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CHAPTER 37 MOUNTING OPTICAL COMPONENTS

Paul R . Yoder , Jr . Consultant in Optical Engineering Norwalk , Connecticut

3 7 . 1 GLOSSARY

A acceleration factor (mach number) and area (with subscript) D diameter E Young’s modulus K special factors m reciprocal of … P total preload p linear preload R radius of curvature S stress T temperature t thickness

W weight a thermal expansion coef ficient D decentration

D r radial clearance D T temperature change

f , w angle θ r roll angle … Poisson’s ratio

Subscripts A axial c other contact

E lens edge G glass

37 .1

37 .2 OPTICAL DESIGN TECHNIQUES

M metal R radial T toroid t tangent contact

3 7 . 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 ef fects 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 Re y iews , vol . CR43 , Paul R . Yoder , Jr ., editor , (1992) .

3 7 . 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 10 8 N / m 2 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 10 6 N / m 2 . 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 10 6 N / m 2 .

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 . 1 a , 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 . 1 b , uses a continuous ring of rectangular cross section and outside diameter (OD) slightly smaller (typically by 5 to 15 m m) than the ID of the mount . An interference fit will then be obtained if the ring is pressed into the cell . It is quite dif ficult 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 .


In both designs , temperature decreases will increase axial preload on the lens , while temperature increases will decrease that preload . In the design of Fig . 1 a , 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 , D r , 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 D r and the lens may tilt (or roll) within the mount through an angle θ r as large as 2 D r / t E in radians , where t E is the lens edge thickness in mm .

The ring of Fig . 1 a can be removed if necessary for maintenance purposes , but it is virtually impossible to remove that of Fig . 1 b 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 45 8 and located at 120 8 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 dif ficult . 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 Hopkins 4 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 of fers 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 90 8 intersection between a cylindrical hole and a plane (Fig . 4 a ) or an obtuse angle such as a 135 8 intersection between a conical surface and a plane (Fig . 4 b ) . 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 Ú 2 8 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


FIGURE 2 Lens burnished into a cell made of malleable metal . [ From Ref . 1 2 . ]

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 ) 90 8 corner on convex surface and ( b ) 135 8 corner on concave surface . [ From Ref . 8 . ]


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 . ]


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 , y c , usually is just slightly greater than the radius of the lens’ clear aperture .

Tangential contact at a height y c (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 90 8 -arcsin ( y c / R ) (1)

where R is the lens’ radius of curvature in mm and y c in mm is typically one-half the arithmetic average of the lens’ clear aperture and its OD . The typical tolerance on w is Ú 2 8 .

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 of f the axis by the dimensions y T and lies on the local normal to the lens surface at y c where y c is as defined for tangent contact . Preferred values for the sectional radius of the toroids are $ 10 R for a convex surface and $ 0 . 5 R 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 ,


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 Yoder 6–8 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


radius y c in mm during assembly at a temperature of (typically) 20 8 C , the resulting axial stress S A in N / m 2 developed within the contact area on the glass can be estimated using the following equation : 7 , 8

S A 5 2 0 . 798( K 1 p / K 2 ) 1 / 2 (2)

where p 5 linear preload 5 P / (2 π y c ) in N / mm

K 1 5 ( D 1 1 D 2 ) / D 1 D 2 for a sharp corner contacting a convex surface

5 ( D 1 2 D 2 ) / D 1 D 2 for a sharp corner contacting a concave surface

5 1 / D 1 for a conical surface contacting a convex surface (tangent interface)

5 1 . 1 / D 1 for a toroid surface of sectional radius 10 D 1 contacting a convex surface

5 1 / D 1 for a toroid surface of sectional radius 0 . 5 D 1 contacting a concave surface

D 1 5 twice the lens radius of curvature in mm

D 2 5 0 . 1 mm 5 twice the sharp corner radius

K 2 5 ((1 2 … 2 G ) / E G ) 1 ((1 2 … 2

M ) / E M )

