Rotational Risley prisms are one of the fastest two-dimensional (2D) optomechanical scanning systems. Their drawback is the strong non-linearity of the scan patterns they produce, in contrast to the most common (but slower) raster scanning modalities of 2D dual axis galvanometer scanners (GSs) or Micro-Electro-Mechanical Systems (MEMS) with oscillatory mirrors. The aim of this work is to develop a graphical method, which, to our knowledge, we have introduced to determine and characterize, using a commercially-available mechanical design program (for example CATIA V5R20 (Dassault Systems, Paris, France)) to simulate the exact scan patterns of rotational Risley prisms. Both the maximum and minimum angular and linear deviations of this type of scanner are deduced theoretically to characterize the outer diameter/Field-of-View (FOV) and the inner diameter (of the blind zone) of its ring-shaped patterns, respectively. This multi-parameter analysis is performed in correlation with the shape of the scan patterns, considering the four possible configurations of laser scanners with a pair of rotational Risley prisms, as well as all their parameters: prisms angles, refractive indexes, rotational speeds, distance between the two prisms, and the distance from the system to the scanned plane. Marshall’s synthetic parameters are also considered, i.e., the ratios of the rotational velocities and of the angles of the prisms. Rules-of-thumb for designing this optomechanical scanner are extracted from this analysis, regarding both shapes and dimensions of the scan patterns to be produced. An example of experimental validation completes the mathematical analysis and the performed simulations.
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.
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