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# Class Note for OPTI 521 at UA

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Date Created: 02/06/15

OPTI 521 7 Synopsis Grad Requirement 1 G Desroches Synopsis of Technical Report Designing and Specifying Aspheres for Manufacturability By Jay Kumler November 21 2007 Reviewed by Gerard Desroches Abstract Since aspheres have become more common in optical designs papers such as this one have helped us to gain an understanding of how aspheres are manufactured and tested I will highlight the most important points adding comments where appropriate The author focuses on glass aspheres produced by subaperture lap by CNC processes in particular MRF magnetorheological nishing machines by QED Technologiesl It should also be noted that these guidelines might apply to diamond turned surfaces as the author notes The key points from this paper are as follows Conic sections versus higher order aspheres Testing aspheric surfaces Tolerancing Design guidelines including slope steepness size limitations and glass selection OPTI 521 7 Synopsis Grad Requirement 1 G Desroches Conic Sections or Higher Order Aspheres The general even order aspheric equation can be found in optical design references and so wares symbol designation of variables may be different from one reference to another 2 or 1 171kczrz Where c is the radius of curvature c IRo r is the radial aperture component and k is the conic constant Surface mg 2 mm 124 135 1143 15quot oc r 2 117 may Conic sections parabolic elliptical hyperbolic or circular sections created When a plane intersects a cone can be defined in the equation by varying the radius of curvature c and the conic constant k The diameter is defined by the radial component r k lt 71 gt Hmrboloid k 71gt Paraboloid 71 lt k lt 0 gt Prolafe Ellipsoidmajor k gt 0 gt Oblafe Ellipxoidminor 39 Circle Ellipse Pzrzhnlz Hyperhnlz k 0 gt Spherecircle Higher order aspheres can have all the same variables as the conic sections but can also include the higher order deformation terms is from the equation A very important point designers should remember is that although some optical design sofrwares allows optimization using the m term not all machines support its use in the expansion The author gives the rule of thumb It is safer to use the conic constant and keep the m coefficient equal to 0 I fact in my experience allowing the conic constant and uz sometimes referred to the A4 term can cause con icts during optimization In this section the author gives a detailed performance summary of a twolens f1 all spherical system versus the same system with an aspheric surface added to it comparing the effects of using only the conic constant and several higher order terms He goes even further by adding a third spherical element and comparing all the performances The amount of aspheric departure from a spherical surface is used as a metric to identify a OPTI 521 Synopsis Grad Requirement 1 G Desroches more manufacturable surface see Table l in the appendix for an example It should be noted that this depends on the aspheric guring method the MRF method which starts with a polished spherical surface and aspherizes it therefore more departure does mean longer polishing times The conclusion from these comparisons is that a higher order asphere is more effective at reducing transmitted wavefront error than adding an additional spherical element What I noticed in the examples used is that the aspheric surface was located at the pupil which is the most effective position to control most aberrations Testing Aspheric Surfaces While designers can come up with wonderful aspheric shapes the difficulty is ensuring the desired surface is produced The author gives strong arguments to stay with conic sections as they can be tested interferometrically at their natural conic foci A concave parabola concave hyperbola and concave ellipse can be tested without any additional null optics2 Even oblate spheroids concave and convex3 convex hyperbolic mirrors in re ection4 and convex hyperbolic mirrors5 Test configurations for these conic sections are also included which I found particularly interesting m 39 quotW4 Figure 1 Null testing concave ellipse at conic foci Figure 1 shows one of the test configurations from the paper Although this interferometric test does work I found it to be sensitive to decenter and tilt errors due to the stages moving when testing large mirrors Alignment of the mirror to foci can be tricky