High-precision liquid reference Fizeau interferometry with motionless phase-shifting method and tilt-suppressed...

This paper presents a high-precision liquid reference Fizeau interferometry system, which consists of a source phase-shifting module and an interference module. In the source phase-shifting module, a motionless temporal polarization phase-shifting method based on a liquid crystal variable retarder is utilized, and large carrier frequency interferograms are collected and analyzed to calibrate the voltage-induced retardation, which ensures the stability of the phase-shifting process. In the interference module, 100cSt dimethyl Silicone oil is selected as the liquid reference. While a liquid surface is conventionally assumed to be a perfectly flat, edge-infiltration effect, liquid properties, and other factors can modify its surface shape and will last for a long time. Here, the conjugate differential method is used to orthogonally translate the liquid reference to obtain its surface shape. Compared with the translation operation in traditional absolute testing methods, it is important to note that the movement of the liquid reference can suppress tilt error caused by guidance errors of the motorized stage, benefitting from the liquid properties and the effect of gravity. The tilt errors caused by environmental vibrations, mechanical movement, and drift, which can be effectively suppressed through the screening of multiple-average measurement results and the constraints of the high-precision measurement results, as well as the vertical diameter line calculated by the traditional three-flat method. The experimental results show that the standard deviation of residual vertical diameter lines improves 1.07 nm after removing the calibrated liquid reference.