURE 4 Techniques for holding a lens with sharp corner interfaces: (a ) 908 corner on convex
surface and (b ) 1358 corner on concave surface. [From Ref. 8.]
37.5
37.6
OPTICAL DESIGN TECHNIQUES
FIGURE 5 Technique for holding a lens with a conical
(tangential) interface. Note this is applicable only to
convex surfaces. [From Ref. 8.]
FIGURE 6 Techniques for holding a lens with toroidal interfaces:
(a ) convex surface and (b ) concave surface. [From Ref. 8.]
MOUNTING OPTICAL COMPONENTS
37.7
FIGURE 7 Techniques for holding a lens with spherical interfaces:
(a ) convex surface and (b ) concave surface. [From Ref. 8.]
by Hopkins.4 The radial height of line contact, yc , usually is just slightly greater than the
radius of the lens’ clear aperture.
Tangential contact at a height yc (in mm) is illustrated in Fig. 5. It can be used only with
convex lens surfaces. The half-angle w of the right-circular cone in such an interface is
given by the following equation:
w 5 908-arcsin ( yc / R )
(1)
where R is the lens’ radius of curvature in mm and yc in mm is typically one-half the
arithmetic average of the lens’ clear aperture and its OD. The typical tolerance on w is
Ú28.
Toroidal contact between the mechanical and optical components can be provided for
either convex or concave lens surfaces. (See Fig. 6.) In each case, the center of curvature
of the circular arc defining the doughnut-shaped toroid is located off the axis by the
dimensions yT and lies on the local normal to the lens surface at yc where yc is as defined
for tangent contact. Preferred values for the sectional radius of the toroids are $10R for a
convex surface and $0.5R for a concave surface, where R is the radius of the lens surface.6
If the mechanical interface with the lens is lapped to the same spherical radius as the
lens surface within a few fringes of visible light, a spherical interface mount can be
produced. (See Fig. 7.) If the radii of the mechanical and optical surfaces do not match
adequately, the interface will degenerate into line contact at the inner or outer edge of the
annular mechanical area. Manufacture of the spherical interface mount is costly due to this
need for radius matching. Hence, it is generally used only in special designs.
In each of the above-described lens mounts, contact of the metal occurs on polished
glass surfaces. These surfaces are usually accurately made and well aligned to each other
due to the inherent nature of the optical polishing and edging processes. In most lenses,
37.8
OPTICAL DESIGN TECHNIQUES
FIGURE 8 Techniques for holding plane parallel plates or
lenses with flat bevels on convex and concave surfaces. [From
Ref. 8.]
contact occurs at a zone where the optical surface is inclined with respect to the axially
directed force imposed by the retainer. Radial components of that force tend to center the
lens with respect to the axis. The magnitude of this centering tendency depends upon the
radius of curvature of the lens surface, with sharply curved surfaces centering more easily
than flatter ones.
Contact against flat bevels ground into the edges of the lens’ spherical surfaces can be
provided as shown in Fig. 8. Such interfaces have the advantage of distributing axial
preload due to the clamping action of the retaining ring over a large area on the lens,
thereby reducing stress buildup within the glass. They have the disadvantages of not being
able to help self-center the lens and of referencing against secondary surfaces of potentially
reduced angular accuracy as compared to the polished lens surfaces. While accurate flat
bevels can be produced, they add significantly to the cost of the lens. In the sections which
follow, a simplistic treatment of forces and stresses at the optomechanical interface as
summarized by Yoder6–8 is given. These analytical methods can be used to compare
alternate designs or to assess the need for experimental verification or more rigorous
analyses using, for example, finite element analysis methods.
