• Title/Summary/Keyword: 제르니케 다항식

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A Study on Structural-Thermal-Optical Performance through Laser Heat Source Profile Modeling Using Beer-Lambert's Law and Thermal Deformation Analysis of the Mirror for Laser Weapon System (Beer-Lambert 법칙을 적용한 레이저 열원 프로파일 모델링 및 레이저무기용 반사경의 열변형 해석을 통한 구조-열-광학 성능 연구)

  • Hong Dae Gi
    • Journal of Aerospace System Engineering
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    • v.17 no.4
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    • pp.18-27
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    • 2023
  • In this paper, the structural-thermal-optical performance analysis of the mirror was performed by setting the laser heat source as the boundary condition of the thermal analysis. For the laser heat source model, the Beer-Lambert model considering semi-transparent optical material based on Gaussian beam was selected as the boundary condition, and the mechanical part was not considered, to analyze the performance of only the mirror. As a result of the thermal analysis, thermal stress and thermal deformation data due to temperature change on the surface of the mirror were obtained. The displacement data of the surface due to thermal deformation was fitted to a Zernike polynomial to calculate the optical performance, through which the performance of the mirror when a high-energy laser was incident on the mirror could be predicted.

Topology Optimization of the Primary Mirror of a Multi-Spectral Camera (인공위성 카메라 주반사경의 위상최적화)

  • Park, Kang-Soo;Chang, Su-Young;Lee, Eung-Shik;Youn, Sung-Kie
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.26 no.6
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    • pp.1194-1202
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    • 2002
  • A study on the topology optimization of a multi-spectral camera for space-use is presented. The optimization is carried out under self-weight and polishing pressure loading. A multi-spectral camera for space-use experiences degradation of optical image in the space, which can not be detected on the optical test bench on the earth. An optical surface deformation of a primary mirror, which is a principal component of the camera system, is an important factor affecting the optical performance of the whole camera system. In this study, topology optimization of the primary mirror of the camera is presented. As an objective function, a measure of Strehl ratio is used. Total mass of the primary mirror is given as a constraint to the optimization problem. The sensitivities of the objective function and constraint are calculated by direct differentiation method. Optimization procedure is carried out by an optimality criteria method. For the light-weight primary mirror design, a three dimensional model is treated. As a preliminary example, topology optimization considering a self-weight loading is treated. In the second example, the polishing pressure is also included as a loading in the topology optimization of the mirror. Results of the optimized design topology for the mirror with various mass constraints are presented.

Topology Optimization of the Primary Mirror of a Multi-Spectral Camera (인공위성 카메라 주반사경의 위상 최적화)

  • Park, Kang-Soo;Chang, Su-Young;Lee, Enug-Shik;Youn, Sung-Kie
    • Proceedings of the KSME Conference
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    • 2001.06a
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    • pp.920-925
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    • 2001
  • A study on the topology optimization of a multi-spectral camera for space-use is presented. A multi-spectral camera for space-use experiences degradation of optical image in the space, which can not be detected on the optical test bench on the earth. An optical surface deformation of a primary mirror, which is a principal component of the camera system, under the self-weight loading is an important factor affecting the optical performance of the whole camera system. In this study, topology optimization of the primary mirror of the camera is presented. Total mass of the primary mirror is given as a constraint to the optimization problem. The sensitivities of the objective function and constraint are calculated by direct differentiation method. Optimization procedure is carried out by an optimality criterion method using the sensitivities of the objective function and the constraint. As a preliminary example, topology optimization considering a self-weight loading is treated. For practical use, the polishing pressure is included as a loading in the topology optimization of the primary mirror. Results of the optimized design topology for the primary mirror with varying mass ratios are presented.

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Development of Free-form PALs for Correcting Wavefront Refraction (파면굴절력 교정을 위한 자유형상 누진가입도렌즈 개발)

  • Baarg, Saang-Bai;Jeong, Mee-Suk
    • Journal of the Korean Society for Precision Engineering
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    • v.27 no.2
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    • pp.50-59
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    • 2010
  • In this paper, two kind of free-form progressive addition lenses (PALs) were designed with Zernike polynomial surface and anatomically accurate finite presbyopic schematic eyes which have aspheric cornea, aspheric GRIN crystalline lens, aspheric retina, and Gaussian apodization factor. Geometrical and diffraction MTFs were used for the optimization process in sequence. 5th orders of Zernike polynomials were used for the evaluation of progression zones of the two examples. The target MTF was set as 0.22 at 100 lp/mm which satisfies the standard visual resolution. These examples were fabricated with a CNC diamond turning machine controlled by slow tool servo (STS). After polishing process, the wavefront aberrations were measured with a laser interferometer on the ten test points across the progression zones and then compared with three current commercially available PALs on the optical performance. Astigmatic aberrations of the examples are very lower than the three selected PALs and have more increased stabilized progressive intermediate zones and near zones. It is expected to give better clear and comfortable distance, intermediate and near visions than other conventional PALs and to improve the adaptability of presbyopic patients to PALs.

