We report a fully-developed theory of laser scanners with rotational Polygon Mirrors (PMs). The deduced scanning function, velocity, and acceleration of PMs have been deduced and discussed in comparison to those of Galvanometer Scanners (GSs). All other characteristic parameters have been obtained, including angular and linear field-of-view (FOV), as well as duty cycle [Proc. of the Romanian Acad. Series A 18, 25-33, 2017]. Although this developed theory considered the laser beams reduced to a single ray (i.e., the center axis of the beam), the specific approach has allowed further on for a complete analysis for scanning laser beams with finite diameters. The multi-parameter optomechanical analysis of these PM functions was performed as well, considering all constructive and functional parameters [Appl. Sci. 12, 5592 (2022)]. The non-linearity of scanning functions (i.e., the non-constant scanning velocities) has been approached. In order to linearize the PM or GS scanning function, a two supplemental mirrors device was developed. This increases the distance between the PM and its objective lens within a reasonable dimension of the system, by folding the scanned laser beam. Rules-of-thumb have been obtained for the design of these scanning heads. The optical part has been completed with a Finite Element Analysis (FEA) of rotational PMs, assessing their structural integrity. An optomechanical design scheme completes the PM scanning heads study, highlighting the links between optical and mechanical aspects. This type of scheme can be utilized for other optomechanical scanners, as well.