• Journal of Korean Ophthalmic Optics Society
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• v.8 no.2
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• pp.77-83
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• 2003

To investigate the influence of the variation of conic coefficient of the front surface on the RMS SD(Root Mean Square Spot Diameter) in a back focal plane, we use programs which are Cove V and LOSA 2.0. We consider a spectacle lens with back vertex power of -4.00D, diameter of 70 mm, the front surface powers which are 2.00D, 4.00D, 6.00D, and 8.00D, and the indices which are $n_d$=1.498, 1.523, 1.586, and 1.660, respectively. The RMS SD in the back focal plane and the thickness of an aspherical tens having the optimized conic constant are smaller than those of a spherical lens. The RMS SD in the back focal plane decreases as the front surface power decreases. From these results, we determine the optimized conic constant to improve the optical image quality and decrease RMS SD in the back focal plane.

• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1211-1226
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• 2021

The study of reducible Hilbert curves of conic fibrations over a smooth surface is carried on in this paper and the question of when the main component is itself the Hilbert curve of some ℚ-polarized surface is dealt with. Special attention is paid to the polynomial defining the canonical equation of the Hilbert curve.

• Korean Journal of Computational Design and Engineering
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• v.5 no.4
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• pp.336-346
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• 2000

This paper presents a geometric method that can detect and compute all conic sections in the intersection of two tori. Conic sections contained in a torus must be circles. Thus, when two tori intersect in a conic section, the intersection curve must be a circle as well. Circles in a torus are classified into profile circles, cross-sectional circlet, and Yvone-Villarceau circles. Based on a geometric classification of these circles, we present a procedural method that can detect and construct all intersection circles between two tori. All computations can be carried out using simple geometric operations only: e.g., circle-circle intersections, circle-line intersections, vector additions, and inner products. Consequently, this simple structure makes our algorithm robust and efficient, which is an important advantage of our geometric approach over other conventional methods of surface intersection.

• Journal of the korean Society of Automotive Engineers
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• v.15 no.3
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• pp.89-95
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• 1993

This paper presents the development of CAD system for the design of lens of the Turn Signal Lamp that can model and simulate its optical performance. The system consists of three main modules: skin surface modeling module, inner lens modeling module and optical performance simulation module. Skin surface geometry can be modeled by the input of data file and inner lens can be modeled by the input of only four parameter using its geometric characteristics. Also light distribution pattern, the barometer of optical performance is generated by means of finite ray tracing method. The system display modeled geometry, ray tracing and generated light distribution pattern.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.3
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• pp.217-224
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• 2009

In this paper we present an approximation method of quadric surface using quartic spline. Our method is based on the approximation of quadratic rational B$\acute{e}$zier patch using quartic B$\acute{e}$zier patch. We show that our approximation method yields $G^1$ (tangent plane) continuous quartic spline surface. We illustrate our results by the approximation of helicoid-like surface.

• Journal of Sericultural and Entomological Science
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• v.36 no.1
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• pp.30-36
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• 1994

choChorion(egg-shell) morphology of the F1 hybrid between Bombyx mori and Bombyx mandarina has been observed by scanning electrom microscope and chorion protein was analyzed by electrophoresis. The chorion surface structure of F1 hybrids in the lateral(flat) region was similar to that of maternal line. The F1 hybrids chorion was found to have basically a three layer structure. The middle and inner layer were very much like those of the Bombyx mandarina and Bombyx mori. There were many conic pillar structures in the outer layer of the F1 hybrid, which was similar to Bombyx mandarina. This conic pillar structure had a thin cover layer was more clear in the dorsal and ventral side of the F1 hybrid chorion. The conic pillar structure of Bombyx mandarina was found to be dominant in F1 hybrid chorion irrespective of their maternal line. Major components of chorion protein were analyzed by two-dimensional electrophoresis and found to have isoelectric points in the range of pH 4.0-6.5 and molecular weight 10 to 50 kd. F1 hybrid chorion protein components related directly to those of the maternal line. The conic pillar structure was dominat characteristic and it was present in all F1 hybrid.

• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1859-1871
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• 2017

We compute the Jordan constant for the group of birational automorphisms of a projective plane ${\mathbb{P}}^2_{\mathbb{k}}$, where ${\mathbb{k}}$ is either an algebraically closed field of characteristic 0, or the field of real numbers, or the field of rational numbers.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.430-433
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• 2004

The ophthalmic lens manufacturing processes need to extract the aspherical surface equation from the unknown surface since its real profile can be adjusted by the process variables to make the ideal curve without the optical aberration. This paper presents a procedure to get the aspherical surface equation of an aspherical ophthalmic lens. Aspherical form generally consists of the Schulz formula to describe its profile. Therefore, the base curvature, conic constant, and high-order polynomial coefficient should be set to the original design equation. To find an estimated aspherical profile, firstly lens profile is measured by a contact profiler, which has a sub-micrometer measurement resolution. A mathematical tool is based on the minimization of the error function to get the estimated aspherical surface equation from the scanned aspherical profile. Error minimization step uses the Nelder-Mead simplex (direct search) method. The result of the refractive power measurement is compared with the curvature distribution on the estimated aspherical surface equation

• Current Optics and Photonics
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• v.8 no.5
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• pp.493-501
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• 2024

This study proposes an effective visualization method for image distortion in high-resolution, machinable Fresnel mirrors, which offer significant advantages over traditional convex mirrors by being thinner and lighter. While commercial optical design programs are excellent at optimizing aberrations, they have some limitations in visualizing images from complex optical configurations. Therefore, NX^TM CAD software is employed to achieve photorealistic ray-traced visualization with high-fidelity image rendering due to its flexible two-dimensional and three-dimensional modeling environments. In comparative simulations with various mirror profiles, we identified an aspherical Fresnel mirror with a conic constant of k = -3 that can reduce distortion to 1.79%, according to Zemax OpticStudio^® calculations. Finally, the NX^TM software successfully validated the distortion image of our machinable aspherical Fresnel mirror design. Subsequent practical experiments validated the consistency between the predicted distortion and the actual visualization results. We anticipate that this specialized visualization technique holds the potential to radically transform the interactive design of optical systems that incorporate aspherical Fresnel mirrors.

• Korean Journal of Optics and Photonics
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• v.1 no.2
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• pp.217-222
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• 1990

A general ray tracing scheme has been developed for using a personal computer which trace finite rays through any non-rotationally symmetric system. This scheme may be used for the surface type such as conic section with or without aspherics, toric surfaces, sagittal and tangential cylindrical sections and axicons. Specially, any combinational of decentered, tilted and rotated surfaces has been considered. Before transfering to the next surfaces, the local coordinates are refered back to an initial reference coordinate system. We can get a mathmtical model of a non-rotationally symmetrical finite ray trace running on an inexpensive personal computer.