Axial Preload and Axial Stress Relationships at Assembly Temperature . If we know the
total preload P in newtons exerted by the retainer against the lens at the zonal contact
MOUNTING OPTICAL COMPONENTS
37.9
radius yc in mm during assembly at a temperature of (typically) 208C, the resulting axial
stress SA in N / m2 developed within the contact area on the glass can be estimated using the
following equation:7,8
SA 5 20 .798(K 1 p / K 2)1/2
where
(2)
p 5 linear preload 5 P / (2π yc ) in N / mm
K 1 5 (D1 1 D2) / D1 D2 for a sharp corner contacting a convex surface
5 (D1 2 D2) / D1 D2 for a sharp corner contacting a concave surface
5 1 / D1 for a conical surface contacting a convex surface (tangent interface)
5 1.1 / D1 for a toroid surface of sectional radius 10D1 contacting a convex surface
5 1 / D1 for a toroid surface of sectional radius 0.5D1 contacting a concave surface
D1 5 twice the lens radius of curvature in mm
D2 5 0.1 mm 5 twice the sharp corner radius
K 2 5 ((1 2 … 2G) / EG ) 1 ((1 2 … 2M) / EM )
… G 5 Poisson’s ratio for the glass
… M 5 Poisson’s ratio for the metal
EG 5 Young’s modulus for the glass in N / m2
EM 5 Young’s modulus for the metal in N / m2
Equations for the contact stresses introduced into a lens with flat bevel or spherical
interfaces are not included here because those stresses would be relatively insignificant as
compared to those with the interfaces listed. As shown by Yoder,6 the contact stresses
computed for the toroidal interface cases would be within 5 percent of those computed for
the tangential case and much smaller than those for sharp corner interfaces.
Axial Preload Required to Restrain the Optical Component at Eley ated
Temperature . As the temperature rises, the metal of the mount expands more than the
glass component within. Any axial preload existing at assembly will then be reduced. If the
temperature rises sufficiently, this preload may disappear and the optic is free to move
within the mount due to external forces. Ideally, unless the position and orientation of the
lens are not critical in the application, the design should prevent such freedom at the
highest temperature that the instrument is to survive without damage. For military
applications, this highest temperature is typically 718C. Instruments for laboratory,
commercial, or consumer use may have lower survival temperature requirements.
One way of preventing this release of preload is to provide a sufficient preload at
assembly, P1 , in newtons, so that the force on the lens is just reduced to zero at the highest
survival temperature. Defining the change in temperature from that at assembly to the
highest value as DT , we can use the following equation to estimate the axial preload
required at assembly:7,8
P1 5 K 3(DT )
where K 3 5 2EG AG EM AM (a M 2 a G ) / (2)((EG AG / 2) 1 EM AM ) if 2yc 1 tE , DG
9 EM AM (a M 2 a G ) / (2)((EG AG
9 / 2) 1 EM Am ) if 2yc 1 tE . 5DG
K 3 5 2EG AG
AM 5 2π tc ((DM / 2) 1 (tc / 2)) in mm2
tc 5 cell wall thickness in mm at lens rim
(3)
37.10
OPTICAL DESIGN TECHNIQUES
AG 5 2π yc tE in mm2
tE 5 lens edge thickness in mm at height yc
A9G 5 (π / 4)(DG 2 tE 1 2yc )(DG 1 tE 2 2yc ) in mm2
DG 5 lens OD in mm
a M 5 thermal expansion coefficient of the metal in ppm / 8C
a G 5 thermal expansion coefficient of the glass in ppm / 8C
and all other terms are as defined earlier.
Axial Preload Required to Restrain the Optical Component Against Acceleration
Forces . If the optic is expected to experience acceleration forces due to gravity, shock, or
vibration and its axial location within the mount must remain unchanged during such
exposure, it should be constrained by an axial preload P2 in newtons, as given by the
following equation:
P2 5 29.807WA
(4)
where W 5 weight of optical component in kg
A 5 maximum imposed acceleration factor (expressed as a multiple of gravity)
Total Axial Preload to Restrain the Optic Against Acceleration and Release of Preload
at the Highest Sury iy al Temperature . By adding the preloads computed by Eqs. (3) and
(4) one obtains the approximate total axial preload PT , in newtons, required to constrain
the optic against axial acceleration forces and to prevent complete release of assembly
preload at the highest temperature. This preload may be very high if the lens and cell
materials do not match closely in thermal expansion properties. A lower preload can be
used if the motion of the lens within the clearance created by expansion of the cell away
from the lens is tolerable.
Retaining Ring Torque Required to Produce a Giy en Axial Preload . The magnitude of
the torque M , in N-cm, that should be applied to the retaining ring to introduce a given
axial preload PT , in newtons, to the edge of the lens can be approximated from the
following empirically derived formula given by Kowalski:9
M 5 0.2PT DR
(5)
where DR is the pitch diameter in cm of the thread on the ring.
