Absolute calibration of optical flats using the three-flat test by considering the relative humidity change

In a Fizeau interferometer measurement, one of the factors that reduces long-term measurement reproducibility is variation in the shape of the reference flat. The purpose of the present work is to improve the measurement accuracy of a Fizeau interferometer by establishing the causes of the reference flat deformation. We discovered that the deformation is caused by a change in environmental humidity. We confirmed that a reference flat with a diameter of 152 mm deforms to a paraboloidal shape with a peak-to-valley height of 1 nm in response to a relative humidity change of 11%. The cause of the deformation can be interpreted as being a change in the film stress in an antireflective coating on the reverse side of the reference flat due to the adsorption of water molecules. We carried out the three-flat test for an absolute calibration of optical flats by considering the effect of a relative humidity change. The calibration results indicate that the uncertainty in the measurements of the Fizeau interferometer was successfully improved to 0.7 nm (σ: standard deviation) along a length of more than 145 mm.