Prism design based on changes in image orientation

We present a method of designing a prism to produce an image with a specific orientation. Traditional prism design of this kind is done by trial and error with the aid of geometrical drawing and cannot provide analytical results. Using skew ray tracing sensitivity analysis, we present a merit function that can specify changes in image orientation after the image is reflected by an arbitrary number of flat boundary surfaces. Two design approaches are proposed. One can produce a prism with a minimum number of flat boundary surfaces with the aid of an auxiliary unit vector. The other can produce many configurations of prisms but without the above feature. An illustrative example is used to demonstrate the validity of the proposed approaches. Eight new configurations, which can produce the same change in image orientation, are obtained from the proposed design approaches.