Axial Stress Introduced at Reduced Temperatures . If the temperature decreases by 2DT
in 8C from that existing at assembly, the preload exerted by the retaining ring increases
due to differential expansion of the mount and the optical component. The change in axial
preload on the glass, P1 , in newtons, is given by Eq. (3) as defined above. The usual lower
limit for survival temperature of military optical instrumentation is 2628C. It should be
noted that the preload PT at assembly should be added to that estimated by this application
of Eq. (3) to give the total preload at reduced temperature. Contact stress within the glass
can be computed by use of Eq. (2) and the average (or bulk) stress SBG within the glass can
9 as appropriate. The average (or bulk)
be estimated as 2(P1 1 PT ) / AG or 2(P1 1 PT ) / AG
stress SBM within the cell wall can be estimated as (P1 1 PT ) / AM . These bulk stresses are
generally much smaller than the corresponding contact stresses computed by Eq. (2).
Radial Stress Introduced at Reduced Temperatures . In all designs considered above,
radial clearance was assumed to exist between the optic and the mount. In some designs,
this clearance is the minimum allowing assembly so, at some reduced temperature, the
metal touches the rim of the optic and, at still lower temperatures, a so-called ‘‘hoop’’
MOUNTING OPTICAL COMPONENTS
37.11
stress develops. The magnitude of this stress SR (N / m2) for a given temperature drop DT ,
in 8C can be estimated by the following equation:7
SR 5 K 4 K 5 DT
(6)
where K 4 5 (a M 2 a G ) / ((1 / EG ) 1 (DG / 2EM tC ))
K 5 5 (1 1 ((2Dr ) / (Dg DT )(a M 2 a G )))
DG 5 optical component OD in mm
tC 5 mount wall thickness outside rim of the optic in mm
Ar 5 radial clearance in mm
If Dr exceeds DG DT (a M 2 a G ) / 2 , the lens will not be constrained by the cell ID, and
hoop stress will not develop within the temperature range DT due to rim contact.
Combined Axial / Radial Stress at Reduced Temperatures . Bayar10 indicated that the
combined effect of axial and radial stresses within the optical component can be estimated
as the root sum square (rss) of the orthogonal stresses. This is most significant at
worst-case reduced temperature. Hence:
Srss 5 ((SBG )2 1 (SR)2)1/2
(7)
where all terms are as defined above.
Growth of Radial Clearance at Increased Temperatures . The increases in radial and
axial clearances, DgapR and DgapA , in mm, between the optic and the mount due to a
temperature increase of DT in 8C from that at assembly can be estimated by the following
equations:
DgapR 5 K 6DT
(8)
DgapA 5 K 7DT
(9)
where K 6 5 (a M 2 a G )DG / 2
K 7 5 (a M 2 a G )tE
and all terms are as defined above.
Stresses Due to Bending of the Component . If the lines of contact between the mount
and optical component occur at different radii from the axis, axial forces applied through
those contacts can cause bending of the surfaces. (See Fig. 9.) One of the surfaces must
FIGURE 9 Schematic diagram of axial forces tending
to bend an optical element when contact areas are not
at the same radius. [From Ref. 7.]
37.12
OPTICAL DESIGN TECHNIQUES
necessarily be placed in tension; this is the condition in which glass is the weakest. Bayar10
applied the following equation for the tensile stress induced by bending:
ST 5
F
3PT
Y2
Y 21
0
.
5(
m
2
1)
1
(
m
1
1)
ln
2
(
m
2
1)
2π mt 2E
Y1
Y 22
G
(10)
where ST 5 tensile stress in the component (N / m2)
PT 5 applied axial load (N)
m 5 1 / Poisson’s ratio
tE 5 edge thickness of component
Y1 5 innermost contact radius (cm)
Y2 5 outermost contact radius (cm)
As mentioned earlier, the general tolerance for tensile stress is 6.9 3 106 N / m2.
