[Sander, Daniel]

We met with Rodica Martin of LIGO to image our silicon optics from Knight Optical using some sort of 4D Technology instrument that we have previously used. We want to evaluate whether they need to be "super-polished" or if their surface quality is good enough as is to be coated. A rough surface is problematic as it scatters light into higher order spatial modes. The loss due to scattered light from surface roughness is roughly  [1,2]

\[ \text{Loss} = (2 k \cdot  \text{rms})^2 = \frac{16 \pi^2 \text{rms}^2}{\lambda^2}. \]

where k is the wavenumber of the laser light with wavelength \lambda, rms is the root mean squared surface roughness. The factor of 2 in the middle expression comes from light being reflected. Given a rough budget of 10 parts per million (ppm) due to surface roughness and a wavelength of 1550 nm, this sets a maximum rms surface roughness of 0.4 nm = 4 Å.

We imaged the front and back of 5 optics: two spoked optics with an octagonal barrel, two spoked optics with a cylindrical barrel, and a cylindrical optic without spokes.

We labeled and collected the data from the optics and will formally analyze it at a later date. We could not image all of the optics in our 3 hours because it took 10 to 15 minutes to set up the optic and get a good reading.

The initial data indicated an rms surface roughness of 0.25 nm +/- 0.1 nm over a 4.5 x 4.5 mm square sample in the middle of the optical faces. The cylindrical optic without spokes was closer to 0.45 nm, we think because it is dirty (it looks dirty). Rodica said machine is limited to 0.1 nm, so the results might be even better. This would indicate consistency in our samples and no need to polish further.