Understanding the diffractive bifocal contact lens.
How a diffractive bifocal contact lens works is not intuitively obvious. This is because the diffractive bifocal operates by an unusual blend of refraction and interference. The present article seeks to clarify how it achieves its two focal powers. Most of this article, however, is devoted to the conceptually simpler case of diffraction gratings in order to develop an intuition for how a double focus is produced. Single slit, double slit, and multiple slit gratings are considered using two formalisms: Feynman's "arrow" method (also called phasors) and the Fourier method. When dealing with linear diffraction gratings we are interested in the light intensity in the focal plane. By a simple redefinition of variables, all of the mathematics for diffraction gratings can be applied to circular lenses. For this latter case instead of looking at the light intensity in the focal plane, we look at light intensity on the optic axis. The appearance of two focal points is a simple consequence of a combined interference and diffraction pattern. The goal of this article is to present an introduction to Fourier optics and an analysis of the bifocal contact lens in a reader-friendly manner.
Diffraction light analysis method for a diffraction grating imaging lens.
We have developed a new method to analyze the amount and distribution of diffraction light for a diffraction grating lens. We have found that diffraction light includes each-order diffraction light and striped diffraction light. In this paper, we describe characteristics of striped diffraction light and suggest a way to analyze diffraction light. Our analysis method, which considers the structure of diffraction grating steps, can simulate the aberrations of an optical system, each-order diffraction light, and striped diffraction light simultaneously with high accuracy. A comparison between the simulation and experimental results is presented, and we also show how our analysis method can be used to optimize a diffraction grating lens with low flare light.
Numerical analysis of surface crack propagation in flexible pavements using XFEM and cohesive zone model
Surface initiated (top-down) cracking in the longitudinal direction of pavements has become a predominant mode of failure in thick asphalt pavements. Most previous researchers studied crack propagation using the traditional Linear Elastic Fracture Mechanics (LEFM) method by calculating the stress intensity factor around the crack tip. In this paper, Extended Finite Element Method (XFEM) was used to study the key factors causing surface initiated crack propagation under surface tension and/or shear. A two-dimensional (2-D) finite element (FE) model for a two-lane flexible pavement was built to predict pavement responses and crack propagation potential under various scenarios. It was found that surface tension is the major driving force for crack propagation when the crack is at some distance away from tire loading. The results show that the distance from the location of crack to tire loading, the depth and direction of the crack, and the modulus ratio between the hot-mix asphalt (HMA) layer and the base layer have significant influences on crack propagation under surface tension. On the other hand, this study shows that shear stress can induce surface initiated crack propagation near the loading area as the shear resistance of material becomes low at the high temperature.