Stresses Under Operating Conditions . Any of the above equations for stress induced into
an optical component by forces exerted by the mount can be applied to operating
conditions as well as worst-case conditions. In general, the stress levels will be reduced, but
they still may be significant in terms of their effects upon system performance. Surface
deformations due to mount-induced forces may also occur. Within limits, the effects of
axial forces can be reduced by making the retainer somewhat resilient. Some techniques
for doing this are illustrated schematically in Fig. 10.
FIGURE 10 Typical resilient retainer configurations intended to more uniformly distribute axial forces
and reduce surface distortions. [From Ref. 7.]
MOUNTING OPTICAL COMPONENTS
37.13
FIGURE 11 Technique for holding a lens in a cell with an
annular layer of cured-in-place elastomer. [From Ref. 7.]
Elastomeric Mounting Designs
Resilient materials such as RTV compounds are frequently used to seal optical
components into their mounts with or without mechanical constraint. Registry of at least
one optical surface against a machined surface of the mount (as shown in Fig. 3) helps
align the optic. The resilient layer can provide some degree of protection against shock and
vibration as well as thermal isolation. Epoxy or urethane compounds are sometimes used
for the same purpose. These materials are generally somewhat less resilient than RTV
compounds, but they are superior in regard to structural bond strength.
Figure 11 illustrates a common technique for mounting a lens in an annular ring of
elastomer. Centration can be retained by temporary shimming or external fixturing during
the curing process. If the elastomer layer’s radial thickness tE (mm) is in accordance with
the following equation, the design becomes relatively insensitive to temperature change:10
tE 5 (DG / 2)(a M 2 a G ) / (a E 2 a M )
(11)
where all terms are as defined above.
Valente and Richard11 reported an analytical technique for estimating the decentration
D, in m, of a lens mounted in a ring of elastomer when subjected to radial gravitational
loading. Their method can be expanded to include more general radial acceleration forces
resulting in the following equation:
D 5 AWtE / (π Rd ((EE / (1 2 … 2E)) 1 ES ))
where A 5 acceleration factor
W 5 weight of optical component in N
tE 5 thickness of elastomer layer in m
R 5 optical component OD / 2 in m
d 5 optical component thickness in m
EE 5 Young’s modulus of elastomer in N / m2
ES 5 Shear modulus of elastomer in N / m2
… E 5 Poisson’s ratio of elastomer
(12)
37.14
OPTICAL DESIGN TECHNIQUES
FIGURE 12 A simple eyepiece configured for assembly by dropping the lenses in place and clamping
with a retainer. [From Ref. 12.]
The decentrations of modest-sized optics corresponding to normal gravity loading are
generally quite small.
37.4 MULTICOMPONENT LENS ASSEMBLIES
Drop-In Assembly Techniques
A drop-in lens assembly is one in which the optical components are edged to diameter
typically 0.075 to 0.150 mm smaller than the minimum ID of the cell or housing in which
they are to be mounted. After installation of the optics and spacers as appropriate, the
parts are typically held in place with a single retaining ring. The fixed-focus eyepiece for a
military telescope shown in Fig. 12 typifies this type assembly. The optomechanical
interfaces are all square corners. Sealing provisions are indicated. Many camera lenses and
most terrestrial telescope, binocular, and microscope optics are assembled in this manner.
Figure 13 shows another design for a drop-in assembly. In this case of a fixed aperture
relay lens, the lenses are individually mounted in recesses bored into the front housing and
into the rear cell. Radial clearances are typically no greater than 0.013 mm and the lenses
are precisely edged and beveled with respect to their optical axes to ensure alignment.
Adjustment of axial spacings is accomplished by customizing thicknesses of two spacers
and by machining axial dimension Y of the housing at the time of assembly.
Machine-at-Assembly Techniques
In this type assembly, the rims of optical components are precision ground to a high degree
of roundness, but not held to tight diametrical tolerances. Actual ODs are measured and
the IDs of the mating mechanical seats are machined to fit those lenses with radial
clearances of the order of 5 mm. Axial locations of the lenses are established while the
seats are being machined. This technique, sometimes referred to as ‘‘lathe assembly,’’ is
employed in high-performance applications such as aerial camera lenses or assemblies that
must withstand high vibration and / or shock loads.12 Figure 14a shows an airspaced
MOUNTING OPTICAL COMPONENTS
37.15
FIGURE 13 A relay lens assembly configured for dropping the lenses in place and clamping
with individual retainers. [From Ref. 7.]
doublet mounted in this manner, while Fig. 14b shows the lenses. Measured values are
recorded in the numbered boxes on the drawings for reference during machining. Both
optical and mechanical parts are usually serialized for identification and traceability. Since
the mechanical parts are customized for a specific set of lenses, replacement of a damaged
lens may require considerable effort to match dimensions adequately.
