Precise Phase Measurement for Fringe Reflection Technique through Optimized Camera Response

Abstract

The Fringe Reflection is a robust and non-contact technique for optical measurement and specular surface characterization. The periodic alternation between dark and light cycles of the fringe patterns encodes the geometric information and provides a non-contact method of spatial measurement through phase extraction. Precisely expressing the positions of the points of the fringe pattern is a fundamental requirement for an accurate fringe reflection measurement. However, the nonlinear processes, both in generating the fringe pattern on a screen and capturing it using pixel values, cause inevitable errors in the phase measurement and eventually reduce the system’s precision. Aiming at reducing these nonlinear errors, we focus on constructing a new quantity from the pixel values of the photos of the fringe patterns that could linearly respond to the ideal fringe pattern. To this end, we hypothesize that the process of displaying the fringe pattern on a screen using a control function is similar to the process of capturing the pattern and converting the illuminating information into pixel values, which can be described using the camera’s response function. This similarity allows us to build a scaled energy quantity that could have a better linear relation with the control function. We optimize the extracted camera response function using an objective to increase the precision and reduce the quoted error. Experiments designed to determine the positions of points along the quartile lines verify the effectiveness of the proposed method in improving fringe reflection measurement precision.