Study of symmetries of scan patterns generated by laser scanners with a pair of rotational Risley prisms

The present paper builds upon the novel, graphical method that we have introduced [V.-F. Duma, A. Schitea, <i>Proc. of the Romanian Acad. Series A</i> 19, 53-60, 2018] and developed [V.-F. Duma, A-L. Dimb,<i> Applied Sciences</i> 11, 8451, 2021] in order to study laser scanning with Risley prisms. An advantage of these scanning systems (and modality) is speed, while its main issue concerns the non-linearity of the generated scan patterns. The advantages of the proposed graphical method are that it provides (simulated) exact scan patterns (in contrast to the most utilized approximate methods) and that it is fast and easy to use (in contrast to rather complicated analytical methods). An essential aspect is highlighted in the present work regarding the functioning of the most common scanner with such components, i.e. with a pair of rotational Risley prisms. Thus, we approach the symmetries of generated scan patterns, presenting results that we recently obtained in [AL. Dimb, V.-F. Duma, <i>Symmetry</i> 15, 336, 2023]. Several aspects have been determined, starting with the number of symmetry axes. A novel notion, of <i>structures of symmetry </i>was proposed and developed. We showed how it is possible to generate (with high resolution) only a (small) part of the scan pattern, and further on to reproduce the entire pattern by using symmetries, including by (simply) rotating one of the proposed <i>structures of symmetry</i>. These were optimally defined and utilized in order to simplify the process of generating scan patterns for an increase in their resolution and/or a decrease in the simulation time. Characteristic geometrical aspects of the scan patterns have been determined, as well. Future directions of work to advance the domain are discussed.