• Current Optics and Photonics
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• 제8권2호
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• pp.151-155
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• 2024

Optical systems often suffer from optical aberrations caused by imperfect hardware, which places significant constraints on their utility and performance. To reduce these undesirable effects, a comprehensive understanding of the aberrations inherent to optical systems is needed. This article presents an effective method for aberration detection using Zernike polynomials. The process involves scanning the object plane to identify the optimal focus and subsequently fitting the acquired focus data to Zernike polynomials. This fitting procedure facilitates the analysis of various aberrations in the optical system.

• Current Optics and Photonics
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• 제7권6호
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• pp.692-700
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• 2023

We present a method for improving the accuracy of the modal wavefront reconstruction in the radial shearing interferometers (RSIs). Our approach involves expanding the reduced radial terms of Zernike polynomials to high-order, which enables more precise reconstruction of the wavefront aberrations with high-spatial frequency. We expanded the reduced polynomials up to infinite order with symbolic variables of the radius, shearing amount, and transformation matrix elements. For the simulation of the modal wavefront reconstruction, we generated a target wavefront subsequently, magnified and measured wavefronts were generated. To validate the effectiveness of the high-order Zernike polynomials, we applied both low- and high-order polynomials to the wavefront reconstruction process. Consequently, the peak-to-valley (PV) and RMS errors notably decreased with values of 0.011λ and 0.001λ, respectively, as the order of the radial Zernike polynomial increased.

• 전자공학회논문지A
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• 제28A권9호
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• pp.662-670
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• 1991

Fast analysis method for calculating the radiation pattern of offset dual reflector antenna are presented. The validity of proposed method was verified by comparing with results of PO/PO, GO/PO, and the equivalent paraboloid method. Proposed method is the series expansion method using the Zernike polynomials. The calculated results by using the Zernike polynomials are in good agreement with obtained results by GO/PO and equivalent paraboloid method except PO/PO.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2005년도 추계학술대회 논문집
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• pp.208-211
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• 2005

The volumetric interferometer, which uses the interference of wavefronts emitted from two single mode fibers, measures the target position in 3-D. In this paper, we suggest a new calculation method which doesn't need a non-linear optimization and an initial guess. We find the relationship between the coefficients of the Zernike polynomials for a spherical wavefront and its center and reconstruct a spherical wavefront by using the Zernike polynomials from two interference fringes like a lateral shearing interferometer. The target position can be obtained from the coefficients of the Zernike polynomials of the reconstructed wavefront. We can get the target position in 3-D with $sub-{\mu}m$ errors in a simulation.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1995년도 추계학술대회 논문집
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• pp.384-387
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• 1995

Two axes lateral-shearing interferometer(LSI) specially devised for production line inspection lenses is presented. The interferometer composed with four prisms and a dove prism can test the lens performance including asymmetric aspheric lens. The dove prism which rotates the input image with respect to optical axis makes it possible. The wavefront passing through the test lens is reconstsucted by the phase derivative obtained form the two axes LSI system. Zernike-polynomials fitting of this wavefront is presented for determinating quantitative aberration of aspherical lenses.

• 천문학회보
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• 제45권1호
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• pp.67.2-67.2
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• 2020

Not only the magnitude of the mirror surface error, the pattern matters as it produces certain aberrations. In particular, the surface error of the freeform mirrors, which are optimized to eliminate specific aberrations, might show much higher sensitivity in optical performance. Therefore, we analyze the mirror surface error with Zernike polynomials with the goal of generating a realistic error surface. We investigate the surface error of the freeform mirror fabricated by diamond turning machine to analyze the realistic tendency of the error. The surface error with 0.22 ㎛ root-mean-square value is fitted to the Zernike terms using the incremental fitting method, which increases the number of the fitting coefficients through steps. Furthermore, optical performance via surface error pattern based on Zernike terms is studied to see the influences of each term. With this study, realistic error surface generation may allow higher accuracy not only for the feasibility test but also for all tests and predictions using optical simulations.

• 한국광학회지
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• 제13권2호
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• pp.98-104
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• 2002

비구면 광학부품의 수차 측정 및 성능 평가를 위해 특별 설계된 층밀리기 간섭계를 소개하고, 이와 더불어 층밀리기 간섭계가 갖는 자체의 계통오차를 측정결과로부터 제거하기 위한 보정 방법을 제안한다. 층밀리기 간섭계의 계통오차는 크게 간섭광학계가 갖는 광학오차와 간섭계의 기구부의 불완전에 기인한 층밀리기 방향의 직교오차로 구분할 수 있다. 이들 두 계통 오차들은 모두 본 논문에서 제안하는 방법으로 모두 보정될 수 있다. 보정 방법은 측정 대상물을 간섭계의 광축을 중심으로 회전하여 측정결과로부터 계통오차를 분리하는 자가보정 원리에 근거한다.

• Journal of the Optical Society of Korea
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• 제20권1호
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• pp.101-106
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• 2016

A pupil filter is a useful technique for modifying the light intensity distribution near the focus of an optical system to realize depth of field (DOF) extension and superresolution. In this paper, we proposed a new design of the phase only pupil filter by using Zernike polynomials. The effect of design parameters of the new filters on DOF extension and superresolution are discussed, such as defocus Strehl ratio (S.R.), superresolution factor (G) and relative first side lobe intensity (M). In comparison with the other two types of pupil filters, the proposed filter presents its advantages on controlling both the axial and radial light intensity distribution. Finally, defocused imaging simulations are carried out to further demonstrate the effectiveness and superiority of the proposed pupil filter on DOF extension and superresolution in an optical imaging system.

• 한국안광학회지
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• 제14권2호
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• pp.35-39
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• 2009

목적: 본 연구는 각막지형검사기의 각막형상을 이용하여 각막수차를 구현하는 프로그램을 개발하고자 하며, 개발된 프로그램을 이용하여 저니케 다항식(Zernike Polynomial)으로 파면과 각막수차를 구현하고자 한다. 방법: 각막지형검사기인 ORBSCAN의 각막형상 데이터로부터 각막의 형상을 재구성하기 위해 저니케 다항식을 사용하였으며, 이때 동공의 유효구경은 6 mm를 고려하였다. 구현된 각막형상으로부터 광선추적을 사용하여 동일한 광학적 거리의 파면을 구현하는 프로그램을 개발하였으며, 파면으로부터 6차 28항의 저니케 계수로 각막수차를 구현하였다. 결론: 본 연구에서는 각막지형검사기의 각막형상으로부터 각막의 수차와 파면을 구현하는 프로그램을 개발하였으며, 이러한 결과는 각막지형검사기 개발과 콘택트렌즈 및 OK렌즈 처방에 유용하게 적용될 수 있으리라 사료된다.

• 한국정밀공학회지
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• 제27권2호
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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.