the spherical re ector typically a ball has to be located exactly at the second focus of the ellipse under test For testing higher order aspheres computer generated holograms CGH s are often used But to separate the desired diffractive order enough aspheric departure is required Offaxis surfaces can also be tested with CGH s because they can be made to compensate OPTI 521 7 Synopsis Grad Requirement 1 G Desroches between interferometer and asphere axes which sometimes usually aids in separating the diffraction orders Drawbacks to the use of CGH s are that they are expensive and unique to each aspheric surface Hologram manufacturers have also progressed in developing easier to setup null tests by adding alignment aids on the CGH as well as the diffractive null I will include tolerancing in this section as it follows nicely from the previous testing information In general the author would like to see aspheres toleranced as loose as possible As a rule of thumb he suggests the figure requirements for aspheric surfaces be two of three times that for spherical surfaces From a lens manufacturing point of view this is very desirable but from an optical standpoint may not always be possible If surface figure accuracy of the asphere is 1 micron or looser contact profilometry can be used to qualify the surface in place of a CGH or null lens This can significantly affect the manufacturing budget for a lens To this I would like to add that if contact profilometry is used more than one trace should be used Minimum 3 traces spaced 120O apart should be used to ensure that the surface doesn t suffer from astigmatism or some other nonrotationally symmetric defect Some of the newer profilometers make this task easier to do and can be programmed to do various tests automatically Design Guidelines The author states the following guidelines about using higher order aspheres When optimizing higher order aspheric coefficients you must design for a larger aperture than required for the clear aperture of the surface in order to control the polynomial inside the clear aperture and safely outside the margin of the clear aperture Design for an aperture radius at least one polishing lap footprint larger than the clear aperture When optimizing an optical system that uses a higher order aspheric surface you must optimize for more field points than you would when designing using only spherical surfaces Onaxis full field and 07 field points will sufficiently sample a system with all spherical surfaces but a system with generalized aspheres should have seven to nine field points in the model Higher order aspheres improve performance in diamond turned optics and molded optics with little or no increase in cost or complexity When designed correctly higher order aspheres can improve the aspheric fit and reduce the departure and difficulty of an aspheric surface My comments about these guidelines are that in general they are good rules of thumb but there are occasions where following these would be difficult For example optimizing the asphere over an aperture one lap footprint larger than the clear aperture is good practice but special mechanical constraints may make this difficult to adhere to Also the optical designer would need to know the actual size of the polishing footprint OPTI 521 7 Synopsis Grad Requirement 1 G Desroches Allowing this size to be a variable could lead to very small footprints being required which could potentially result in surface slope problems This brings us to the steepness of the slope aspheric slope section Designing with higher order terms in the polynomial can lead to surfaces with steep slope and even slope reversals To allow proper figuring of such surfaces the size of the polishing footprint must get smaller to address these small features The author notes that if the departure from best fit sphere is greater than 2 microns aspheric departure per mm of aperture the aspheric figuring will be slow it will be difficult to keep the surface smooth and the interferometric testing will likely be sensitive to decenter errors Size and geometry of the asphere should be considered carefully to ensure we don t exceed the mechanical limits of the machine The author includes some machine capabilities as well as some practical guidelines of aspheric limitations with MRF technology including max diameters lt240mm thickness lt90mm surface figure accuracy 0008waves rms on aspheres lt50mm diameter to name a few of the more interesting ones See appendix