# Optomechanical Analysis and Design of Polygon Mirror-Based Laser Scanners
###### Abstract
Various SS configurations have been developed, with on-axis [19] and off-axis PMs [20], as well as telescope [19, 20, 21, 22] and telescope-less, the latter in Littrow [23], Littman [24], and Littrow-Littman [25] setups. One of the most critical features of PM scanners for today's applications, i.e., the maximum limit of their rotational velocity (\(\omega\)), has been approached by the industry. Thus, high-end PM scanners have rotational motors that commonly reach 54 krpm and even 70 krpm, while developments to reach 120 krpm exist. This results in scan frequencies \(\langle f_{\rm s}\rangle\) equal to this rotational frequency multiplied by the number of PM facets. This pushes forward the design of motors and (especially aerodynamic) bearings, as well as fast and robust sensors and control structures. It also imposes performing a Finite Element Analysis (FEA) for each particular design, to assess the structural integrity and level of deformations, as highlighted in the literature [1]. Another direction of research in the scanners field, especially in the last decade, is related to handheld scanning probes (for example, for OCT [52, 53, 54, 55, 56, 57]), and scanning heads in general (for applications such as 3D printing or laser manufacturing [58, 59, 60]). While the former usually implies GSs or Micro-Electro-Mechanical Systems (MEMS), the latter also utilizes PM plus GS 2D systems to increase scanning velocity, and therefore productivity in industrial processes, for example. Starting from the necessity to clarify their fundamental characteristics, the basis of a theory regarding the optical functions and parameters of PM scanning heads has been approached in a preliminary study [32], based on a series of previous works [28, 29, 30, 31]. The focus has been to develop a theory that is both simple to use and rigorous, in the context of valuable but rather complex existing approaches [1, 14, 15, 16, 17]. PM-based SSs optimization is one of its field of interest [26], but the preliminary theory developed in [32] has raised interest for other applications as well, such as additive manufacturing/3D printing. In [35], for example, the functions developed in [32] were applied by using the suggestion made regarding the capability of the theory to pass from single rays to finite diameter laser beams, as we aim to complete in the present study. Moreover, in [61, 62] steps have been taken to develop monogon-type PMs with a curved facet to avoid using an objective lens, by linearizing PM scanning functions starting from the study and equations in [32]. Another motivation of the present study is the necessity to better unite optical analysis and design with other essential PM issues, such as mechanical ones, as pointed out in the literature [1]. Such mechanical (but also electrical and control) aspects of PM scanners are usually left to manufactures, to come with as-good-as-possible solutions between various (and commonly contradictory) aspects of scanner analysis and design. Therefore, the aim of the present work is to study optical aspects of PMs, which are essentially related to the kinematics of the laser beam, but also to relate them to mechanical issues. The latter is performed through a multi-parameter FEA that must consider constructive elements of the system. A limitation of the present work in this respect is the fact that only examples of these parameters are considered, as the scope is not to complete an exhaustive FEA (for all possible configurations, materials, and dimensions of PMs), but to develop connections of optical and mechanical aspects in order to complete both an analysis and design methodology of such scanners. Another limitation is not approaching control and automation aspects of the PMs, with their fast motors, because this is an entirely different topic, as in the case of GSs [11; 12; 13]. Finally, one must point out that, similar to scanners with oscillatory elements, the work completed on macro-devices can be applied, at least in part, to MEMS, as shown in the case of GSs [10].