Metrology of LIGO core optics

Core optical substrates for the Laser Interferometer Gravitational Wave Observatory (LIGO) are being manufactured and tested at CSIRO. These substrates are for use in long baseline Michelson interferometers with Fabry Perot cavities up to 4 km in length in each arm. The optics consist of 32 high quality fused silica substrates, comprising folding mirrors, end test masses, input test masses, recycling mirrors and beamsplitters. The dimensions of the substrates are 250 mm diameter by up to 100 mm thick. The optical surfaces are either flat or curved, with radii of curvature between 7 km and 15 km and tolerance bands on the radius equivalent to variations in sag (over 200 mm) of about 20 nm. Strict tolerances are also placed on the surface finish (scratches and defects), astigmatism and on the surface errors, averaged over a 200 mm aperture, within two extended spatial frequency bands. The surface errors integrated over a band of low spatial frequencies up to 4.3 cm(-1) ("waviness") are specified to be less than 1.6 nm and the errors integrated over spatial frequencies between 4.3 cm(-1) - 7,500 cm(-1) ("roughness") are to be less then 0.2 nm for the best surfaces. The surface figure and the waviness were measured on a 300 mm aperture digital interferometer with respect to an absolutely calibrated reference flat. This interferometer has a short term repeatability of 0.5 nm rms and allows absolute characterisation of the LIGO surfaces to an accuracy of a few nanometres over the 250 mm aperture. Special measurement and analysis procedures were developed to allow the certification of the surfaces to the tight tolerances specified. The surface roughness was measured on a profiling microscope fitted with two different magnification heads (2.5X and 40X). Since neither of these two heads covers the entire high spatial frequency band specified above, it was necessary to combine the data from the two heads to calculate the roughness.