for the complete table A concave or convex surface can also affect the manufacturability In general a convex surface is desired because it isn t limited by the polishing wheel diameter as in the case of a concave surface The polishing tool for a concave surface must be smaller than the radius of curvature of the surface but a short convex radius can be polished with a large diameter polishing wheel Additionally the actual footprint of the polishing tool limits the defect size that can be corrected The rule of thumb here is for the smallest diameter feature that needs to be corrected a tool with a footprint of half that diameter should be used to effectively correct the defect A defect can be a local defect like a bump and it can be rotational like spatial periods on the lens The next guidelines target glass selection In my experience these are universal guidelines as most lens manufacturers like to work with stable nonstaining glasses without steep curvatures whether it is an aspheric surface of not Unfortunately the glass types often desired in high performance optical design are the ones that manufacturers don t like to work with because they are stain sensitive very soft heat sensitive etc generally poor mechanical properties Conclusion Although some of the information at first glace seems to be obvious to someone who has worked with or designed aspheres before it does provide a very good base knowledge of the potential problems and pitfalls for a relatively new designer I believe that author s intent was to make optical designers new and experienced more aware that real mechanical difficulties exist in manufacturing and testing aspheres and staying within a set of soft rules of thumb can help both the optical designer and the lens manufacturer achieve success OPTI 521 Synopsis Grad Requirement 1 G Desroches Appendix Table 1 Transmitted wavefront and aspheric departure for 2 and 3 element designs EH and Fused Eilioa Three elem err BHTJ39EiE39Fused Silica aspher o aeoherio departure at391 aspiherio departure at 1111 aepherio wavefront wavee mm diameter departure at 11213 wavefront waves mm diameter depa rture at 120 aqaherio order rme 1mm mm diameter rmeli mm mm diameter spherian 4351MDED DJIHZIEI 11121501 151 391 E 1 eonie En l BEBEE 113961 01357 CI 1QT1 ISLET 32 am order spherioai Eu x d REESE aaror EMEEE ELEM 391 Ei1 5th order spherioai EaEl EBBE FEEE LBFEE 1131121345 115151 ISLE11511 3th order spherioai 1113131311 LESEE 1583 EMEEIE 1433 ELTETE quot1Eth order spherical LEIGHQE 14534 112136 LDEEEF39E 1415135 ELTEIE1 quotilth order spherioal EtlJrEIEEIEE RATES 1198 euros44 ELI15H H724 Table 2 Practical limitations of aspheric figuring by polishing With MRF Technology at Coastal aspirate amplitude wrishieg eeiy 5 misreer demeasirareci er 99 13331 diameter surface from a petisiaed sweetest eerfaee Asmara ameliteae aspirate gendered are 350 decrees epertere ever 45 em diameter see figure 8 eeiishee Aepherte slepe em 21 aliases per ream as eleeg as east is 126 mm ritemeier Sarfeee Egress erasures sees were rare demeaetra e a powered errsprayer 233 to 3 331123133 diameter Amazes of Sarfaee grape 13 mierered aaa 3er tie demonstrated or some qrmt ed parebeiie mirrors iii are is diameter we effaxis era eee m e QZZX and 400X capabilities 400 M 539 439 some f meeeeeew g convex f wfa hem39SPhere WW QZZX small 50 mm wheel 7 aeeeeeeeeeeeeeeer aeeeeeeeeeeeeeeee W Q22 X large 150 mm wheel eweWWWWWW arrZ g ge 022 400X ConcaVe mam44 hemispher 444444 5444444444444444444M41394 M 44quot 44 4444444444444444444 i t t a we as age a age g i 1539 39439 4quot m ifff ffffffffffw f 200 400 Flat 400 200 radius of curvature mm Figure 2 Size capabilities of QED MRF machines courtesy of QED 35 V 50 75 400 100 OPTI 521 7 Synopsis Grad Requirement 1 G Desroches References J Kumler Designing and Specifying Aspheres for Manufacturability in Current Developments in Lens Design and Optical Engineering VI Proc of SPIE 5874 2005 Endnotes 1 QED Technologies 1040 University Avenue Rochester NY 13607 Daniel Malacara Optical System Testing WileyInterscience39 2nd edition January 1992 Null tests of Oblate spheroids by John M Rogers and Robert E Parks Applied Optics Vol 23 No 8 15 April 1984 Null test for hyperbolic convex mirrors Donald Bruns Applied Optics Vol 22 No 1 1 January 1983 Selfnull corrector test for telescope hyperbolic secondaries Aden B Meinel and Marjorie P Meinel Applied Optics Vol 22 No 4 15 February 1983

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