2-D Interpolated Discrete Fourier Transform for High-Accuracy In-Plane Displacement and Rotation Measurement

This article introduces a novel two-dimensional interpolated discrete Fourier transform (2-D IpDFT) algorithm, specifically developed to achieve high-accuracy in-plane displacement and rotation measurements in machine vision applications. The 2-D IpDFT algorithm addresses the limitations of current methods by providing enhanced precision in estimating both frequency and phase, which are crucial for accurate pose estimation. The underlying principles of the algorithm are thoroughly detailed. To evaluate the effectiveness of the 2-D IpDFT, comprehensive simulations were conducted, analyzing the impact of varying pattern pitches and signal-to-noise ratio (SNR) levels on measurement accuracy. Beyond simulations, the algorithm's practical applicability was validated through experiments using a high-precision nanopositioning stage. The experimental results were compelling, revealing that the 2-D IpDFT algorithm achieved root mean square errors (RMSEs) as low as 10.7 nm and 13.6 nm for x and y displacements, respectively, and 2.1 μrad for z-axis rotation. Notably, these precise measurements were obtained even with a relatively low-resolution camera of 640x480 pixels. These findings underscore the significant potential of the 2-D IpDFT algorithm for high-precision pose estimation in various machine vision systems, including automated manufacturing, quality control, and robotics. By offering substantial improvements in both precision and reliability over existing techniques, this study positions the 2-D IpDFT algorithm as a promising tool for advancing the capabilities of vision-based measurement technologies.