Fizeau interferometer calibration method: correction of the retrace error

Fizeau interferometers are used for high precision control of the shape of the surfaces of optical components. Fizeau interferometers with a common path are used to measure such parameters as deviation from fatness and sphericity (maximum range) PV (peak-valley), since this design prevents the influence of optical system aberrations on the measurement results. When adjusting the Fizeau interferometer to the zero fringe the reference and object beams travel along the same optical path after reflections from the object and the reference mirror, the interferometer’s aberrations are compensated, including the nonflatness of the surface of the reference plate. However, under real operating conditions of the interferometer, vibrations and heat flows may cause a tilt between the reference and object beams. In this case, the optical path of the reference and object beams will be different, which will lead to the so called retrace error in the determination of the wavefront phase. The retrace error introduces distortions into the reconstructed phase and reduces the accuracy of measurements of deviations from flatness. In this work, the Fizeau interferometer is considered as a black box that has its own wave aberrations. The method of calibrating a Fizeau interferometer proposed in this work, which makes it possible to reduce the retrace error, is based on adding a reference channel with a liquid mirror to the Fizeau interferometer. This results in a combined optical setup consisting of a wide-aperture Fizeau interferometer and a low-aperture Twyman-Green interferometer. The reference channel of the Fizeau interferometer is blocked, and in the Twyman-Green interferometer mode, an interferogram of the wave fi eld of the radiation reflected from the flat reference plate of the Fizeau interferometer is recorded. The phase reconstructed from the obtained interferogram contains all the wave aberrations of the black box in the reverse path of the radiation. The correction of the retrace error of the radiation is theoretically justified using a wave approach to describe the operation of the Fizeau interferometer and has been experimentally verifed. The proposed method for calibrating a Fizeau interferometer can be used to control the surface shape of large-sized optical elements in modern production environments.