Tolerance analysis of lenses with high zoom ratio

Transcription

1 Tolerance analysis of lenses with high zoom ratio Chir-Weei Chang, a, Gung-Hsuan Ho a, Chy-Lin Wang a, Wei-Chung Chao a, John D. Griffith b a Opto-Electronics & Systems Laboratories/Industrial Technology Research Institute, 195, Sec.4, Chung Hsing Rd., Chutung, Hsinchu, 31, Taiwan, R.O.C. b Optical Products, Eastman Kodak Company, 8 Lee Road Rochester, NY ABSTRACT Axial and lateral compensators are used for zoom systems tolerancing to improve the manufacturability of high zoom ratio lenses. An investigation into the tolerance distribution for various zoom ratios, and compensation conditions and corresponding performance is presented. A flexible method is applied to a rear focusing four-groups 1X zoom to demonstrate the effectiveness of different compensators Keywords: zoom lens, tolerance analysis, compensators 1. INTRODUCTION The demanding of lens with high zoom ratio is increasing from the growing of commercial market such as digital video camcorder (DVC) and digital still camera (DSC). While compactness is a general requirement for these commercial products, the trade-off between manufacturing tolerances, cost, and performance become critical 1, 2. Moreover, in such case, certain adjustment with the lens during assembly process seems inevitable and deciding the compensators for adjustment is a challenge issue. Therefore, a reasonable strategy of analyzing the tolerance distribution amount various zoom positions and compensating conditions for lens with high zoom ratio is desirable Errors in zoom lens assembly Optical and mechanical errors can both happen in a lens system. Optical errors are from lens manufacturing process such as curvature, thickness, surface irregularity, and material. In another aspect, opto-mechanical errors originate from lenses mounting and assembling such as lens decenter, tilt, and positioning. In general, all these optical and mechanical errors can be categorized into centered errors and decentered errors, these errors will cause a significant loss of image quality if tolerances can not be controlled within reasonable manufacturing capabilities. To compensate these two kinds of errors, axial compensators together with non-axial compensators are needed. In a zoom lens assembly, these errors should be specially considered due to the lens consists multiple moving groups and mounting the lens become more complex Tolerance in lens with high zoom ratio For present commercial zoom lens for DVC or DSC, the specifications are in a relatively high standard i.e. the f-number might be at least 1.8, the field of view (FOV) might be higher than 6 (2ω) degree at the wide end, and zoom ratio might require higher than 1. Other important requirement is compactness and less lens elements. For a high pixel count 4 Mega or 5 Mega digital camera, the typical diagonal length of image sensor is around 1/2.5, the total track is often required to be less than 8mm. These requirements make a lens usually have more number and higher terms of aspheric surfaces, larger angle of incident, more special material is used, and more moving parts comprised. As shown in the Fig.1, the zoom lens consisting 9 lens elements meets the specification of the main stream requirement of DVC and DSC dual mode lens. The power allocation for zooming groups is well-known (+, -, +, +) ChirWeeiChang@itri.org.tw; phone ; fax ; ICO2: Optical Design and Fabrication, edited by James Breckinridge, Yongtian Wang, Proc. of SPIE Vol. 634, 6341P, (26) X/6/$15 doi: / Proc. of SPIE Vol P-1

2 distribution. It provides 1 zoom ratio while maintains compactness which inherited from its zooming motion design. When the lens zooming from tele to wide end, the second lens group moves from image to object side, the third and forth lens group move from object to image side. There are totally 4 aspheric surfaces distributed on 3 lenses. 4HH Fig1. Example zoom lens for digital image capturing device Thus the tolerance of such a lens assembly would be tighter than a conventional lens with medium level of zoom ratio. To loosen the tolerance, more detail balancing of the tolerance distribution amount various zoom position is required. This article discusses the relationship between tolerance distributions in difference focal length and how effective the compensators could be under such conditions. 2. TOLERANCING METHOD 2.1. Tolerance classification To examine the tolerance analysis and the above mentioned characteristic, we prepared a series of tolerance sets, from e1 to e1, which represent the ranking of manufacturing tolerance. As shown in Fig.2, it provides 1 classes of tolerance set for all the optical and mechanical errors including spherical elements, aspheric elements, flat element, and assembly tolerance. The tolerances in the table are reference from various sources 3, 4 that would be considered reasonable for most of the case. Each class of tolerance represents different manufacturing difficulty. For example, in e1, all the tolerances approach to the manufacturing limit and on the contrary, in e1, all the tolerances represent the down-to-earth optics manufacturing technology. Proc. of SPIE Vol P-2

3 Spherical lens Aspherical lens power-irr thickness index V-num% surf single double asph thickness index V-num% surf asph surf tilt(min) asph P/I P/I decenter tilt e1 / /.1 / e2 1/ /.1 1/ e3 1/ /.25 1/ e4 2/ /.25 2/ e5 2/ / 2/ e6 3/ / 3/ e7 3/ /1 3/ e8 5/ /2 5/ e9 1/ /3 1/ e1 12/ /8 12/ Flat element Assembly tolerance power-irr thickness index V-num% lens tilt lens group tilt group group position decenter position e1 / e2 1/ e3 1/ e4 2/ e5 2/ e6 3/ e7 3/ e8 5/ e9 1/ e1 12/ Fig.2 Tolerance table for 1 classes of tolerance sets A rear focusing four-group zoom system with 1X zoom ratio is designed 5. As shown in the flowchart of Fig.3. Each tolerance set is input sequentially into optical analysis software, in this paper CODEV, to calculate the corresponding performance degradation. We defined a field-weighted MTF at a third of Nyquist frequency to suit the general requirement of commercial zoom lens for digital image. Proc. of SPIE Vol P-3

