• Current Optics and Photonics
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• v.8 no.2
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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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• v.7 no.6
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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.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.28A no.9
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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.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.10a
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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.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1995.10a
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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.

• The Bulletin of The Korean Astronomical Society
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• v.45 no.1
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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.

• Korean Journal of Optics and Photonics
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• v.13 no.2
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• pp.98-104
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• 2002

We present a new self-calibration method to remove the systematic error of a 2-axis lateral shearing interferometer that has been specially designed for optical testing of aspheric optics. The method takes multiple measurements by rotating the test optics and extracts the systematic error by fitting the measured wavefronts into the Zernike polynomials. The method works with arbitrary azimuthal angles for test optics rotation, which offers an advantage of correcting the error induced by the non-orthogonality of the two axes of wavefront shearing as well as the error caused by the optical components of the interferometer system itself.

• Journal of the Optical Society of Korea
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• v.20 no.1
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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.

• Journal of Korean Ophthalmic Optics Society
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• v.14 no.2
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• pp.35-39
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• 2009

Purpose: In this study a program was developed to determine corneal aberrations using corneal shape of topographer and represented a wavefront and corneal aberrations using zernike polynomial. Methods: When the pupil size was 6 mm, we calculated new corneal shape data with zernike polynomials using corneal shape data of ORBSCAN topographer. We programmed the wavefront construction using ray tracing for corneal shape, then represented corneal aberrations having zernike polynomial with 6th order and 28 terms. Conclusions: We developed programs to determine a wavefront and corneal aberrations using corneal shape of ORBSCAN topographer. Theses results will be applied to a development of new topographer and prescription of contact lens and OK lens.

• 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.