Computation of Analytical Zoom Locus Using Padé Approximation

Kang Min Kim, Sun-Ho Choe, Jae-Myung Ryu and Hojong Choi
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Kang Min Kim: Department of Optical Engineering, Kumoh National Institute of Technology, Gumi 39253, Korea
Sun-Ho Choe: R&D Center, Metabiomed Corporation 215 Osongsaenmyeong1-ro, Chenongu 28161, Korea
Jae-Myung Ryu: Department of Optical Engineering, Kumoh National Institute of Technology, Gumi 39253, Korea
Hojong Choi: Department of Medical IT Convergence Engineering, Kumoh National Institute of Technology, Gumi 39253, Korea

Mathematics, 2020, vol. 8, issue 4, 1-19

Abstract: When the number of lens groups is large, the zoom locus becomes complicated and thus cannot be determined by analytical means. By the conventional calculation method, it is possible to calculate the zoom locus only when a specific lens group is fixed or the number of lens groups is small. To solve this problem, we employed the Padé approximation to find the locus of each group of zoom lenses as an analytic form of a rational function consisting of the ratio of polynomials, programmed in MATLAB. The Padé approximation is obtained from the initial data of the locus of each lens group. Subsequently, we verify that the obtained locus of lens groups satisfies the effective focal length (EFL) and the back focal length (BFL). Afterwards, the Padé approximation was applied again to confirm that the error of BFL is within the depth of focus for all zoom positions. In this way, the zoom locus for each lens group of the optical system with many moving lens groups was obtained as an analytical rational function. The practicality of this method was verified by application to a complicated zoom lens system with five or more lens groups using preset patents.

Keywords: lens design; zoom locus; Padé approximation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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