A variation of the lathe-assembly principle is illustrated in Fig. 15 which shows the
optomechanical configuration of a 22.8-cm focal length, f / 1.5 objective.13 Designed to
image a military target at low light levels onto an image intensifier in a visual periscope
and to project a coaxial laser beam for target ranging, the lenses of this objective are
mounted with very small radial clearances into an aluminum barrel. Because of their large
sizes, high manufacturing precision, and special coatings, the lenses were quite expensive.
In order to reduce the chance of chipping the edges if inadvertently tilted as these
close-fitting lenses were installed, the rims were ground spherical as shown in Fig. 16. This
feature has been successfully used in several other designs involving optics with high value
at the critical time of assembly.
Stacked-Cell Assembly Techniques
Figure 17 illustrates a design described by Carnel et al.14 for a wide-field objective lens
used for bubble chamber photography. A large amount of optical distortion of particular
form was designed into the lens. To provide this distortion accurately, the lenses had to be
precisely centered. In this assembly, the lenses were mounted in individual cells and the
ODs of those cells machined to specific dimensions with each cell’s mechanical axis
colinear with the lens’ optical axis. All the cells were then installed into the ID of the
barrel with spacer rings to provide appropriate axial separations.
37.16
OPTICAL DESIGN TECHNIQUES
(a)
(b)
FIGURE 14 Example of the ‘‘lathe assembly’’ method of optical
assembly: (a ) mounted lenses and (b ) lenses only. Measured values for
serialized parts are recorded in boxes. [From Ref. 12.]
MOUNTING OPTICAL COMPONENTS
37.17
FIGURE 15 Sectional view of a low light level periscope objective. [From Ref. 13.]
This same principle was used by Fischer15 in designing a low-distortion telecentric
projection lens in which all lenses but one were mounted within individual stainless steel
cells and the ODs of those cells machined precisely so as to just slide into the ID of a
stainless steel barrel. (See Fig. 18.) The lenses were aligned to the ODs of the cells and
held in place with nominally 0.38-mm-thick annular layers of epoxy. Cell 1 of this design
acts as a retaining ring to hold the other cells against a shoulder in the barrel.
Figure 19 shows another design, a 2-m focal length, f / 10 astrographic telescope
objective, which also has its lenses mounted into cells and the cells stacked into a barrel.16
In this case, all mechanical parts are titanium. The lenses are constrained within annular
epoxy layers having nominal radial thicknesses of typically 5.08 mm. Richard and
FIGURE 16 Detail view of spherical rim lenses used in the lens of Figure 15. [From Ref.
13.]
37.18
OPTICAL DESIGN TECHNIQUES
FIGURE 17 Optomechanical configuration of a bubble chamber objective with lenses
individually mounted in cells and stacked in a barrel. [From Ref. 14.]
FIGURE 18 Optomechanical configuration of a low-distortion objective with stacked cell-mounted lenses.
[From Ref. 15.]
MOUNTING OPTICAL COMPONENTS
37.19
FIGURE 19 Optomechanical configuration of an astrographic telescope objective with stacked cell-mounted lenses.
[From Ref. 16.]
Valente17 described how the cells were designed for interference fits within the barrel and
pressed in place. Valente and Richard11 showed that the decentrations of the lenses due to
radially directed gravitational force driving the lenses into the resilient layer would be only
on the order of a tolerable 2.5 mm.
