Symmetries of Scan Patterns of Laser Scanners with Rotational Risley Prisms

Abstract

Laser scanners with rotational Risley prisms produce scan patterns that can be classified as a type of rhodonea curve, because of their symmetry. The present study builds upon the novel, graphical method that we have developed to simulate and analyze such patterns using a commercially available mechanical design program, CATIA V5R20 (Dassault Systems, Paris, France). This graphical method has both the advantage of simplicity (regarding analytical methods) and of generating exact scan patterns (in contrast to approximate methods). The aim of this work is to utilize this method to study symmetry properties of scan patterns produced by a pair of rotational Risley prisms. A multi-parameter analysis is performed, considering the characteristic parameters of the approached scanner: refractive indexes and angles of the prisms, as well as their rotational velocities. Furthermore, Marshall’s parameters are considered: ratios of the rotational velocities and of the prism angles. Because the symmetries are identical for scan patterns generated by all the four possible configurations of a pair of prisms (and only their dimensions are different), the shape of these patterns is studied only for one of these configurations. Therefore, without losing generality, the symmetries of the patterns produced by such scanners are determined, as well as some of their characteristic dimensions. Rules-of-thumb were obtained to be able to generate patterns that are appropriate for a specific application. Moreover, we demonstrated that the existing symmetries simplify the process of obtaining the scan patterns by identifying repetitive parts (defined as structures of symmetry) of a pattern.

Experimental versus simulated secondary scan patterns produced by a pair of Risley prisms

“…Figure 1(a) presents the way the "main" scan pattern is produced, i.e. the pattern generated by the beam that passes with pure refraction through the system, as discussed in detail in our previous works [13][14][15]. In Figs.…”

“…In order to perform the simulation, as in or previous studies, we utilize a commercially-available mechanical design program, CATIA V5 (Dassault Systèmes, Paris, France) for the graphical ray-tracing [14,15]. In order to perform experiments, a simple stand (Fig.…”

“…Laser scanners come in a variety of solutions, including without mechanical movements (electro-or acousto-optical, as well as holographic [1,2]) or opto-mechanical (such as galvanometer scanners (GSs) [3][4][5], with polygon mirrors [6,7], or with refractive elements). The latter category includes scanning systems with Risley prism, rotational [8][9][10][11][12][13][14][15], oscillatory [16], as well as in combinations of rotational and oscillatory prisms. Simple prisms are the most common, but doublets are also useful to minimize chromatic aberration [17], while other devices (for example with diffraction gratings [18]) are being explored.…”

“…The major disadvantages of Risley scanners refer to their non-linear scanning process (i.e., with variable scanning velocities) and to the complex shape of the scan patterns. In order to address the latter issue, we have introduced [13] and developed [14,15] a graphical method in order to obtain and (to be able to) analyze exact scan patterns in an easy-to-use way. This is in contrast to approximate methods [8], as well as to rather complicated analytical approaches [9][10][11], respectively.…”

Measurement analysis of optical micrometers with polygonal mirror-based laser scanners

“…For 2D scanners PMs are employed mainly in laser manufacturing and 3D printers (in order to provide the fast scan line) in competition to the most common dual axis galvanometer scanners (GSs) [11,12], Micro-Electro-Mechanical Systems (MEMS) with oscillatory elements [13], and rotational Risley prisms [14][15][16][17][18][19].…”