Risley prisms as a conformal transformation device: II. Derivatives of the absolute functions and an attributive analysis of the control singularities

Risley prisms have quite a few advantages over their competitive mirror scanning systems, a highly commendable one being the conformal transformation of the angular motions of the two prisms into a 2D pattern in the polar frame. However, in such a transformation, knotty problems relating to the so-called control singularities unpreventably occur when the two prisms are either in parallel with their apexes aligned or in opposition to each other. The aim of Part II of this study is an extension of the theories and their applications presented in Part I of this study [ J. Opt. Soc. Am. A 39 , 1540 ( 2022 ) JOAOD6 0740-3232 10.1364/JOSAA.463724 ] to a parametric analysis of the singularities and their describing functions for a better understanding of how the scanning geometry affects the attributes of the singularities and how we can reduce their unfavorable influence by properly selecting the parameters of this two-prism system.