The determination of positions and orientations of a prism’s surfaces based on image orientation change

Abstract

Optical prisms are commonly employed because of their ability to output an image with a certain orientation and redirect and relocate the emergent beam of light in a given manner. Consequently, in order to design a prism that fulfills the above purposes, the following problem must be solved: how can the pose matrices, which define the positions and orientations of the prism’s boundary surfaces, be determined so as to produce the required image orientation change (IOC)? Previous papers presented a methodology to determine the unit normal vectors of a prism’s boundary surfaces for a given IOC. In this paper, a parameter L, referred to as image offset, is used to characterize the length of the common normal segment between the entrance chief ray and its exit chief ray for a prism. The methodology to determine the pose matrices of a prism’s boundary surfaces with a given image offset L is addressed. Further, the conditions for which a circular bundle of entrance rays can pass through a prism without being blocked by the prism’s boundary surfaces are also discussed. Two illustrative examples are given to demonstrate the proposed approaches.