Assemblies Using Plastic Parts
Near the other end of the complexity spectrum from the designs so far considered here are
a multitude of optomechanical devices using plastic lenses, cells, retaining means, and
structures. A few examples are camera viewfinders and objectives, magnifiers, television
projection systems, optics and structural parts for telescopes and binoculars, compact disc
player systems, and military helmet-mounted night-vision goggles. General features of such
devices are use of low-cost, lightweight materials, freedom to employ aspherics, large
quantity production, consolidation of optical and mechanical functions into integrated
molded components, and compatibility with automated assembly. In the following sections,
we describe two optomechanical subsystem designs that illustrate some of these important
features.
Figure 20 shows two configurations for an airspaced triplet consisting of plastic lenses,
spacers and retainers, and a two-part molded plastic housing. In each case, the lenses are
inserted axially into the housing and held by retainers that are glued or fused in place.
Design a in the upper half of the figure has the joint between the mount components (i.e.,
the parting line of the mold) just to the right of the negative lens. The two lenses and the
spacer shown on the left are inserted from that side, while the third lens is inserted from
the right. In design b shown in the lower half of the figure, the housing joint is located at
the extreme right end of the assembly. In this case, the IDs of the recesses for the lenses
are formed by a single-stepped mold so concentration is improved over that inherent in
37.20
OPTICAL DESIGN TECHNIQUES
(a)
(b)
FIGURE 20 An all-plastic, three-lens optomechanical subassembly with the twopart mount designed for joining at alternate axial locations. Design a has lower cost
but design b has improved centration and somewhat better performances. [Courtesy
of U.S. Precision Lens , Inc.]
design a. Design a is less expensive to produce than design b so a trade-off between optical
performance and cost must be considered in choosing which design to adopt.
A distinct advantage of plastic optics is that multiple optical elements, structural
mounts, and interfaces for light sources, detectors, and mechanisms can frequently be
integrated into single parts. To illustrate this, Fig. 21 shows a two-lens assembly with
FIGURE 21 Economical construction of a one-piece optomechanical subassembly with two integral
lenses, prealigned interfaces for two sensors and mounting features. [Courtesy of U.S. Precision Lens , Inc.]
MOUNTING OPTICAL COMPONENTS
37.21
integral mounting flange and preformed interfaces for two sensors. Used in an automatic
coin changer mechanism, this assembly is prefocused and uses an aspheric element. Given
large enough production quantities to amortize mold costs, this subassembly is considerably more economical than one consisting of the equivalent separate parts that would
require labor to manufacture, inspect, assemble, and align.
37.5 MOUNTING SMALL MIRRORS AND PRISMS
General Considerations
The appropriateness of designs for mechanical mountings for small mirrors and prisms
depends upon a variety of factors including: the tolerable movement and distortion of the
refracting and / or reflecting surface(s); the magnitudes, application locations, and orientations of forces tending to move the optic with respect to its mount; steady-state and
transient thermal effects (including gradients); the sizes and kinematic compatibility of
interfacing optomechanical surfaces; and the rigidity and long-term stability of the
structure supporting the mount. In addition, the designs must be compatible with
assembly, maintenance, package size, weight, and configuration constraints, as well as be
cost-effective. Examples of some very simple designs and of one more complex design are
described briefly in the following sections to illustrate proven mounting techniques.
Mechanically Clamped Mountings
Figure 22 shows a simple means for attaching a first surface flat mirror to a mechanical
mount such as a metal bracket or flange. The reflecting surface is pressed against three
coplanar lapped pads by three leaf springs or clips. The spring contacts are directly
opposite the pads to minimize bending moments. This design constrains one translation
and two tilts. Translations in the plane of a circular mirror can most easily be constrained
by dimensioning the spacers supporting the springs so as to just clear the rim of the
FIGURE 22 Typical construction for a spring clipmounted flat mirror subassembly. [From Ref. 18.]
37.22
OPTICAL DESIGN TECHNIQUES
FIGURE 23 Diagram of a typical strap mounting for a Porro prism erecting subassembly.
[From Ref. 18.]
mirror. Lengths of those spacers and the free lengths and stiffnesses of the cantilevered
springs are typically chosen so as to load the mirror against the pads against expected
acceleration forces with a safety factor of at least 2. Yoder7 summarized standard
techniques for design of such springs.
