Two key criteria govern the characterization of nominal shapes for aspheric optical surfaces. An efficient
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 effective 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.
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