Asphere, O asphere, how shall we describe thee?

Abstract

Two key criteria govern the characterization of nominal shapes for aspheric optical surfaces. An <i>efficient</i> representation describes the spectrum of relevant shapes to the required accuracy by using the fewest decimal digits in the associated coefficients. Also, a representation is more <i>effective</i> if it can, in some way, facilitate other processes - such as optical design, tolerancing, or direct human interpretation. With the development of better tools for their design, metrology, and fabrication, aspheric optics are becoming ever more pervasive. As part of this trend, aspheric departures of up to a thousand microns or more must be characterized at almost nanometre precision. For all but the simplest of shapes, this is not as easy as it might sound. Efficiency is therefore increasingly important. Further, metrology tools continue to be one of the weaker links in the cost-effective production of aspheric optics. Interferometry particularly struggles to deal with steep slopes in aspheric departure. Such observations motivated the ideas described in what follows for modifying the conventional description of rotationally symmetric aspheres to use orthogonal bases that boost efficiency. The new representations can facilitate surface tolerancing as well as the design of aspheres with cost-effective metrology options. These ideas enable the description of aspheric shapes in terms of decompositions that not only deliver improved efficiency and effectiveness, but that are also shown to admit direct interpretations. While it's neither poetry nor a cure-all, an old blight can be relieved.