A common design for clamping a two-component Porro prism image erecting system to
a mounting plate for use in a telescope or binocular is shown in Fig. 23.18 The prisms fit
into recesses machined into opposite sides of the plate and configured to fit the contours of
the hypotenuse faces of the prisms. Straps typically made of spring-tempered phosphor
bronze hold the prisms against the plate. The thin sheet metal light shields cover the
reflecting surfaces to reduce stray light. Flexible adhesive (such as RTV) applied locally
along the edges of the metal-to-glass interface helps prevent translation of the prisms in
the recesses. Mounts for other types of prisms can be designed using the same principles
described here.
Generally, clamping forces are exerted against ground surfaces of prisms rather than
optically active ones to minimize surface deformations. As in the case of the mirror mount
just described, spring loading against the plate should typically constrain the prisms against
at least twice the expected maximum acceleration force.
Bonded Mountings
A popular technique for mounting mirrors and prisms is to bond them directly to a
mounting plate or bracket. Dimensional and alignment stability are enhanced if required
adjustment provisions are built into the mount rather than into the glass-to-metal interface.
Figure 24 shows a typical configuration for a flat mirror bonded to a mounting bracket.
It is quite feasible to mount first surface mirrors of aperture about 15 cm or smaller directly
to a mechanical support. The ratio of largest mirror dimension to mirror thickness should
be at least 10 : 1 in order not to distort the reflecting surface. In the design shown, the
mirror is crown glass with about a 6 : 1 diameter-to-thickness ratio. The mount is stainless
steel so thermal expansion characteristics match rather well. The bonding area is circular.
The adhesive layer is epoxy approximately 0.075 mm thick. Care should be exercised in
MOUNTING OPTICAL COMPONENTS
37.23
FIGURE 24 Typical construction for a first-surface mirror subassembly with glass-to-metal bond securing the mirror to its mount.
[From Ref. 18.]
assembling such an optical component to not allow fillets of epoxy to form around the
interface due to overflow, as these could lead to excess stress concentrations due to
contraction during cure or at low temperatures.
A simple design for bonding a right-angle prism to a mounting bracket is illustrated in
Fig. 25. The prism is cantilevered from a nominally vertical surface. Here the bond area is
maximized and is adequate to maintain joint integrity under high vibration and shock
loading. Yoder19 outlined a method for determining the appropriate bonding area to hold a
variety of common prism types against acceleration forces.
Flexure Mountings
Mounts for mirrors frequently consist of parts made from different types of materials
so their thermal expansion properties do not match. Differential expansion as the
temperature changes may cause optical components to decenter or tilt, thereby affecting
critical alignment. One technique to combat such errors is to mount the optic on flexure
FIGURE 25 Typical configuration for a large prism bonded in cantilever fashion to a
nominally vertical bracket. Dimensions are inches. [From Ref. 18.]
37.24
OPTICAL DESIGN TECHNIQUES
FIGURE 26 Conceptual design for mounting a circular aperture mirror on three tangent flexure blades. [From Ref. 7.]
FIGURE 27 Exploded view of a flexure mounting for a small secondary mirror for a spaceborne
telescope. [From Ref. 20.]
MOUNTING OPTICAL COMPONENTS
37.25
FIGURE 28 Configuration of a large prism assembly mounted on three flexure posts. [From Ref. 7.]
blades or posts designed to bend or twist symmetrically and maintain alignment. Three
examples are considered here.
Figure 26 shows the design principle of a flexure support for a flat or curved mirror. The
mirror is mounted into a cell which is connected to instrument structure by three flexure
blades attached tangentially to the cell wall. The blades are stiff axially to prevent axial
motion or tilt, but they bend as indicated by the curved arrows if dimensions of the
mirror / cell combination or of the structure change radially. The mirror tends to remain
centered, but undergoes a very small rotation about its axis as the blades flex. This
mounting technique is applicable to larger mirrors as well as small ones. Examples of
tangential flexure mountings for low-expansion mirrors as large as 1.5-m aperture in
aluminum mounts and used in astronomical telescope or laser beam expander applications
were described by Yoder.7
A flexure support for a telescope secondary mirror described by Hookman20 is shown in
Fig. 27. In this design, a small (3.9-cm aperture) mirror made of low-expansion ULE
material is mounted in an Invar cell which is supported on three flexure blades machined
integrally into an aluminum mount. Used in the telescope of a satellite-borne environmental sensor, this mirror undergoes the rigors of launch and variable temperature operation
within minimum adverse effects on optical alignment or surface figure.
