  High precision, high numerical aperture mirrors are desirable for mediating
strong atom-light coupling in quantum optics applications and can also serve as
important reference surfaces for optical metrology. In this work we demonstrate
the fabrication of highly-precise hemispheric mirrors with numerical aperture
NA = 0.996. The mirrors were fabricated from aluminum by single-point diamond
turning using a stable ultra- precision lathe calibrated with an in-situ
white-light interferometer. Our mirrors have a diameter of 25 mm and were
characterized using a combination of wide-angle single- shot and small-angle
stitched multi-shot interferometry. The measurements show root- mean-square
(RMS) form errors consistently below 25 nm. The smoothest of our mirrors has a
RMS error of 14 nm and a peak-to-valley (PV) error of 88 nm, which corresponds
to a form accuracy of $\lambda$=50 for visible optics.
