Synopsis of Technical Report: Designing and Specifying Aspheres for Manufacturability By Jay Kumler

Transcription

1 OPTI 51 Synopsis (Gad Requiement #1) G. Desoches Synopsis of Technical Repot: Designing and Specifying Asphees fo Manufactuability By Jay Kumle Novembe 1, 007 Reviewed by: Gead Desoches Abstact Since asphees have become moe common in optical designs, papes such as this one have helped us to gain an undestanding of how asphees ae manufactued and tested. I will highlight the most impotant points adding comments whee appopiate. The autho focuses on glass asphees poduced by sub-apetue lap by CNC pocesses, in paticula MRF (magnetoheological finishing) machines by QED Technologies 1. It should also be noted that these guidelines might apply to diamond tuned sufaces as the autho notes The key points fom this pape ae as follows: - Conic sections vesus highe ode asphees - Testing aspheic sufaces - Toleancing - Design guidelines, including slope steepness, size limitations and glass selection 1

2 OPTI 51 Synopsis (Gad Requiement #1) G. Desoches Conic Sections o Highe Ode Asphees The geneal even ode aspheic equation can be found in optical design efeences and softwaes (symbol designation of vaiables may be diffeent fom one efeence to anothe): Suface sag = Z = 1+ 1 c ( 1+ k ) c Whee c is the adius of cuvatue (c = 1/R 0 ), is the adial apetue component and k is the conic constant. Conic sections, paabolic, elliptical, hypebolic o cicula sections ceated when a plane intesects a cone, can be defined in the equation by vaying the adius of cuvatue c and the conic constant k. The diamete is defined by the adial component. k < 1 Hypeboloid k = 1 Paaboloid 1 < k < 0 P olate k > 0 Oblate k = 0 Ellipsoid Ellipsoid Sphee( cicle) ( majo) ( mino) Highe ode asphees can have all the same vaiables as the conic sections but can also include the highe ode defomation tems α s fom the equation. A vey impotant point designes should emembe is that although some optical design softwaes allows optimization using the α 1 tem, not all machines suppot its use in the expansion. The autho gives the ule of thumb: It is safe to use the conic constant and keep the α 1 coefficient equal to 0. I fact, in my expeience, allowing the conic constant and α (sometimes efeed to the A 4 tem) can cause conflicts duing optimization. In this section the autho gives a detailed pefomance summay of a two-lens, f/1, all spheical system vesus the same system with an aspheic suface added to it, compaing the effects of using only the conic constant and seveal highe ode tems. He goes even futhe by adding a thid spheical element and compaing all the pefomances. The amount of aspheic depatue (fom a spheical suface) is used as a metic to identify a

3 OPTI 51 Synopsis (Gad Requiement #1) G. Desoches moe manufactuable suface, see Table 1 in the appendix fo an example. It should be noted that this depends on the aspheic figuing method; the MRF method, which stats with a polished spheical suface and aspheizes it, theefoe moe depatue does mean longe polishing times. The conclusion fom these compaisons is that a highe ode asphee is moe effective at educing tansmitted wavefont eo than adding an additional spheical element. What I noticed in the examples used is that the aspheic suface was located at the pupil, which is the most effective position to contol most abeations. Testing Aspheic Sufaces While designes can come up with wondeful aspheic shapes, the difficulty is ensuing the desied suface is poduced. The autho gives stong aguments to stay with conic sections as they can be tested intefeometically at thei natual conic foci. A concave paabola, concave hypebola and concave ellipse can be tested without any additional null optics. Even oblate spheoids (concave and convex) 3, convex hypebolic mios in eflection 4 and convex hypebolic mios 5. Test configuations fo these conic sections ae also included which I found paticulaly inteesting. Figue 1: Null testing concave ellipse at conic foci Figue 1 shows one of the test configuations fom the pape. Although this intefeometic test does wok, I found it to be sensitive to decente and tilt eos due to the stages moving when testing lage mios. Alignment of the mio to foci can be ticky; the spheical eflecto (typically a ball) has to be located exactly at the second focus of the ellipse unde test. Fo testing highe ode asphees, compute geneated hologams (CGH s) ae often used. But to sepaate the desied diffactive ode, enough aspheic depatue is equied. Off-axis sufaces can also be tested with CGH s because they can be made to compensate 3

