Optical path length self-calibration method based on form measured surface data

Abstract

High-precision measurement of lenses and mirrors of free-form surface figures is necessary owing to the increasing functionality of optical elements. Previously, we developed a nanoprofiler measurement technology. The nano-profiler calculates the form from a slope distribution on the measurement surface. The slope distribution is calculated from the measurement result of the optical system that directly measures the slope of the surface using laser light and a quadrant photodiode, as well as the rotary encoder output that indicates the position of the optical system and the object to be measured. The slope distribution and optical path length are required to calculate the form. The geometrical length is between the measured surface of the object and the photodetector's surface. The optical path length was designed to be 400 mm when the instrument was manufactured; however, because assembly errors were included, the optical path length must be calibrated to obtain measurements with higher accuracy. Therefore, we herein propose a multistep self-calibration method to calibrate the optical path length. In this method, a plurality of forms is measured on the surface to be measured while changing the optical path length by a known amount. The optical path length was estimated based on the results of the multiple form measurements. Before the evaluation was performed, the optimum measurement conditions for the evaluation were determined via simulation, and the optical path length was obtained from the actual measurement results under the optimum conditions. The results show that the optical path length is 399.698 mm, and the standard deviation of the calculated variation in the optical path length is 5.3 μm.