[논문]재귀적 수치 계산법을 이용한 등가 렌즈의 곡률 계산

이규행

doi:10.3807/kjop.2022.33.6.275

재귀적 수치 계산법을 이용한 등가 렌즈의 곡률 계산
Curvature Radius of Equivalent Lens Obtained by Recursive Numerical Solving of Gaussian Equations 원문보기

한국광학회지 = Korean journal of optics and photonics, v.33 no.6, 2022년, pp.275 - 286

이규행 (수원대학교 공과대학 전자재료학부 전자물리학과)

초록
AI-Helper

광학설계 과정의 첫 단계에서 근축 광선이 만족하는 Gauss 방정식에 대한 해를 구할 수 있는 재귀적 수치 계산법을 도출하였다. 설계 사양으로 렌즈 모듈의 굴절력, 렌즈 제1 주요면으로의 입사각과 제2 주요면으로부터의 출사각이 주어지면 렌즈의 주요면 사이의 거리를 선택한 후, 재귀적 수치 계산법을 적용하여 렌즈의 두께, 렌즈 앞면의 곡률 반경과 뒷면의 곡률 반경을 구할 수 있다. 즉, 설계 사양을 만족하는 두께가 다른 여러 등가렌즈를 얻을 수 있다. 모듈이 2개 이상의 렌즈로 구성되는 경우에도 렌즈의 개수를 하나씩 증가하면서 렌즈의 주요면 사이의 거리를 설계 사양에 맞추어 선택한 후 각 렌즈의 두께와 곡률 반경을 결정할 수 있다.

Abstract ▼ AI-Helper

As a first step in the optical design process, we derive a recursive numerical calculation method that can give a solution to the Gaussian equation that the paraxial rays satisfy. Given the refractive power, the angle of incidence to the first principal plane of the lens, the angle of exit to the second principal plane of the lens, and the distance between the principal planes, the radii of curvature of the front and back surfaces of a lens can be obtained by applying the recursive numerical calculation method proposed in this paper according to the thickness of the lens. If a module consists of two or more lenses, the thickness and radius of curvature of each lens can be similarly determined after selecting the distance between the principal planes of the lens under the condition of the design specification while increasing the number of lenses one by one.

주제어

표/그림 (14)

$Fig. 1. Sectional view of a single lens with a refracted paraxial ray and the principal points of H and H' of the lens.$ 그림 Fig. 1. Sectional view of a single lens with a refracted paraxial ray and the principal points of H and H' of the lens.
그림 Fig. 2. Flow chart for the recursive numerical calculation of equivalent lens's curvature radius and thickness.
그림 Fig. 3. Curvature radius of the equivalent single lens with positive power according to its thickness. r₁ and r₂ are the curvature radii of the 1st and 2nd surfaces of the lens, respectively.
그림 Fig. 4. Aberration values of the positive equivalent single lens according to its thickness with an aperture stop at the 1st surface, 0.65 mm of half object height, and the height of marginal ray at the 1st surface. (a) S_I. (b) S_II and S_III. (c) S_IV and S_V.
그림 Fig. 5. Curvature radius of the equivalent double lens with negative power according to its thickness. r₁ and r₂ are the curvature radii of the 1st and 2nd surfaces of the lens, respectively.
그림 Fig. 6. Aberrations of the negative equivalent single lens according to its thickness with an aperture stop at the 1st surface, 0.65 mm of half object height, and the height of marginal ray at the 1st surface. (a) S_I, S_II, and S_III. (b) S_IV. (c) S_V.
$Fig. 7. Sectional view of the double lens with a refracted paraxial ray and four principal points of the two lenses.$ 그림 Fig. 7. Sectional view of the double lens with a refracted paraxial ray and four principal points of the two lenses.
$Fig. 8. Curvature radii of the 3rd and 4th refractive surfaces of the double lens according to the thickness (d2) of the 2nd lens. r21 and r22 are the curvature radii of the 3rd and 4th surfaces of the double lens, respectively. (a) r21. (b) r22.$ 그림 Fig. 8. Curvature radii of the 3rd and 4th refractive surfaces of the double lens according to the thickness (d2) of the 2nd lens. r₂₁ and r₂₂ are the curvature radii of the 3rd and 4th surfaces of the double lens, respectively. (a) r₂₁. (b) r₂₂.
그림 Fig. 9. Aberrations of the double lens according to the thickness (d₂) of the second lens with an aperture stop at the 1st surface, 0.63 mm of half object height, and the height of marginal ray at the 1st surface. (a) S_I, S_II, and S_IV. (b) S_III. (c) S_V. (d) C_L. (e) C_T.
$Fig. 10. Sectional view of the doublet lens with a refracted paraxial ray, the first refraction surface, and the two principal planes.$ 그림 Fig. 10. Sectional view of the doublet lens with a refracted paraxial ray, the first refraction surface, and the two principal planes.
$Fig. 11. Curvature radii of the 2nd and 3rd refractive surfaces of the doublet according to the thickness of the 2nd lens. r21 and r22 are the curvature radii of the 2nd and 3rd surfaces of the doublet, respectively. (a) r21. (b) r22.$ 그림 Fig. 11. Curvature radii of the 2nd and 3rd refractive surfaces of the doublet according to the thickness of the 2nd lens. r₂₁ and r₂₂ are the curvature radii of the 2nd and 3rd surfaces of the doublet, respectively. (a) r₂₁. (b) r₂₂.
$Fig. 12. Aberrations of the doublet according to the thickness (d2) between the second and third refractive surfaces with an aperture stop at the 1st surface, 0.65 mm of half object height, and the height of marginal ray at the 1st surface. (a) SI, SII, and CL. (b) SIII. (c) SIV. (d) SV and CT.$ 그림 Fig. 12. Aberrations of the doublet according to the thickness (d₂) between the second and third refractive surfaces with an aperture stop at the 1st surface, 0.65 mm of half object height, and the height of marginal ray at the 1st surface. (a) S_I, S_II, and C_L. (b) S_III. (c) S_IV. (d) S_V and C_T.
표 Table 1. Curvatures and thickness of the doublet when D₁ (the thickness between the 1st and 2nd principal points) is 3 mm, D2 (the thickness between the 2nd and 3rd principal points) is 1 mm, and the initial powers the 1st, 2nd, and 3rd surfaces are 0.003038, 0.00015, and -0.00575 mm^-1, respectively
표 Table 2. Third-order Seidel aberration of the doublet with an aperture stop at the 1st surface, 0.65 mm of half object height, and the height of marginal ray at the 1st surface

