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.