# Optomechanical Analysis and Design of Polygon Mirror-Based Laser Scanners
## 2 Characteristic Functions and Parameters of PMs versus GSs  
### 2.1. GSs and PM Scanning Heads  
The schematics of 1D GSs and of PM-based scanning heads are presented in Figures 1 and 2, respectively. GSs have a mirror mounted on the mobile element (i.e., on the shaft of its electric motor) that performs oscillatory movements with a certain angular amplitude \(\theta_{\text{m}}\) (of up to \(30^{\circ}\) for modern devices [1; 2; 3; 4; 58; 60])--Figure 1a. In contrast, PMs perform a continuous rotational movement--Figure 2a. This gives the PMs the advantages of a much higher scanning velocity and of a one-direction scan, which is important, for example, for SSs [19; 20; 21; 22; 23; 24; 25; 26] and for lateral scanning in imaging, for example, with CM or OCT [43; 44; 45; 46; 47; 48; 49; 50]. The GS oscillatory mirror must stop and turn, which is where mechanical inertia comes into play, therefore its deceleration and acceleration periods cannot provide a constant scanning velocity \(v\)--Figure 1b. This proves to be a major drawback. Thus, for the most common triangular and sawtooth input signals of the device, non-linearities occur in the corresponding time intervals (\(\Delta t\) in the example in Figure 1c for triangular signals). This phenomenon was demonstrated and studied in detail in [7], with examples of galvoscanning in OCT. For such imaging methods, it means that the corresponding distorted portions (i.e., with non-equally spaced pixels) must be discarded, as performed in [8] based on the study in [7]. This reduces the useful angular scan amplitude from \(\theta_{\text{m}}\) to \(\theta_{\text{a}}\), and the useful linear scanning field (i.e., the one scanned with constant velocity), from \(2H\) to \(2x_{\text{a}}\)--Figure 1a. In consequence, the duty cycle (i.e., the time efficiency of the scanning process) decreases as well--as modelled mathematically in [9] to perform collations of individual GS-based OCT images. Thus, (larger) mosaic images can be obtained, to reach a higher FOV than the one for individual scans. For other common, sinusoidal inputs applied to the GS, the scan is performed with variable velocity over the entire FOV, therefore the duty cycle is even lower than for triangular or sawtooth scanning, as only a small portion of the characteristic can be considered approximately linear. In fact, the entire scan (i.e., the image in the case of CM or OCT) is distorted and must be post-processed, and this can produce artefacts. On the other hand, sinusoidal inputs have the advantage of a smoother mechanical regime, therefore the maximum scan frequency \(f_{s}\) is higher than for sawtooth scanning, for example, as indicated by manufacturers [58; 59; 60]. Figure 1: Galvanometer scanner (GS): (**a**) Principle scheme and main components; (**b**) beam deflection and corresponding angles and functions; (**c**) a common triangular signal of a GS, with a comparison between input and output (the latter given by the angular position of the GS mirror). Figure 2: Polygon mirror (PM) scanning head: (**a**) 3D view with characteristic torques (\(T\)), parameters, incident, and reflected beams; (**b**) PM facet in three characteristic positions: for \(\theta=\theta_{1}\), \(\pi/4\), and \(\theta_{2}\), where \(\theta_{1}\) and \(\theta_{2}\) are the angles for which the margins of the objective lens are reached. Finally, there is a clear trade-off for GSs between \(f_{\rm s}\) and \(\theta_{\rm m}\): As modelled from experimental data [7; 9; 10], the maximum possible/limit scan amplitude (i.e., the one that still corresponds to a controlled and not to a chaotic movement of the mobile element) drops almost exponentially with \(f_{\rm s}\), therefore one cannot utilize the higher \(f_{\rm s}\) of GSs for a larger FOV [10]; the FOV is significantly reduced for \(f_{\rm s}\) close to the maximum value of 1 kHz that is specific to a GS with an aperture of around 4 mm used in OCT or CM, for example [58].