A flexure support for a large (14-cm aperture) Zerodur roof mirror constructed from
three optically contacted prisms is illustrated in Fig. 28. This prism, part of a highperformance optical mask aligner for microlithography wafer production, is supported by
three flexure posts configured with multiple orthogonal blades and cruciform sections to
minimize rigid-body movements and surface distortions when mounted to a structure made
of materials with significantly higher expansion properties. As indicated in the diagram at
upper right, two flexures include blades allowing motion toward the third post. Two lateral
translations and three rotations are controlled by this mounting arrangement.7
37.26
OPTICAL DESIGN TECHNIQUES
37.6 REFERENCES
1. E. B. Shand, Glass Engineering Handbook , 2d ed., McGraw-Hill, New York, 1958.
2. R. M. Scott, ‘‘Optical Manufacturing,’’ chap. 2, Applied Optics and Optical Engineering , vol. III,
Rudolf Kingslake (ed.), Academic Press, New York, 1965.
3. D. F. Horne, Optical Production Technology , Adam Hilger, Ltd., Bristol, 1972.
4. Robert E. Hopkins, ‘‘Lens Mounting and Centering,’’ chap. 2, Applied Optics and Optical
Engineering , vol. VIII, Robert R. Shannon and James C. Wyant (eds.), Academic Press, New
York, 1980.
5. R. F. Delgado and M. Hallinan, ‘‘Mounting of Lens Elements,’’ Opt. Eng. 14:S-11 (1975).
6. Paul R. Yoder, Jr., ‘‘Axial Stresses with Toroidal Lens-to-Mount Interfaces,’’ Proc SPIE 1533:2
(1991).
7. Paul R. Yoder, Jr., Opto -Mechanical Systems Design , 2d ed., Marcel Dekker, New York, 1993.
8. Paul R. Yoder, Jr., ‘‘Advanced Considerations of the Lens to Cell Interface,’’ Proc. SPIE
CR43:305 (1992).
9. Brian J. Kowalski, ‘‘A User’s Guide to Designing and Mounting Lenses and Mirrors,’’ Digest of
Papers , OSA Workshop on Optical Fabrication and Testing , North Falmouth (1980).
10. Mete Bayar, ‘‘Lens Barrel Optomechanical Design Principles,’’ Opt. Eng. 20:181 (1981).
11. Tina M. Valente and Ralph M. Richard, ‘‘Analysis of Elastomer Lens Mountings,’’ Proc. SPIE
1533:21 (1991).
12. Paul R. Yoder, Jr., ‘‘Lens Mounting Techniques,’’ Proc. SPIE 389:2 (1983).
13. Paul R. Yoder, Jr., ‘‘Opto-Mechanical Designs for Two Special-Purpose Objective Lens
Assemblies,’’ Proc. SPIE 656:225 (1986).
14. K. H. Carnel, M. J. Kidger, A. J. Overill, R. W. Reader, F. C. Reavell, W. T. Welford, and G. C.
Wynne, ‘‘Some Experiments on Precision Lens Centering and Mounting,’’ Optica Acta 21:615
(1974).
15. Robert E. Fischer, ‘‘Case Study of Elastomeric Lens Mounts,’’ Proc. SPIE 1533:27 (1991).
16. Daniel Vukobratovich, private communication (1991) Univ. of Arizona at Tucscon, Tucson,
Arizona.
17. Ralph M. Richard and Tina M. Valente, ‘‘Interference Fit Equations for Lens Cell Design,’’ Proc.
SPIE 1533:12 (1991).
18. Paul R. Yoder, Jr., ‘‘Non-Image-Forming Optical Components,’’ Proc. SPIE 531:206 (1985).
19. Paul R. Yoder, Jr., ‘‘Design Guidelines for Bonding Prisms to Mounts,’’ Proc. SPIE 1013:112
(1988).
20. Robert Hookman, ‘‘Design of the GOES Telescope Secondary Mirror Mounting,’’ Proc. SPIE
1167:368 (1989).