4 Begin Input Tolerance Sets (e1,e2,..e1) Tolerance Calculation Yes Add Compensators Input Next Error Sets? No Output Results End Fig.3 Tolerance calculation flowchart MTF Examople tolerance vs MTF BFL, axial and non-axial BFL plus axial BFL e1 norminal e2 e3 e4 e5 e6 e7 e8 e9 e1 Tolerance sets Fig.4 MTF varies with tolerance sets and compensators 2.2. Compensators test During the calculation, compensators are added. There are three cases, first, back focal length (BFL) adjustment, second, BFL plus one group of lens as axial compensator, and third, further plus a single decentering as the non-axial compensator. Considering a 2σ yield distribution, 97.7% yield rate, and follow the procedure of the flowchart and calculate different cases of error sets and compensators in term, we can obtain the curves as shown in the Fig.4, which correspond to the 1X zoom lens at the wide configuration. These curves show that for a high zoom ratio compact lens, simply adjusting the BFL is inadequate for loosen the tolerance to a reasonable level. Even under e2 or e3 tolerance set that represents a nearly manufacturing limit standard the system MTF is almost dropped to zero. Further adding the Proc. of SPIE Vol P-4

5 first group lens as an axial compensator, system tolerances can be loosen to e6 class but still drop to zero when in e7 class. And once a decentering compensator is added, the tolerances are much relief. The field-weighted MTF can still be maintained to an acceptable level with very easy-to-reached tolerance level, e1, which is a low cost commercial tolerance level. 3. RESULTS 3.1 Overall performance for zoom positions The above analysis procedure allowed us to examine the tolerance budget thoroughly for all the focal lengths of a zoom lens. In particular, we can use the results of this analysis to identify the suitable tolerance set and, under this condition, test how the compensators can affect the overall performance of a zoom lens assembly. As shown in Fig.5, the three curves show the MTF at a quarter of Nyquist at different focal length for three different tolerance sets, which corresponds to above mentioned tolerance sets e5, e7, and e9 respectively. All the compensators: BFL, axial, and non-axial are used. The curves show that e5 give satisfactory performance however might result relative high manufacturing cost. In contrast, e9 though could largely reduce the cost, give poor performance especially at the long focal length. The e7 seems to be a better compromise. MTF EFL e5 e7 e9 Fig.5 Lens performance versus zoom ratio for different tolerance sets 3.2 Effectiveness of compensators In the procedure of lens assembly, less compensators for adjusting usually also means less mechanical complexity and cost saved. Take e5 and e7 for consideration, and sequentially eliminate the compensators from the non-axial compensator. As shown in Fig.6 although e7 demonstrates a better tradeoff between tolerance sets and performance, its overall performance is less durable while the compensators are eliminated. When non-axial compensator is disabled, the performance is at a relative low level. It becomes totally ruined when only BFL is left as compensators. Proc. of SPIE Vol P-5

6 MTF EFL BFL+axial+nonaxial BFL+axial Fig.6 eliminating compensators for e7 MTF EFL BFL+axial+nonaxial BFL+axial BFL Fig.7 eliminating compensators for e5 The e5 case, as shown in Fig.7, showed better durability. For lacking of non-axial compensator, the performance only slightly dropped from its original performance. Even when only BFL is adjusted, the performance can still be maintained in part of the middle zoom positions. Fig.6 and 7 clearly show that there is a cost-effective strategy of the compensator such that the axial and lateral compensators are particularly efficient in error balancing of an optical system. This kind of design process bridges the gap between design and manufacturing considerations ultimately affecting the cost, performance, and manufacturability of a product. 4. CONCLUSIONS Fabrication errors always degrade optical performance if the nominal design is optimized. That is why the major cost issue of lens system manufacturing is related to the tolerance sensitivity. Therefore, fabrication errors and tolerancing procedure must be considered in the design process and a compromise between error levels and compensation conditions become crucial in production. By perturbing zoom lens with different error levels, we can decide a suitable tolerance set that best compromise the cost and performance. Furthermore the durability of the performance can be examined by testing the effects of individual compensators. Proc. of SPIE Vol P-6

7 REFERENCES 1. M. Jeffs, Reduced manufacturing sensitivity in multi-element lens systems, in International Optical Design Conference, P. K. Manhart, J. M. Sasian, ed., Proc. SPIE 4832, pp , M. Isshiki, L. Gardner and G. G. Gregory, Automated control of manufacturing sensitivity during optimization, in Optical Design and Engineering, L. Mazuray, P. J. Rogers, R. Wartmann, ed., Proc. SPIE 5249, pp , R.R. Shannon, The art and science of optical design, Cambridge University Press, Cambridge, W.J. Smith, Modern Optical Engineering 3 rd edition, McGraw-Hill, New York, K.Tanaka, Recent development of zoom lenses, in Zoom Lenses II, E. I. Betensky, A. Mann, I. A. Neil, ed., Proc. SPIE 3129, pp , Proc. of SPIE Vol P-7