Numerical Calculation Method for Paraxial Zoom Loci of Complicated Zoom Lenses with Infinite Object Distance by Using Gaussian Bracket Method

Yoo, Nam-Jun; Kim, Won-Seob; Jo, Jae-Heung; Ryu, Jae Myung; Lee, Hae-Jin; Kang, Geon-Mo

doi:10.3807/hkh.2007.18.6.410

Cited by 7 publications

(8 citation statements)

References 3 publications

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“…The programming tool used is MATLAB [23]. Subsequently, Equations (8)- (10) are calculated in further detail. Using the characteristics of the Gaussian bracket, the unknown k i is exported out of the Gaussian bracket and written as the first equation for k i [24][25][26][27].…”

Section: Methodsmentioning

confidence: 99%

“…Therefore, to solve this problem, a method estimating the movement of some lens groups to satisfy a desired back focal length (BFL) or effective focal length (EFL) after spline interpolation from nodes of each lens group has been proposed. At this time, when calculating the movement of lens groups, it is possible to calculate the differential matrix and iterative calculation by considering the zoom equations and constraints as nonlinear simultaneous equations [10,11]. However, this iterative calculation method has the disadvantage of a complicated calculation method, which takes a long time.…”

Section: Introductionmentioning

confidence: 99%

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Computation of Analytical Zoom Locus Using Padé Approximation

Kim

Choe²,

Ryu

et al. 2020

Mathematics

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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.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Computation of Analytical Zoom Locus Using Padé Approximation

Kim

Choe²,

Ryu

et al. 2020

Mathematics

Self Cite

View full text Add to dashboard Cite

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“…첫째 줌렌즈 설계 [4][5][6][7][8][9][10] 에서 필요한 줌 궤적 계산을 해야 하고, 둘째 광각의 2군 렌즈를 가장 효과적으로 표현할 수 있는 구조함수를 정의해야 한다. 줌 궤적 계산은 각 군별 굴절능 배분의 문제와 직결되므로 2군 렌즈의 굴절 능에 대한 표현식에서 출발한다.…”

Section: 전역구조함수의 정의와 토의unclassified

Design of Two-group Zoom Lens System with Wide Angle of View Using Global Structure Function

Kwon¹,

Rim²

2009

Korean Journal of Optics and Photonics

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We introduce a new design technique by treating a two-group zoom lens system with a wide angle of view. First, the concept of the global optimization is introduced in the initial design stage, and from this, the global design technique is completed by analyzing and summarizing large quantities of modern design data. That is, we define the global structure function to achieve a new conceptual design technique for global optimization. And the function is put in a simple form by referring lots of patent data, manipulated with other algebraic equations, and solved finally such that we obtain the global solution region. The global solution region corresponds to the global optimization and suggests insightful systematized directions for the design of two-group zoom lens systems. These directions are attractive compared to global optimization.

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“…앞서 예를 든 경우들처럼 최근 카메라 광학계는 줌 렌즈의 군수가 많아지는 새로운 형태를 가지기 때문에 참고문헌 1 과 같은 방법으로는 줌 궤적을 구할 수 없다. 이를 해결하기 위해서 최근에는 수치해석적으로 줌 궤적을 구하는 방법 [7,8] [1,7,8] 을 통해 근축광선추적을 한다면 프로그램밍에 상당히 편리 하다. 광학계의 전체 초점거리와 상면에서의 상고에 관한 식 은 아래와 같이 식 (1)로 표현된다.…”

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Analytic Calculation Method of Zoom Loci for Zoom Lens System with Infinite Object Distance

Oh¹,

Ryu²,

Jo³

2013

Korean Journal of Optics and Photonics

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In case of the optical camera system with an infinite object distance, optical designs different from previous systems are required to speed up the auto-focus. As the number of lens groups is increased due to this, the conventional analytic method found it difficult to calculate the locus, and even the one-step advanced calculation method also had the trouble of taking a lot of time. In this paper, we suggested an analytic method for calculating the zoom loci by analyzing movement of one or two groups for situations corresponding to the given back focal length and effective focal length after taking a spline interpolation for each lens group. With this method, we would not only calculate the analytic zoom loci without iterations in every optical system without placing a limit on the group number at the zoom lens systems with the infinite object distance, but we would also show the utilities of this method through many examples.

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Numerical Calculation Method for Paraxial Zoom Loci of Complicated Zoom Lenses with Infinite Object Distance by Using Gaussian Bracket Method

Cited by 7 publications

References 3 publications

Computation of Analytical Zoom Locus Using Padé Approximation

Computation of Analytical Zoom Locus Using Padé Approximation

Design of Two-group Zoom Lens System with Wide Angle of View Using Global Structure Function

Analytic Calculation Method of Zoom Loci for Zoom Lens System with Infinite Object Distance

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