Measurement and correction of lateral distortion in a Fizeau interferometer based on the self-calibration technique

The lateral distortion of a surface measuring Fizeau interferometer may cause distorted image features in the lateral direction, as well as the surface form error in the axial direction (which is a source of the retrace error). Traditional method for lateral distortion measurement requires a high-accuracy calibration plate featuring a grid pattern. Such a calibration plate is not always available, especially when the required accuracy of the grid pattern comes to the order of sub-micrometer or even nanometer level. To remove the dependence on the plate accuracy, we propose a self-calibration method for the measurement and correction of lateral distortion in Fizeau interferometer. The self-calibration technique may separate the lateral distortion and the geometric error of the calibration plate. This method is verified using a 108-mm-aperture Fizeau interferometer. The experiments show that the form measurement error of a surface tilted at approximately 5° and 16° can be reduced from 92 nm to 43 nm and from 251 nm to 144 nm (peak-to-valley value), respectively, after the distortion correction.