KANs-based method for chromatic confocal microscopy

Abstract

Chromatic Confocal Microscopy (CCM) is a highly precise measurement tool that has a wide range of applications. However, traditional CCM data processing methods, such as spectral curve peak extraction and curve fitting, have been observed to introduce errors in the measurement of spectral peak position, fitting parameter values, and data noise. These errors can negatively affect the measurement characteristics of the sensor, including its repeatability and resolution. To address these issues, this study proposes a regression prediction model based on Kolmogorov-Arnold Networks (KANs), which is designed to mitigate the impact of computational errors on the accuracy of CCM measurements. The deep learning model is capable of learning complex non-linear relationships, and inspired by the Kolmogorov-Arnold representation theorem, KANs replace traditional linear weights with spline-parametrized univariate functions, allowing them to learn activation patterns dynamically, thereby circumventing the errors associated with traditional data processing. The experimental results demonstrate that KANs exhibit better performance in CCM relative to one-dimensional convolutional neural networks (1D-CNN) and traditional method. In particular, 1D-CNN demonstrated a 70.0 % enhancement in terms of measurement repeatability in comparison to the traditional method(Gaussian fitting of curves to extract peak and polynomial fitting), whereas KANs method improved by 62.63 % compared to 1D-CNN method. Regarding the axial resolution, KANs demonstrate a 50 nm improvement over traditional methods. Furthermore, the KANs model exhibited a stronger rebuilding capacity in 3D reconstruction. The results demonstrate that the KANs model is capable of markedly enhancing the precision of data processing while preserving the high-resolution attributes inherent to CCMs. This study demonstrates the effectiveness and convenience of KANs model in CCM data processing and shows that the KANs model is effective in maintaining the high-accuracy performance of CCM.