  We computationally investigate the transmission efficiency through moth-eye
nanostructures that are fabricated on $\mathrm{SiO}_{2}$ windows in the
wavelength range from 0.4 to 2 $\mathrm{\mu m}$. We investigated both truncated
cones and truncated pyramids, and we varied the height, bottom width, and top
width of these shapes in order to maximize the transmission efficiency. We
found that there is no substantial difference in transmission between truncated
cone and pyramid structures. Using the constraints from the current achievable
experimental limits, a relatively uniform transmission coefficient of larger
than 98.8% can be obtained from 0.4 $\mathrm{\mu m}$ to 2 $\mathrm{\mu m}$.
These transmission results are only 0.4% in absolute value lower than the
transmission of a structure that is not constrained by current experimental
limits.
