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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.

Edge mis-figure is regarded as one of the most difficult technical issues for manufacturing the segments of extremely large telescopes, which can dominate key aspects of performance. A novel edge-control technique has been developed, based on 'Precessions' polishing technique and for which accurate and stable edge tool influence functions (TIFs) are crucial. In the first paper in this series [D. Walker Opt. Express 20, 19787-19798 (2012)], multiple parameters were experimentally optimized using an extended set of experiments. The first purpose of this new work is to 'short circuit' this procedure through modeling. This also gives the prospect of optimizing local (as distinct from global) polishing for edge mis-figure, now under separate development. This paper presents a model that can predict edge TIFs based on surface-speed profiles and pressure distributions over the polishing spot at the edge of the part, the latter calculated by finite element analysis and verified by direct force measurement. This paper also presents a hybrid-measurement method for edge TIFs to verify the simulation results. Experimental and simulation results show good agreement.

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.

Segment-edges for extremely large telescopes are critical for observations requiring high contrast and SNR, e.g. detecting exo-planets. In parallel, industrial requirements for edge-control are emerging in several applications. This paper reports on a new approach, where edges are controlled throughout polishing of the entire surface of a part, which has been pre-machined to its final external dimensions. The method deploys compliant bonnets delivering influence functions of variable diameter, complemented by small pitch tools sized to accommodate aspheric mis-fit. We describe results on witness hexagons in preparation for full size prototype segments for the European Extremely Large Telescope, and comment on wider applications of the technology.

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