• Journal of the Korean Mathematical Society
• /
• v.40 no.6
• /
• pp.951-962
• /
• 2003

In this paper we address focal points and treat manifolds (M, g) whose Lorentzian metric tensors g have a spacelike $C^{0}$-hypersurface $\Sigma$ [10]. We apply Jacobi fields for such manifolds, and check the local length maximizing properties of $C^1$-geodesics. The condition of maximality of timelike curves(geodesics) passing $C^{0}$-hypersurface is studied.ied.

• Bulletin of the Korean Mathematical Society
• /
• v.38 no.2
• /
• pp.285-292
• /
• 2001

The authors compute the Ricci curvature of the GRW space-time to obtain two conditions for the conjugate points which appear as the Timelike Convergence Condition(TCG) and the Jacobi inequality. Moreover, under such two conditions, we obtain a lower bound of the length of a unit timelike geodesic for focal points emanating form the immersed spacelike hypersurface, the graph over the fiber in the GRW space-time.

• Journal of the Microelectronics and Packaging Society
• /
• v.20 no.2
• /
• pp.23-28
• /
• 2013

Microlens array as basic element of the optical system have been fabricated with various focal length (mainly with long focal length) depending on the purpose of application. In this paper, the microlens arrays were fabricated for observing fluorescent images within sol-gel. Though the fluorescent signal is very low, the microlens array can help obtaining clear images through extracting the fluorescent light from sol-gel. We fabricated microlens arrays with short focal length, which can extract the light using photoresist thermal reflow method. In the experiment, the diameter of microlens decreased after thermal reflow because the solvent within the photoresist was vaporized. Therefore, to compensate the shape error by this reduction, microlens diameter in photomask was altered and spin-coat recipe of photoresist were modified.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.41 no.3
• /
• pp.213-218
• /
• 2017

In this study, a reverse design of the F-theta lens was proposed for a 2D scanner in remote welding applications. The curvature and distance of the lens were set as variables, and the focal length of the lens was set as the marginal ray height. The ZEMAX commercial software was used to perform a simulation with unlimited iterations for the optimization process. The target value was optimized using the internal Merit function with the weight factors of focal length and spot diameter. The number of lenses was four, and the focal length obtained from the results was 135mm that is slightly less than that of the commercial lens, which is set with a focal length of 185 mm. The calculated spot diameters are $1.3{\mu}m$, $6.2{\mu}m$, and $16.1{\mu}m$ for $0^{\circ}$, $12.5^{\circ}$ and $23^{\circ}$ of incident laser beam, respectively. It is expected that an optimized lens design is possible by performing the reverse design of a lens by the ray tracing method.

• Current Optics and Photonics
• /
• v.3 no.3
• /
• pp.227-235
• /
• 2019

With slimmer, lighter and all-reflective imaging systems in high demand for consumer and military applications, coaxially folded optical image systems are widely considered because they can extend focal length and reduce track length. Most of these systems consist of multiple surfaces, and these surfaces are machined on one element or grouping processing on two elements. In this paper, we report and first experimentally demonstrate an all-aluminum all-reflective optical system which consists of two optical elements, with two high order aspherical surfaces in each element. The coaxially folded system is designed with Seidel aberration theory and advanced optimization with Zemax. The system is made of all-aluminum material processing by single point diamond turning (SPDT). On this basis, we completed the system integration and performed an imaging experiment. The final system has the advantages of short track length and long focal length and broad application prospects in the micro-unmanned aerial vehicle field.

• Journal of the Korean Society of Manufacturing Process Engineers
• /
• v.19 no.6
• /
• pp.96-101
• /
• 2020

In this paper, we present the results of our research to perform 3D laser scanning functions by adding a focusing lens to a conventional 2D laser scanner. For the optical design, the ray-tracing technique was used along with a total of four lenses as the variable incident focusing lens, the collimating lens, and the F-Theta lens. As design variables, the curvature of the incident focusing lens (Lens #1) was assumed to be us, l mm and sumed mm, and the incident angles were set at 0cidenus, l. In addition, the distance between the focusing lens and the collimating lens was set to vary from 5 mm to 15 mm. When the incident focal length was varied from 5 mm to 15 mm, the exit focal length was calculated to vary from 67.5 mm to 56.8 mm for the lens with R = 100 mm and from 108.5 mm to 99.0 mm for the lens with R = 150 mm. When the incident angle was 0°, the focal aberration was only slightly observable at 10㎛ in both the x- and y-direction. At 7.5° was the focal aberration of approximately 20~50㎛ was measured at 20㎛. To investigate the chromatic aberration of the designed optical device, the distortion of the focus was observed when the 550 nm beam was simulated on lens designed for a 980 nm wavelength.