참고문헌 (12)

P. Mouroulis and J. Macdonald, Geometrical Optics and Optical Design, (Oxford University Press, UK, 1997), Chapter 10.
D. K. Lee, N. J. Yoo, J. H. Jo, J. M. Ryu, H. J. Lee, and G. M. Kang, "General numerical calculation method for paraxial zoom loci of zoom lenses with finite object distance by using gaussian bracket method," Korean J. Opt. Photonics 20, 156-165 (2009).
S. C. Park and Y. S. Kim, "Optical system design using lens modules I: optimum first order design in zoom lens," Korean J. Opt. Photonics 8, 81-87 (1997).
N. J. Yoo, W. S. Kim, J. H. Jo, J. M. Ryu, H. J. Lee, and G. M. Kang, "Numerical calculation method for paraxial zoom loci of complicated zoom lenses with infinite object distance by using Gaussian bracket method," Korean J. Opt. Photonics 18, 410-420 (2007).
J. H. Jo, D. K. Lee, S. O. Lee, J. M. Ryu, G. M. Kang, and H. J. Lee, "Numerical calculation for autofocus of zoom lenses by using Gaussian brackets," Korean J. Opt. Photonics 20, 166-177 (2009).
H. S. Park and J. H. Jo, "Design and performance of a catadioptric omnidirectional zoom optical system using a hybrid lens for visible light," Korean J. Opt. Photonics 31, 96-104 (2020).
J. U. Lee and K. S. Kim, "Generalization of equivalent lens conversion and third order aberration formulae of the generalized equivalent lens system," Korean J. Opt. Photonics 7, 305-313 (1996).
J. U. Lee and S. C. Park, "Generalized lens group conversion to their equivalent lenses," Korean J. Opt. Photonics 9, 251-257 (1998).
J. U. Lee, "A study for an analytic conversion between equivalent lenses," Korean J. Opt. Photonics 23, 17-22 (2012).
Y. S. Chun, H. S. Kim, J. U. Lee, and S. C. Park, "Optical design of cemented doublets by using equivalent lens system," Korean J. Opt. Photonics 9, 282-290 (1998).
S. S. Lee, Geometrical Optics (Kyo Hak Sa, Seoul, Korea, 1985).
W. T. Welford, Aberrations of Optical Systems, 1st ed. (CRC Press, USA, 1986).

표제어: PCR

동의어: Packet Collision Rate

용어 설명 출처 목록 (6)

용어 설명: PCR은 세균 특이성이 있는 primer를 이용하여 적은 수의 세균이 있을지라도 쉽게 검출할 수 있는 유용한 방법이며, 이를 이용하여 구강 내 치면세균막이나 타액에서 직접 세균을 검출할 수 있게 되었다[8].

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