Exact Scan Patterns of Rotational Risley Prisms Obtained with a Graphical Method: Multi-Parameter Analysis and Design

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.