The PrecessionsTM process has been developed for the control of texture ('polishing'), preservation of form during polishing, and control of form ('figuring'), on flat, spherical and aspheric surfaces. In this first and introductory paper, we summarize the need for aspherics, review some aspheric technologies, and then distill a 'wish-list' of attributes for an aspheric process. Within this context, we focus on special properties of Precessions tools, their use in a family of 7-axis CNC polishing machines, and present experimental results.

The Precessions process polishes complex surfaces from the ground state preserving the ground-in form, and subsequently rectifies measured form errors. Our first paper introduced the technology and focused on the novel tooling. In this paper we describe the unique CNC machine tools and how they operate in polishing and correcting form. Experimental results demonstrate both the '2D' and '2(1/2)D' form-correction modes, as applied to aspheres with rotationally-symmetric target-form.

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We summarise the reasons why aspheric surfaces, including non-rotationally-symmetric surfaces, are increasingly important to ground and space-based astronomical instruments, yet challenging to produce. We mainly consider the generic problem of producing aspheres, and then lightweight segments for the primary mirror of an Extremely Large Telescope. We remark on the tension between manufacturability of spherical segments, and performance with aspheric segments. This provides the context for our presentation of the novel Precessions process for rapid polishing and formcorrection of aspheric surfaces. We outline why this is a significant step beyond previous methods to automate aspheric production, and how it has resulted in a generalized, scaleable technology that does not require high capital-value tooling customized to particular types of optical form. We summarise implementation in the first two automated CNC machines of 200mm capacity, followed by the first 600mm machine, and the current status of the process-development programme. We review quantitative results of polishing trials, including materials relevant to large and instrumentation optics. Finally, we comment on the potential of the technology for space optics and for removing quilting in honeycomb substrates.

We first consider the potential impact of a technology that could deliver polished, accurate aspheric surfaces in a routine and automated manner. We then summarise the technical challenge, and present an appraisal of the performance of the novel 'Precessions' process, which is a major advance in this direction. We outline the design concepts behind the productionized CNC polishing machines which executes the process, and then describe the progress developing strategies to preserve form when polishing ground surfaces, and to correct form on both pre-ground and polished surfaces. Particular consideration is given to resolving the inherent difficulties of control of centres on rotationallysymmetric parts. We then report on experimental results achieved with the machines. Finally, we present our programme to extend the control-algorithms to handle fully free-form surfaces, and draw conclusions about the effectiveness and generality of the 'Precessions' technique.