Graphical method to determine exact scan patterns generated with rotational Risley prisms

Risley prisms are utilized in a variety of applications, including precision pointing and scanning, interferometry, holography, polarimetry, and light attenuation. Laser scanning with such systems is fast, but the generated scan patterns are complicated. Analytical methods to determine them are rather difficult, while approximate methods do not provide exact patterns. While we point out these issues, the present study is built on a new, graphical method that, to our knowledge, we have introduced [V.-F. Duma, A. Schitea, Laser scanners with rotational Risley prisms: Exact scan patterns, Proc. of the Romanian Acad. Series A 19, 53-60, 2018] to obtain scan patterns produced by Risley prisms. A commercially available mechanical design program, CATIA V5R20 (Dassault Systèmes, Paris, France) has been used to perform the ray tracing, using the prisms equations, for all four possible configurations of laser scanners with a pair of rotational Risley prisms. One of these four configurations is considered in this study, to present the developed method. A deviation angle of 2° for the optical wedges is considered in this study. A brief comparison between the obtained exact scan patterns is made for different values of the parameter M (introduced by Marshall), which represents the ratio of the rotational speeds of the two prisms. The study also presents the cartesian coordinates of the points which define the trajectory of the laser spot on a scanned plane. Advantages of using the graphical method as well as its perspectives are pointed out.