Optical element made from fluoride single crystal, method for manufacturing optical element, method for calculating birefringence of optical element and method for determining direction of minimum birefringence of optical element

The present invention provides a method for calculating the birefringence of an optical element and selecting the direction of minimum birefringence in the optical element. A material for manufacturing the optical element is a fluoride single crystal with a birefringence value that is reduced compared to conventional materials. The fluoride single crystal is cut from a fluoride single crystal ingot obtained by crystal growth so that the {111} crystal planes are two parallel planes, after which the optical performance is improved by subjecting this material to a heat treatment. The birefringence of the optical element is calculated by converting known piezo-optical constants in a specified three-dimensional orthogonal coordinate system for the optical material into piezo-optical constants in an arbitrary three-dimensional orthogonal coordinate system. The amount of change in the refractive index n 1 of the optical material in a first direction along the direction of one coordinate axis of the arbitrary three-dimensional orthogonal coordinate system, and the amount of change in the refractive index n 2 of the optical material in a second direction which is perpendicular to the first direction are calculated using a uniaxial stress that is applied to the optical material along the first direction and the piezo-optical constants in the arbitrary three-dimensional coordinate system. The amount of birefringence as seen from a third direction perpendicular to the first direction and the second direction is determined in the arbitrary three-dimensional orthogonal coordinate system by determining the difference between the amount of change in the refractive index n 1 and the amount of change in the refractive index n 2.