Rhodonea-type Laser Scan Patterns Generated by a Pair of Rotational Risley Prisms

We report our study on the symmetries of scan patterns generated by laser scanners with a pair of rotational Risley prisms [https://doi.org/10.3390/sym15020336]. Such rhodonea curve types have been approached using the approximation of small angles of optical prisms or by employing rather complicated (although exact) approaches. In contrast to both these research avenues, we developed a graphical method for simulating such patterns with a mechanical design program, CATIA V5R20 (Dassault Systems, Paris, France) [https://doi.org/10.3390/app11188451]. This method offers both the advantage of generating exact scan patterns and of simplicity. The presentation starts with the fundamentals of Risley prism-based laser scanners. One of the four possible configurations is chosen and its basic equations are derived. The scan patterns are analyzed with regard to the characteristic parameters of the system: angles of the prisms, refractive indexes, rotational velocities, and the two Marshall parameters (i.e., k, ratios of the prism angles, and M, ratio of the rotational velocities). The symmetries of the scan patterns are studied and repetitive parts are identified (i.e., structures of symmetry). We show how such structures simplify the process of generating the scan patterns, thereby shortening the simulation time. Rules of thumb are extracted for generating patterns that may be appropriate for certain applications.