Rigorous vector-diffraction-based spectral signal model for thickness measurement in chromatic confocal microscopy

Chromatic confocal microscopy (CCM) has been widely applied in materials science and mechanical manufacturing, owing to its excellent capability for precise displacement and thickness measurements. An accurate spectral signal model is essential for CCM to enhance the measurement performance. However, the conventional model based on geometric ray tracing often yields measured thicknesses that deviate from actual values. This discrepancy arises due to the refraction of light when it transitions from air into high-density media, causing the foci of incident light with varying aperture angles to be spatially dispersed along the optical axis. In this study, we propose a vector-diffraction-based spectral signal model that fully accounts for the reflectance, transmittance at layered media and phase differences of incident light rays at all aperture angles by using the vectorial diffraction method. Through the newly proposed model, the distribution form and peak positions of spectral signals can be precisely described. According to the simulation results, a more accurate thickness calculation model is provided. Experimental results indicate that the proposed model significantly enhances measurement accuracy compared to existing model, with the measurement error reduced from 38 μm to 1 μm when measuring a transparent plate with a thickness value of 1.035 mm, demonstrating improved reliability and consistency across diverse sample conditions.