4 OPTI 51 Synopsis (Gad Requiement #1) G. Desoches between intefeomete and asphee axes, which sometimes (usually) aids in sepaating the diffaction odes. Dawbacks to the use of CGH s ae that they ae expensive and unique to each aspheic suface. Hologam manufactues have also pogessed in developing easie to set-up null tests by adding alignment aids on the CGH as well as the diffactive null. I will include toleancing in this section as it follows nicely fom the pevious testing infomation. In geneal, the autho would like to see asphees toleanced as loose as possible. As a ule of thumb, he suggests the figue equiements fo aspheic sufaces be two of thee times that fo spheical sufaces. Fom a lens manufactuing point of view this is vey desiable, but fom an optical standpoint, may not always be possible. If suface figue accuacy of the asphee is 1 micon o loose, contact pofilomety can be used to qualify the suface in place of a CGH o null lens. This can significantly affect the manufactuing budget fo a lens. To this, I would like to add that if contact pofilomety is used, moe than one tace should be used. Minimum 3 taces spaced 10 apat should be used to ensue that the suface doesn t suffe fom astigmatism o some othe non-otationally symmetic defect. Some of the newe pofilometes make this task easie to do and can be pogammed to do vaious tests automatically. Design Guidelines The autho states the following guidelines about using highe ode asphees: - When optimizing highe ode aspheic coefficients, you must design fo a lage apetue than equied fo the clea apetue of the suface in ode to contol the polynomial inside the clea apetue and safely outside the magin of the clea apetue. Design fo an apetue adius at least one polishing lap footpint lage than the clea apetue. - When optimizing an optical system that uses a highe ode aspheic suface, you must optimize fo moe field points than you would when designing using only spheical sufaces. On-axis, full field and 0.7 field points will sufficiently sample a system with all spheical sufaces, but a system with genealized asphees should have seven to nine field points in the model. - Highe ode asphees impove pefomance in diamond tuned optics and molded optics with little o no incease in cost o complexity - When designed coectly, highe ode asphees can impove the aspheic fit and educe the depatue and difficulty of an aspheic suface. My comments about these guidelines ae that in geneal they ae good ules of thumb but thee ae occasions whee following these would be difficult. Fo example, optimizing the asphee ove an apetue one lap footpint lage than the clea apetue is good pactice, but special mechanical constaints may make this difficult to adhee to. Also, the optical designe would need to know the actual size of the polishing footpint. 4

5 OPTI 51 Synopsis (Gad Requiement #1) G. Desoches Allowing this size to be a vaiable could lead to vey small footpints being equied which could potentially esult in suface slope poblems. This bings us to the steepness of the slope (aspheic slope) section. Designing with highe ode tems in the polynomial can lead to sufaces with steep slope and even slope evesals. To allow pope figuing of such sufaces, the size of the polishing footpint must get smalle to addess these small featues. The autho notes that if the depatue fom best fit sphee is geate than micons aspheic depatue pe mm of apetue, the aspheic figuing will be slow, it will be difficult to keep the suface smooth and the intefeometic testing will likely be sensitive to decente eos. Size and geomety of the asphee should be consideed caefully to ensue we don t exceed the mechanical limits of the machine. The autho includes some machine capabilities as well as some pactical guidelines of aspheic limitations with MRF technology, including max diametes (<40mm), thickness (<90mm), suface figue accuacy (0.008waves ms on asphees <50mm diamete) to name a few of the moe inteesting ones. See appendix fo the complete table A concave o convex suface can also affect the manufactuability. In geneal, a convex suface is desied because it isn t limited by the polishing wheel diamete as in the case of a concave suface. The polishing tool fo a concave suface must be smalle than the adius of cuvatue of the suface, but a shot convex adius can be polished with a lage diamete polishing wheel. Additionally, the actual footpint of the polishing tool limits the defect size that can be coected. The ule of thumb hee is fo the smallest diamete featue that needs to be coected, a tool with a footpint of half that diamete should be used to effectively coect the defect. A defect can be a local defect like a bump and it can be otational like spatial peiods on the lens The next guidelines taget glass selection. In my expeience, these ae univesal guidelines as most lens manufactues like to wok with stable, non-staining glasses, without steep cuvatues whethe it is an aspheic suface of not. Unfotunately, the glass types often desied in high pefomance optical design ae the ones that manufactues don t like to wok with because they ae stain sensitive, vey soft, heat sensitive, etc., geneally poo mechanical popeties. Conclusion Although some of the infomation at fist glace seems to be obvious to someone who has woked with o designed asphees befoe, it does povide a vey good base knowledge of the potential poblems and pitfalls fo a elatively new designe. I believe that autho s intent was to make optical designes, new and expeienced, moe awae that eal mechanical difficulties exist in manufactuing and testing asphees and staying within a set of soft ules of thumb can help both the optical designe and the lens manufactue achieve success. 5

6 OPTI 51 Synopsis (Gad Requiement #1) G. Desoches Appendix Table 1: Tansmitted wavefont and aspheic depatue fo and 3 element designs Table : Pactical limitations of aspheic figuing by polishing with MRF Technology (at Coastal) Figue : Size capabilities of QED MRF machines (coutesy of QED) 6

7 OPTI 51 Synopsis (Gad Requiement #1) G. Desoches Refeences J. Kumle, Designing and Specifying Asphees fo Manufactuability, in Cuent Developments in Lens Design and Optical Engineeing VI, Poc. of SPIE 5874 (005) Endnotes 1 QED Technologies, 1040 Univesity Avenue, Rocheste NY Daniel Malacaa, Optical System Testing, Wiley-Intescience; nd edition (Januay 199) 3 Null tests of Oblate spheoids, by John M. Roges and Robet E. Paks, Applied Optics, Vol 3, No. 8 (15 Apil 1984) 4 Null test fo hypebolic convex mios, Donald Buns, Applied Optics, Vol., No. 1 (1 Januay 1983) 5 Self-null coecto test fo telescope hypebolic secondaies, Aden B. Meinel and Majoie P. Meinel, Applied Optics, Vol., No. 4 (15 Febuay 1983) 7