Measurement of Small-Slope Free-Form Optical Surfaces with the Modified Phase Retrieval.

Xinxue Ma,Jianli Wang,Bin Wang,Xinyue Liu

doi:10.3390/mi13010082

Abstract

In this paper, we demonstrate the use of the modified phase retrieval as a method for application in the measurement of small-slope free-form optical surfaces. This technique is a solution for the measurement of small-slope free-form optical surfaces, based on the modified phase retrieval algorithm, whose essence is that only two defocused images are needed to estimate the wave front with an accuracy similar to that of the traditional phase retrieval but with less image capturing and computation time. An experimental arrangement used to measure the small-slope free-form optical surfaces using the modified phase retrieval is described. The results of these experiments demonstrate that the modified phase retrieval method can achieve measurements comparable to those of the standard interferometer.

Highlights

With the rapid development of national defense, aerospace, and other fields, the demand for high-precision and high-quality photoelectric products is increasing, and these photoelectric products are gradually developing toward miniaturization
In order to solve the problem of free-form optical surface metrology, we introduce a feasible non-contact measurement method called Phase Retrieval (PR), a high-precision method and an alternative to interferometry for optical testing, with the advantages of compactness, low-cost, and a stable system
Comparing the results of the modified PR with the results of WYKO interferometer, the RMS difference is less than 2.777 nm, which shows that the proposed improved PR method is feasible for measuring free-form surfaces

Summary

Introduction

With the rapid development of national defense, aerospace, and other fields, the demand for high-precision and high-quality photoelectric products is increasing, and these photoelectric products are gradually developing toward miniaturization. In order to solve the problem of free-form optical surface metrology, we introduce a feasible non-contact measurement method called Phase Retrieval (PR), a high-precision method and an alternative to interferometry for optical testing, with the advantages of compactness, low-cost, and a stable system. As PR is a method of wave-front sensing and a simple experimental arrangement in optical metrology, it has been used in system measurement and alignment; it has, for example, been used in the Hubble Space Telescope and the Micromachines 2022, 13, 82. As PR is a method of wave-front sensing and a simple experimental arrangement in optical metrology, it has been used in system measurement and alignment; it has, for example, been used in the Hubble Space Telescope and the James Webb Space Telescope [14,15]. Some PR algorithms have robustness, multiple solutions, stagnation; for example, the convergence speed the fastest.

The Principle of PR

The Modified Gradient Search Algorithm of PR

Experimental Demonstrations

Conclusions