Centration of optical elements

Centration of optical elements Ezra Milby *a, Jim Burge a a College of Optical Sciences, 163 E University Blvd, Tucson, AZ 85723 ABSTRACT Axisymmetric optical components such as lenses are frequently centered with the use of rotary air bearings, guided by optical instrumentation that use reflected or transmitted light. This report systematically explores methods of adjusting optical elements including wedged-shims, fine pitch screws, and positioning rods with a goal of defining the accuracy that can be expected. Analysis of the performance is supported with experimental data. A characterization and discussion of the merits of each positioning method is additionally presented. Keywords: centration, alignment, air bearing, autocollimator, assembly, lens, shim 1. INTRODUCTION For optical engineers that are involved in the manufacturing of an optical system, the topic of alignment is an assured aspect of the assembly process. Alignment will be defined as the act of positioning the optical axis of an element coincident to a defined mechanical axis. The task of alignment is frequently performed for optical elements housed in a lens barrel. At a point in the design of a system, an optomechanical engineer will place tilt and decenter requirements on the lenses. These tolerances are assigned based on the acceptable image quality degradations to which any tilt or decentration of an optical element induce. The nexus between the optomechanical design tolerances and a manufactured optical system is the alignment process. A common method of alignment is done through the use of a rotary air bearing and an autocollimator. The conducted research investigated different techniques that can be used to position a lens as it is centered during alignment. Specifically this paper characterizes the resolution of the finest movement achievable, and discusses the relative merits of positioning a lens through the use of wedged-shims, fine pitch screws, and positioning rods. 2. LENS ALIGNMENT PRINCIPLES 2.1 Alignment Definition To align an axisymmetrical optical element, the optical axis needs to be adjusted to be coincident to a mechanical datum axis. For a lens, the optical axis is defined as the line connecting the center of curvature of the two surfaces. In the case of a plano convex lens, the optical axis is defined as the line that travels through the center of curvature of the convex surface and is normal to the planar surface. For a perfect lens, symmetry exists about this axis. Figure 1. Optical axis bisects the center of curvatures. * ezra.milby@baesystems.com Optical Manufacturing and Testing IX, edited by James H. Burge, Oliver W. Fähnle, Ray Williamson, Proc. of SPIE Vol. 8126, 812616 211 SPIE CCC code: 277-786X/11/$18 doi: 1.1117/12.894126 Proc. of SPIE Vol. 8126 812616-1

2.2 Lens Assembly and Centration Measurement Methods A variety of methods exist to measure the centration of a lens for alignment. Before discussing these methods, it worth mentioning that perhaps the most simple assembly method is to design a lens barrel with a tight radial clearance between the outer diameter of the lens and the inner diameter of the barrel. By doing this, a lens can be nominally positioned by inserting shims of equal thickness around the edge of the lens. This method thereby relies on the mechanical tolerances placed on both the barrel and the optical elements 1. A more precise technique incorporates a rotating spindle that typically has an air or hydraulic bearing. These instruments are commonly used in precision machining for the purpose of metrology on axisymmetric parts. In the application of optical alignment, the mechanical axis of the lens barrel is positioned to be coincident to the rotation axis of the spindle. This is easily accomplished by using a dial gauge to observe and minimize the total indicator runout (TiR ) of a datum surface on the lens barrel as it spins on the rotating spindle. With the mechanical axis of the lens barrel coincident to the rotation axis, the optical axis of the lens is then subsequently co-aligned. The centration of the lens can be measured through a variety of methods. The first method, and one typically done by a machinist with the task of optical alignment, is to again use the dial indicator but rather placed in contact with the lens to measure the TiR. Another technique to measure lens position is an interferometric method incorporating a Fizeau interferometer. A test plate is fixed in place at a close proximity to the lens under alignment. A collimated light source is incident on the reference test plate, reflected off the lens surface under test, and back through the test plate thereby creating fringes. As the lens assembly is rotated, the observed fringes will move. As adjustments are made, the fringe movement becomes smaller until a point where they no longer move indicating that the lens is aligned. For more information the reader is suggested to consult Yoder 2. The most common method to observe lens position during the centration process is through the use of an autocollimator. For a spherical surface, a focusing lens is placed in front of the autocollimator. The center of curvature of the surface to be aligned is then adjusted to be confocal with the focal point of the focusing lens. Now in the case of plano surface, collimated light is simply sent directly to the surface and reflected back to the autocollimator. Any tilt present in a plano surface will cause the focused spot observed through the autocollimator to have a circular motion as the spindle axis is rotated. 2.3 Alignment Procedure The following procedure gives a brief and general overview to an alignment process that is applicable to optical systems for which lenses are seated into a barrel. The described procedure makes use of a rotary air bearing in conjunction with an autocollimator and was used in the subsequent experiment. Before beginning any alignment, tilt present on the surface of the rotary air bearing must be removed. This ensures that the rotation axis is orthogonal to the planar surface of the air bearing. It is preferential to use an air bearing that has tilt adjustments. In the event that this feature is not present on the air bearing, one can circumvent this through the use of a tip/tilt stage mounted on top of the bearing surface. Tilt of the rotating surface is measured by observing the TiR using a common dial gauge, which has a typical resolution of.5 This rotation axis will defined as the Z axis. The next step is to align the mechanical axis of the lens barrel to the rotation axis of the air bearing. The TiR of a datum surface on the lens barrel can again be measured by a dial gauge. Adjustments of the barrel in X and Y are made to minimize the TiR, which indicates the degree of co-alignment to the rotation axis. TiR values of under.5 are readily obtainable. With the mechanical axis aligned to the rotation axis, it is worth moving the dial indicator to the lens seat to ensure that tilt is not present. For higher precision TiR measurements, a capacitance gauge can be used for conductive surfaces to measure small changes in capacitance between a grounded spinning lens barrel and capacitance sensor head 3. From here the lens under test is placed on its respective seat within the barrel. An autocollimator looks at the reflection generated off the surface of interest. If there is tilt present for the given lens, the observed reflected spot will rotate on a circular path as the system is spun on the rotary air bearing. Centration adjustments are made to position the lens until the reflected spot viewed through the autocollimator is rotating in place. For the benefit of the optical engineering community, the acronym TiR for total indicator runout will be used in attempt to prevent confusion with total internal reflection (TIR) Proc. of SPIE Vol. 8126 812616-2