Prediction Method for Moisture-release Surface Deformation of a Large Mirror in the Space Environment (우주환경에서 대형 반사경의 습기 방출에 의한 형상 변화 예측방법)

  • Song, In-Ung;Yang, Ho-Soon;Khim, Hagyong;Kim, Seong-Hui;Lee, Hoi-Yoon;Kim, Sug-Whan
    • Korean Journal of Optics and Photonics
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    • v.29 no.4
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    • pp.166-172
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    • 2018
  • In this paper, we propose a new method to predict a mirror's surface deformation due to the stress of moisture release by a coating in the environment of outer space. We measured the surface deformation of circular samples 50 mm in diameter and 1.03 mm thick, using an interferometer. The results were analyzed using Zernike fringe polynomials. The coating stress caused by moisture release was calculated to be 152.7 MPa. This value was applied to an analytic model of a 1.25 mm thickness sample mirror, confirming that the change of surface deformation could be predicted within the standard deviation of the measurement result ($78.9{\pm}5.9nm$). Using this methodology, we predicted the surface deformation of 600 mm hyperbolic mirror for the Compact Advanced Satellite, which will be launched in 2019. The result is only $2.005{\mu}m$ of focal shift, leading to 2.3% degradation of modulation transfer function (MTF) at the Nyquist frequency, which satisfies the requirement.

Slim Mobile Lens Design Using a Hybrid Refractive/Diffractive Lens (굴절/회절 하이브리드 렌즈 적용 슬림 모바일 렌즈 설계)

  • Park, Yong Chul;Joo, Ji Yong;Lee, Jun Ho
    • Korean Journal of Optics and Photonics
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    • v.31 no.6
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    • pp.281-289
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    • 2020
  • This paper reports a slim mobile lens design using a hybrid refractive/diffractive optical element. Conventionally a wide field of view (FOV) camera-lens design adopts a retrofocus type having a negative (-) lens at the forefront, so that it improves in imaging performance over the wide FOV, but with the sacrifice of longer total track length (TTL). However, we chose a telephoto type as a baseline design layout having a positive (+) lens at the forefront, to achieving slimness, based on the specification analysis of 23 reported optical designs. Following preliminary optimization of a baseline design and aberration analysis based on Zernike-polynomial decomposition, we applied a hybrid refractive/diffractive element to effectively reduce the residual chromatic spherical aberration. The optimized optical design consists of 6 optical elements, including one hybrid element. It results in a very slim telephoto ratio of 1.7, having an f-number of 2.0, FOV of 90°, effective focal length of 2.23 mm, and TTL of 3.7 mm. Compared to a comparable conventional lens design with no hybrid elements, the hybrid design improved the value of the modulation transfer function (MTF) at a spatial frequency of 180 cycles/mm from 63% to 71-73% at zero field (0 F), and about 2-3% at 0.5, 0.7, and 0.9 fields. It was also found that a design with a hybrid lens with only two diffraction zones at the stop achieved the same performance improvement.

Athermalization and Narcissus Analysis of Mid-IR Dual-FOV IR Optics (이중 시야 중적외선 광학계 비열화·나르시서스 분석)

  • Jeong, Do Hwan;Lee, Jun Ho;Jeong, Ho;Ok, Chang Min;Park, Hyun-Woo
    • Korean Journal of Optics and Photonics
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    • v.29 no.3
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    • pp.110-118
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    • 2018
  • We have designed a mid-infrared optical system for an airborne electro-optical targeting system. The mid-IR optical system is a dual-field-of-view (FOV) optics for an airborne electro-optical targeting system. The optics consists of a beam-reducer, a zoom lens group, a relay lens group, a cold stop conjugation optics, and an IR detector. The IR detector is an f/5.3 cooled detector with a resolution of $1280{\times}1024$ square pixels, with a pixel size of $15{\times}15{\mu}m$. The optics provides two stepwise FOVs ($1.50^{\circ}{\times}1.20^{\circ}$ and $5.40^{\circ}{\times}4.23^{\circ}$) by the insertion of two lenses into the zoom lens group. The IR optical system was designed in such a way that the working f-number (f/5.3) of the cold stop internally provided by the IR detector is maintained over the entire FOV when changing the zoom. We performed two analyses to investigate thermal effects on the image quality: athermalization analysis and Narcissus analysis. Athermalization analysis investigated the image focus shift and residual high-order wavefront aberrations as the working temperature changes from $-55^{\circ}C$ to $50^{\circ}C$. We first identified the best compensator for the thermal focus drift, using the Zernike polynomial decomposition method. With the selected compensator, the optics was shown to maintain the on-axis MTF at the Nyquist frequency of the detector over 10%, throughout the temperature range. Narcissus analysis investigated the existence of the thermal ghost images of the cold detector formed by the optics itself, which is quantified by the Narcissus Induced Temperature Difference (NITD). The reported design was shown to have an NITD of less than $1.5^{\circ}C$.