… G 5 Poisson’s ratio for the glass

… M 5 Poisson’s ratio for the metal

E G 5 Young’s modulus for the glass in N / m 2

E M 5 Young’s modulus for the metal in N / m 2

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 Ele y 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 suf ficiently , 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 71 8 C . 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 suf ficient preload at assembly , P 1 , 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 D T , we can use the following equation to estimate the axial preload required at assembly : 7 , 8

P 1 5 K 3 ( D T ) (3)

where K 3 5 2 E G A G E M A M ( a M 2 a G ) / (2)(( E G A G / 2) 1 E M A M ) if 2 y c 1 t E , D G

K 3 5 2 E G A 9 G E M A M ( a M 2 a G ) / (2)(( E G A 9 G / 2) 1 E M A m ) if 2 y c 1 t E . 5 D G

A M 5 2 π t c (( D M / 2) 1 ( t c / 2)) in mm 2

t c 5 cell wall thickness in mm at lens rim


A G 5 2 π y c t E in mm 2

t E 5 lens edge thickness in mm at height y c

A 9 G 5 ( π / 4)( D G 2 t E 1 2 y c )( D G 1 t E 2 2 y c ) in mm 2

D G 5 lens OD in mm a M 5 thermal expansion coef ficient of the metal in ppm / 8 C a G 5 thermal expansion coef ficient of the glass in ppm / 8 C

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 P 2 in newtons , as given by the following equation :

P 2 5 2 9 . 807 WA (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 Sur y i y al Temperature . By adding the preloads computed by Eqs . (3) and (4) one obtains the approximate total axial preload P T , 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 Gi y 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 P T , in newtons , to the edge of the lens can be approximated from the following empirically derived formula given by Kowalski : 9

M 5 0 . 2 P T D R (5)

where D R is the pitch diameter in cm of the thread on the ring .

Axial Stress Introduced at Reduced Temperatures . If the temperature decreases by 2 D T in 8 C from that existing at assembly , the preload exerted by the retaining ring increases due to dif ferential expansion of the mount and the optical component . The change in axial preload on the glass , P 1 , in newtons , is given by Eq . (3) as defined above . The usual lower limit for survival temperature of military optical instrumentation is 2 62 8 C . It should be noted that the preload P T 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 S B G within the glass can be estimated as 2( P 1 1 P T ) / A G or 2( P 1 1 P T ) / A 9 G as appropriate . The average (or bulk) stress S B M within the cell wall can be estimated as ( P 1 1 P T ) / A M . 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’’


stress develops . The magnitude of this stress S R (N / m 2 ) for a given temperature drop D T , in 8 C can be estimated by the following equation : 7

S R 5 K 4 K 5 D T (6)

where K 4 5 ( a M 2 a G ) / ((1 / E G ) 1 ( D G / 2 E M t C )) K 5 5 (1 1 ((2 D r ) / ( D g D T )( a M 2 a G ))) D G 5 optical component OD in mm

t C 5 mount wall thickness outside rim of the optic in mm A r 5 radial clearance in mm

If D r exceeds D G D T ( 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 D T due to rim contact .

Combined Axial / Radial Stress at Reduced Temperatures . Bayar 1 0 indicated that the combined ef fect 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 :

S r s s 5 (( S B G ) 2 1 ( S R ) 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 , D gap R and D gap A , in mm , between the optic and the mount due to a temperature increase of D T in 8 C from that at assembly can be estimated by the following equations :

D gap R 5 K 6 D T (8)

D gap A 5 K 7 D T (9)

where K 6 5 ( a M 2 a G ) D G / 2 K 7 5 ( a M 2 a G ) t E

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 dif ferent 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 . ]


necessarily be placed in tension ; this is the condition in which glass is the weakest . Bayar 1 0

applied the following equation for the tensile stress induced by bending :

S T 5 3 P T

2 π mt 2 E F 0 . 5( m 2 1) 1 ( m 1 1) ln

Y 2

Y 1 2 ( m 2 1)

Y 2 1

Y 2 2 G (10)

where S T 5 tensile stress in the component (N / m 2 ) P T 5 applied axial load (N) m 5 1 / Poisson’s ratio t E 5 edge thickness of component Y 1 5 innermost contact radius (cm) Y 2 5 outermost contact radius (cm)

As mentioned earlier , the general tolerance for tensile stress is 6 . 9 3 10 6 N / m 2 .

