Simple Graphical Selection of Optical Materials for an Athermal and Achromatic Design Using Equivalent Abbe Number and Thermal Glass Constant

Abstract

This paper presents a new graphical method for selecting a pair of optical glasses to simultaneously achromatize and athermalize an imaging lens made of materials in contact. An athermal glass map that plots thermal glass constant versus inverse Abbe number is derived through analysis of optical glasses and plastic materials in visible light. By introducing the equivalent Abbe number and equivalent thermal glass constant, although it is a multi-lens system, we have a simple way to visually identify possible optical materials. Applying this method to design a phone camera lens equipped with quarter inch image sensor having 8-mega pixels, the thermal defocuses over $-20^{\circ}C$ to $+60^{\circ}C$ are reduced to be much less than the depth of focus of the system.