3. EXPERIMENT The primary goal of this experiment was to characterize techniques used to position a lens as it is being centered within the lens barrel. The positioning techniques investigated included nylon wedged-shims, fine pitch screws, and positioning rods. This characterization was primarily concerned with the resolution of each techniques, or in other words, characterizing the smallest lateral movement that each method can induce upon a lens. The previously described alignment procedure utilizing a rotary air bearing and autocollimator was implemented in order to perform this investigation. 3.1 Experimental Setup The alignment test bed can be observed in Fig. 2. In the bottom left corner is the rotary air bearing with an interface plate and lens assembly on top. In the upper left hand corner is the autocollimator, which has a computer monitor to observe the reflected spot. Figure 2. Alignment test bed A model lens assembly was created in order to facilitate the investigation of the centration techniques. A plano-convex lens with a 2 inch diameter and 6mm focal length was situated into a lens barrel with an autocollimator observing the reflections from the plano surface. The radius on the convex surface situated into the lens seat was 3.9mm. Figure 3. Lens with a small tilt angle Each of the positioning techniques induced a lateral displacement onto the lens, which in turn caused the lens to rotate about its center of curvature while sitting inside of the lens cell. For small tilt angles, a simple tangent relation exists Proc. of SPIE Vol. 8126 812616-3

between the lateral displacement δ and the tilt angle θt. The distance D is the perpindiculat distance from the center of curvature and the contact point of the positioning mechanism: (1) Three variations of a model lens barrel were machined to support each of the positioning techniques. A large clearance of.1 was designed between the outer diameter of the lens and the inner diameter of the lens barrel wall for two purposes. The first purpose was to enable large movement of lens within the barrel. The second was to provide large room to which shim stock could be inserted and maneuvered. In practice, lens barrels are designed to have much smaller clearances. The lens was positioned onto a sharp corner interface. A sharp corner was used to simplify the machining process. A small breadboard interface plate was mounted to the rotary air bearing so that fixtures could be installed to position the lens barrel. The inner diameter of the lens barrel was aligned to the rotation axis of the air bearing by a dial gauge as seen in the following Fig. 4. The barrel positioning fixtures consisted of three ¼ -8 pitched screws spaced 12 degrees around the barrel s outer diameter. Figure 4. Dial gauge used to center lens barrel to rotation axis Fine pitch screws were one of three lens positioning techniques investigated. A 4-48 screw was nominally chosen and inserted into three threaded holes evenly spaced 12 degrees on the lens barrel. As it turns out, and will be discussed more in detail, the interface between the screw and the lens critically affects the nature of the lens movement as it is positioned. To that regard, investigated screw to lens interfaces included a crowned-end and flat-end. The 4-48 screw with the crowned-end was created by polishing a long radius spherical profile using a piece of emery cloth. For both of these screw end-types, the use of a flat.1 thick plastic shim stock placed between the lens and the screw for the purpose of giving a level of compliance was additionally investigated. (a) (b) Figure 5. Fine pitched screws and shim wedges characterized for lens positioning. Proc. of SPIE Vol. 8126 812616-4