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 ef fects upon system performance . Surface deformations due to mount-induced forces may also occur . Within limits , the ef fects 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 . ]


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 t E (mm) is in accordance with the following equation , the design becomes relatively insensitive to temperature change : 1 0

t E 5 ( D G / 2)( a M 2 a G ) / ( a E 2 a M ) (11)

where all terms are as defined above . Valente and Richard 1 1 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 AWt E / ( π Rd (( E E / (1 2 … 2 E )) 1 E S )) (12)

where A 5 acceleration factor W 5 weight of optical component in N t E 5 thickness of elastomer layer in m R 5 optical component OD / 2 in m d 5 optical component thickness in m

E E 5 Young’s modulus of elastomer in N / m 2

E S 5 Shear modulus of elastomer in N / m 2

… E 5 Poisson’s ratio of elastomer


FIGURE 12 A simple eyepiece configured for assembly by dropping the lenses in place and clamping with a retainer . [ From Ref . 1 2 . ]

The decentrations of modest-sized optics corresponding to normal gravity loading are generally quite small .

3 7 . 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 m m . 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 . 1 2 Figure 14 a shows an airspaced


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 . 14 b 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 ef fort 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 . 1 3 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 . 1 4 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 .


(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 . 1 2 . ]


FIGURE 15 Sectional view of a low light level periscope objective . [ From Ref . 1 3 . ]

This same principle was used by Fischer 1 5 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 . 1 6

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 . 1 3 . ]


FIGURE 17 Optomechanical configuration of a bubble chamber objective with lenses individually mounted in cells and stacked in a barrel . [ From Ref . 1 4 . ]

FIGURE 18 Optomechanical configuration of a low-distortion objective with stacked cell-mounted lenses . [ From Ref . 1 5 . ]


FIGURE 19 Optomechanical configuration of an astrographic telescope objective with stacked cell-mounted lenses . [ From Ref . 1 6 . ]

Valente 1 7 described how the cells were designed for interference fits within the barrel and pressed in place . Valente and Richard 1 1 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 m m .

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


FIGURE 20 An all-plastic , three-lens optomechanical subassembly with the two- part 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 . ]

(b)

(a)

design a . Design a is less expensive to produce than design b so a trade-of f 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 . ]


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 con- siderably more economical than one consisting of the equivalent separate parts that would require labor to manufacture , inspect , assemble , and align .

3 7 . 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 orienta- tions of forces tending to move the optic with respect to its mount ; steady-state and transient thermal ef fects (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-ef fective . 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 clip- mounted flat mirror subassembly . [ From Ref . 1 8 . ]


FIGURE 23 Diagram of a typical strap mounting for a Porro prism erecting subassembly . [ From Ref . 1 8 . ]

mirror . Lengths of those spacers and the free lengths and stif fnesses 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 . Yoder 7 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 . 1 8 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


FIGURE 24 Typical construction for a first-surface mirror subassembly with glass-to-metal bond securing the mirror to its mount . [ From Ref . 1 8 . ]

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 . Yoder 1 9 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 dif ferent types of materials so their thermal expansion properties do not match . Dif ferential expansion as the temperature changes may cause optical components to decenter or tilt , thereby af fecting 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 . 1 8 . ]


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 . 2 0 . ]


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 stif f 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 Hookman 2 0 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 ef fects 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 high- performance 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


3 7 . 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) .

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