The key mechanisms & predictive models that determine the spatially dependent material
removal rate (called the tool influence function (TIF) spots) during hemispherical sub-aperture tool
polishing on flat & curved fused silica glass are presented.

1. INTRODUCTION

As freeform optic designs become more complex (such as having peak-to-valley surface heights that increase), the ability to
control the final workpiece shape to the same precision as conventional optics (flats and spheres) becomes more challenging.
Today, freeform optic designs ranging in surface heights from 0.1 to 100 mm, have been typically fabricated with deviations from
the target surface figure ranging from 1 to 10 µm, whereas flat and spherical optics can routinely be fabricated with deviation of
only 10’s of nm. Freeform optics are typically fabricated using sub-aperture tool grinding and polishing. This polishing method
requires a detailed understanding of the local material removal (tool influence function or TIF) at the contact spot between the
workpiece and tool to achieve high removal determinism and hence precision of the optic relative to the desired/design surface
figure.

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