The Laser Interferometer Gravitational-wave Observatory (LIGO) is a long baseline Michelson interferometer, with arms of up to 4 km in length each containing a Fabry Perot cavity. CSIRO has manufactured 32 core optical components for the LIGO interferometer consisting of five different groups of optical elements. Long radii of curvature (7 km - 15 km) and tolerances in the order of plus or minus 200 m in the radius are specified. Although the components are made of hyper pure fused silica there are some residual inhomogeneities in the material. The optics used in transmission must be figured so that the influence of these material inhomogeneities on the transmitted wave front is compensated for. This was done by correcting the surface figure on side 2 of the optics. The approach we took to manufacturing the transmission optics was to calculate the quadratic component of refractive index gradient (Delta) n of the substrate from the measurements of the transmitted wavefront and the surface profile of the two substrate surfaces, determine what shape had to be produced on side two of the substrates to compensate for this gradient and then produce this by optical polishing. The surfaces were polished on rigid solid laps of Zerodur coated with a thin layer of Teflon as the polishing matrix, a technique developed by CSIRO for super-polishing very flat surfaces.
The manufacture and testing of the 'core' optical substrates for the Laser Interferometer Gravitational-wave Observatory (LIGO) are described in this paper. These substrates are for use in long baseline Michelson interferometers with Fabry Perot cavities up to 4 km in length in each arm. The optical surfaces of the substrates (250 mm diameter by up to 100 mm thick) are specified either flat or curved, with radii of curvature varying between 7 and 15 km and tolerance bands on the radius equivalent to variations in the sag (over 200 mm) of twenty nanometers or so. Very strict tolerances were also placed on the astigmatism of the surfaces and the surface errors in two spatial frequency bands, one at low frequencies ('waviness') and another at high frequencies ('roughness'). In some cases the radius of the wavefront emerging from the substrate was also specified (for a collimated test beam).
The wavefronts reflected by and transmitted through a coated substrate will be influenced by the non-uniformities of the coatings and distortion of the substrate produced as a result of coating stress. In this paper we describe the characterization procedure and results of a coated substrate for the Laser Interferometer Gravitational wave Observatory (LIGO) project. The fused silica substrate is 250 mm in diameter, 40 mm thick and on one side a multilayer anti- reflection coating is deposited and a 50% reflectivity multilayer coating on the other. To characterize the coatings, reflected and transmitted wavefront measurements were carried out with a 300 mm aperture phase-shifting Fizeau interferometer in combination with ellipsometric measurements of the coated surfaces. The interferometric measurements allowed the deformation of the substrate by the coatings to be assessed while the ellipsometric measurements allowed the coatings' thickness variation to be measured and the resulting phase variation in the reflected and transmitted wavefronts to be estimated. The measurements revealed substrate deformation of about 45 nm with a coating relief non-uniformity of about 5 nm over a working aperture of 200 mm.
Fizeau interferometers are traditionally used to determine the surface figure of uncoated optics. Since the reflectances from the uncoated reference and test surfaces are usually equal, the intensity of the interference fringe minimum is zero, so the fringe contrast is unity. If the same reference surface is used to measure the figure of a higher reflecting surface, the fringe minimum intensity is no longer zero and the fringe contrast decreases, eventually reaching zero for 100 percent reflecting optics. The problem can be overcome if the reference surface is coated with a lossy reflecting surface. We describe a coating to measure the figure of optical components having reflectance from 100 percent to 3.5 percent at 1064 nm. The spatial variations across the 150 mm working aperture in physical thickness of the two materials used to coat the reference surface were determined to an accuracy better than 1 nm using a single wavelength ellipsometer operating at 633 nm. Variations across the aperture of the phase changes on reflection from both sides of the reference flat substrate and on transmission were estimated. These results are presented together with calculations designed to determine the relative positions of the outside of the coating with respect to substrate surface as well as the position as seen optically. Substrate distortion due to stress in the coatings has also been measured.
CSIRO is manufacturing the `core' optical substrates for LIGO, a Michelson interferometer with arms up to 4 km in length each containing a Fabry Perot cavity. The beam splitter and input test mass mirrors (the entrance mirror to each cavity) have specifications not only for the optical surfaces but also for the radius of curvature of the wave front transmitted through the optical substrate. Our approach to manufacturing the substrates is to calculate the quadratic component of refractive index gradient (Delta) n from measurement of the transmitted wave front and the surface relief of the two substrate surfaces. After one of the surfaces (S1) is polished to specification, the radius on the second side required to achieve the specification on the transmitted wave front is calculated (using the measured value of (Delta) n, the actual value of S1 and the target value of the transmitted wave front). Results of this work and complications of the measurement procedure due to the thermal inertia and poor thermal conductivity of the silica substrates will be presented.
The Laser Interferometer Gravitational-wave Observatory (LIGO) core optical components have been manufactured by CSIRO. These optical substrates are optically polished on a lap surface that is made of Teflon coated onto a thick rigid faceted Zerodur base. To produce the km-scale radii (> 10 km) on these substrates the lap surface is shaped by abrading it with a fine ground silica plate whose radius of curvature corresponds to the one specified for the LIGO component. The plates are measured by a commercial phase stepping interferometer which is used in a grazing incidence arrangement. We describe the process of shaping and measuring the conditioning plates and laps.
Core optical substrates for the Laser Interferometer Gravitational Wave Observatory 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.
Optical interferometers are being built to operate over longer and longer baselines, in some cases more than a few kilometers. Examples include laser interferometers to detect gravitational waves, and stellar interferometers which use starlight to determine the angular diameter of the source. The optics used in these interferometers must satisfy demanding performance criteria. In this paper we review some of those criteria and present results which demonstrate that such optical surfaces can be successfully fabricated and measured.
Metrology procedures for determining the power, astigmatism, low and high spatial frequency variations in the surface profile on flat and curved optical surfaces are described. The procedures are applied to the characterization of optics produced for the Pathfinder program of the laser interferometer gravitational observatory and demonstrate that in the case of low spatial frequency surface errors measured by optical interferometry, measurements to a resolution down to (lambda) /2000 are possible in the measurement of the standard deviation of surface variations.