Next to fine pitch screws, shims are also frequently used to position lenses because of their simplicity. Custom wedge shaped shims made out of a small diameter cylindrical nylon rod were created. The nylon rods were purchased from McMaster-Carr and had an initial diameter of 1/8 and a length of ½. A razor blade was used to cut a sloped surface onto one face of the rod. This wedge shaped shim enabled fine adjustments to be made by pushing down on the end of the shim. This style of shim gave more adjustment versatility than the traditional planar shim stock of fixed width Figure 6 - External positioning rods The last positioning method used was an external apparatus that was placed on the outside of the lens barrel. Similar to the fine pitch screw method, the three fixtures were placed at 12 degree increments around the diameter of the barrel. There fixtures made adjustments to the lens by moving.1 inch diameter rods that traveled via through-holes machined on the lens barrel walls. The positioning rods were adjusted by a micrometer and had a flat end. These fixtures were created to simulate a device that could be constructed in a rapid high volume manufacturing environment. Typically holes machined into lens barrels for positioning purposes are subsequently filled or plugged once the optical system is assembled. 3.2 Autocollimator Calibration The instrument used to measure tilt angle in this experiment was a Point Source Microscope (PSM). Since the reflection from a planar surface was under observation, the PSM was used in the autocollimation mode. This instrument was calibrated by measuring the diffracted angles from a 1lp/mm Ronchi grating. The grating was illuminated by a 632.8nm HeNe laser. The angles of the +/- 1 orders are described by the simple diffraction equation. The PSM has the advantage of being able to measure tilt angles from spherical surfaces by using a microscope objective to create a converging beam. When used in this configuration, the focal point of the objective is placed coincident with the center of curvature of the spherical surface of interest4-5. As within any autocollimator, the experimenter needs to verify if the output angle is describing the wavefront angle or the tilt angle of the optic under test. The wavefront angle has a factor of two larger than the tilt angle because the autocollimator is observing a reflection. 4. DATA 4.1 Resolution of Finest Movement The histograms show the minimum possible lens movements that each of the positioning techniques could generate. These plots represent a series of the most sensitive adjustments made for each technique in order to create the finest resolution of movement. Angular measurements were observed and converted to decenters using Equation 1. The 4-48 screws and the positioning rods began in a non-contact position to the lens. Each of these mechanisms were then advanced in a series of the smallest possible increments until a torque greater than a hand-tighten was needed. The Proc. of SPIE Vol. 8126 812616-5

wedged shim resolution were measured by creating small pushes on the edge of the shim such that a movement to just overcome static friction was achieved. Finest Movement Histogram: Crowned 4-48 Screw 15 Finest Movement Histogram: Crowned 4-48 w/ Shim 1 8 1 6 5 4 2 1 2 3 4 1 2 3 4 1 8 6 4 2 Finest Movement Histogram: Flat-Ended 4-48 Finest Movement Histogram: Flat-Ended 4-48 w/ Shim 12 1 8 6 4 2 1 2 3 4 1 2 3 4 15 Finest Movement Histogram: Positioning Rod 8 Finest Movement Histogram: Wedged Shim 1 6 4 5 2 1 2 3 4 1 2 3 4 Figure 7. Histograms showing an ensemble of minimum increment movements. Proc. of SPIE Vol. 8126 812616-6

