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Modeling of Risley prisms devices for exact scan patterns

We investigate the scan patterns produced using different pairs of Risley prisms. Combinations of optical wedges with different prism angles (corresponding to different deviations angles of the prisms) are considered to complete the exact modeling of the scanning process using specialized mechanical design programs. While this procedure is somehow elaborate with regard to approximate methods, it has the advantage of providing the exact movement laws of the laser spot on various types of surfaces scanned with this type of refractive device. The study is made with regard to the characteristic parameters of the device, such as θ1 and θ2 - the prism angles of the two wedges, ω1 and ω2 - the rotating speeds of the two wedges, and the geometry of the scanner (which includes the distance between the two prisms, their orientation, and the distance to the scanned plane). The scanner is approached for a row of values of the characteristic parameters k=θ2/θ1 and M=ω2/ω1 introduced in Marshall’s classical work. The results allow for choosing the most appropriate patterns for specific scanning applications.