• Korean Journal of Optics and Photonics
• /
• v.13 no.3
• /
• pp.266-271
• /
• 2002

The finite schematic eye based on spherical aberration and Stiles-Crawford effect is designed by an optimization method. It consists of four aspherical surfaces. The radius of curvature, thickness, asphericity, and spherical aberration are used as constraints in the optimization process. Stiles-Crawford effect in the pupil is considered as a weighting value for optimum design. The designed schematic eye has effective focal length of 20.8169 mm, back focal length of 15.4820 mm, front focal length of -13.8528 mm, and image distance of 15.7150 mm. When the pupil diameter is 4 mm, the diameter of entrance pupil and exit pupil are 4.6919 mm and 4.2395 mm, respectively. From the data of 75 measured Korean emmetropic eyes, this finite schematic eye is designed first in Korea.

• Journal of the Optical Society of Korea
• /
• v.16 no.1
• /
• pp.22-28
• /
• 2012

We report a focal-length tunable liquid lens based on thermopneumatically driven fluidic pressure. The fluidic pressure is generated by deformation of an elastomeric diaphragm induced by thermopneumaticity from a laterally integrated microheater sealed within an air chamber. The pressure is transmitted by a confined liquid to a lens diaphragm through an internal fluid channel. The liquid filling under the lens diaphragm functions as a liquid lens for dynamic focusing with properties depending on the curvature of the deformed diaphragm. The diaphragm area of the air chamber is designed five times larger than that of the lens cavity to yield high focal-length tunability by amplified deflection of the lens diaphragm. With our method, we achieved excellent focal-length tunability from infinity (without an input current) to 4 mm (with an input current of 12 mA) with a lens aperture diameter of 2 mm.

• 제어로봇시스템학회:학술대회논문집
• /
• 2000.10a
• /
• pp.81-81
• /
• 2000

We use camera to apply human vision system in measurement. To do that, we need to know about camera parameters. The camera parameters are consisted of internal parameters and external parameters. we can fix scale factor&focal length in internal parameters, we can acquire external parameters. And we want to use these parameters in automatically driven vehicle by using camera. When we observe an camera parameters in respect with that the external parameters are important parameters. We can acquire external parameter as fixing focal length&scale factor. To get lane coordinate in image, we propose a lane detection filter. After searching lanes, we can seek vanishing point. And then y-axis seek y-sxis rotation component(${\beta}$). By using these parameter, we can find x-axis translation component(Xo). Before we make stepping motor rotate to be y-axis rotation component(${\beta}$), '0', we estimate image coordinates of lane at (t+1). Using this point, we apply this system to Kalman filter. And then we calculate to new parameters whick make minimum error.

• International Journal of CAD/CAM
• /
• v.9 no.1
• /
• pp.37-46
• /
• 2010

Existing methods for the registration of blurred images are efficient for the artificially blurred images or a planar registration, but not suitable for the naturally blurred images existing in the real image mosaic process. In this paper, we attempt to resolve this problem and propose a method for a distortion-free stitching of naturally blurred images for image mosaic. It adopts a multi-resolution and robust feature based inter-layer mosaic together. In each layer, Harris corner detector is chosen to effectively detect features and RANSAC is used to find reliable matches for further calibration as well as an initial homography as the initial motion of next layer. Simplex and subspace trust region methods are used consequently to estimate the stable focal length and rotation matrix through the transformation property of feature matches. In order to stitch multiple images together, an iterative registration strategy is also adopted to estimate the focal length of each image. Experimental results demonstrate the performance of the proposed method.