4.2 Centration and Average Time The following table shows the series of trials performed to measure how much residual decentration was left after lens was centered. In addition to the residual decentration, the time elapsed to achieve that decentration is shown. The elapsed time began, once the reflected spot was within the FOV of the autocollimator, which was approximately 25mrad. While the time taken to achieve these centrations is a relative measurement, the values do provide a means for comparison between each of the techniques and provide a quantitative relationship to a qualitative description for each of the techniques. Table 1. Average time to center lens & residual tilt angle. Probe Crowned 4-48 Flat 4-48 Shim Wedge Time Decenter Time Decenter Time Decenter Time Decenter s s s s 48.92 61.248 43.85 9.178 137.27 47.66 94.186 85.169 8.197 43.177 35.69 88.174 22.52 18.151 15.297 77.153 6.72 2.157 85..169 88.174 15.151 16.16 81.161 86.17 Probe w/ Shim Crowned 4-48 w/ Shim Flat 4-48 w/ Shim Time Decenter Time Decenter Time Decenter s s s 57.166 155.177 167.331 17.165 61.125 133.264 23.84 624.313 176.349 18.71 55.219 15.28 49.136 42.241 145.287 132.125 263.215 145.288 5. DISCUSSION The best positioning technique was the use of the wedged-shim with a shallow wedge angle. In the case of the shims, the ability to position the lens completely depends on the shim geometry. A shallow wedge angle provides a higher degree of resolution. With a shallow angle however, there exists a tradeoff between a higher resolution and a smaller range of adjustment. Since the geometry of the shim is critical in order for this technique to be utilized, a downside is a large amount of time can be spent to create the correct shape and sized shim. Though once created, the wedged-shim is one of the fastest position techniques as seen in Table 1. The next best positioning technique was a flat ended 4-48 fine pitch screw. This technique, like the shim, provided a reasonably quick way to position the lens. At this point, it is worth discussing the effects of having a flat versus crowned screw end in contact with the lens. During the course of the experiment the crowned screw had a greater propensity to lift the lens out of the seat. The lens exists in an over constrained state by having three contact points around is edge. A force applied to the edge of the lens will cause a lateral displacement, which in turn will rotate the lens in the seat. Ideally when a positioning screw pushes laterally on the lens, it will cause a roll such that optical axis will rotate towards the positioning screw. Due to the nature of being overconstraint, there is however at times a propensity for the opposite to happen where the lens will pop up and lift out of the seat. This typically occurs after tightening a screw when the lens is already under a large amount of force about its edges from the positioning screws. One can immediately tell when the lens begins to lift out of the seat because the reflected spot seen through the autocollimator will begin to move in the direction opposite to that expected for a given screw adjustment. A keen observation made was that the crowned 4-48 screw had a greater propensity to lift the lens up and out of the seat as compared to the flat-ended 4-48. It is suspected that this propensity was enabled because the round profile of the crowned end created a fulcrum to rotate about than the larger area of contact provided by the flat end. The net result of this is that ability of the crowned 4-48 to center the lens Proc. of SPIE Vol. 8126 812616-7

was more erratic. This erratic nature was the cause for a longer average centering time for the crowned 4-48 as compared to the flat-ended 4-48. Figure 8 also demonstrates this erratic nature by illustrating the angular trace of the reflected spot observed by the autocollimator as the lens is centered using both the flat-ended and crowned 4-48. Notice how for the crowned 4-48, the centroid moves diagonally back and forth over the centered position. This was due to the lens lifting up and out of the seat. Centroid Position - Y (μrad) 5 4 3 2 1 Centroid Trace: Flat-End 4-48 Centroid Position - Y (μrad) 3 2 1-1 -2 Centroid Trace: Crowned 4-48 -3-2 -1 1 2 3 Centroid Position - X (μrad) -3-2 -1 1 2 3 Centroid Position - X (μrad) Figure 8 - Centroid trace showing the erratic nature induced by a crowned screw In all cases, adding a piece of a flat plastic.1 thick shim-stock with idea of giving additional level of compliance actually made the act of centering the lens more difficult. This is reflected in the longer average centering time seen in Table 1. With the regards to the possibility of a lens lifting up and out of its seat, a strong advantage of the wedged-shim technique is that a downward force is always applied thereby eliminating the effect. One can see in Table 1 that the times to center the lens with the wedged-shims were fairly consistent because the erratic nature did not exist that occasionally occurred with the other screw and rod techniques. 6. CONCLUSION Of the characterized techniques used to position a lens as it centered during the alignment process, it was found the wedged-shims provided the easiest, most consistent and reliable method to adjust a lens. The nature of the small angle slope provides a means to make fine adjustments and intrinsically places a downward force onto the lens to preventing it from lifting up and out of the seat while being moved. Caution must be yielded for techniques that place a lens in an overconstrained state because of the risk of the optical element moving in an undesirable direction. 7. REFERENCES [1] Hopkins, R.E. and Walsh, K.F., Alignment of Precision Lens Elements, Proc. SPIE 483, (1984) [2] Yoder, P. R., [Mounting optics in optical instruments]. SPIE Press, Bellingham WA, (28). [3] Bayar, M., Lens barrel optomechanical design principles, Optical Engineering, Vol. 2, No. 2, (1981) [4] Parks, R. E., " Alignment of Optical Systems," International Optical Design Conference - Technical Digest, Paper MB4, (26) [5] Parks. R.E., Lens centering using the Point Source Microscope, Proc. SPIE 6676, 66763-1 (27). Proc. of SPIE Vol. 8126 812616-8