Robust peak localization of the modulation response curve in continuously scanning structured illumination microscopy...

In continuous vertical scanning structured illumination microscopy (CVS-SIM) for three-dimensional (3D) measurement, each scanning position requires only a single exposure, after which the surface topography is reconstructed using the vertical scanning position corresponding to the maximum modulation. However, limited acquisition signals and imaging noise introduced during the continuous scanning process result in significant noise interference in the calculated modulation response (MR), and existing peak localization methods cannot effectively work in signals overwhelmed by noise, leading to reduced accuracy or even complete failure of peak localization. In this paper, we propose a robust peak localization method of modulation response using probability density distribution. The probability density equation for the peak position is formulated using the gradient information from the collected image points across multiple dimensions. Based on the high-weight probability density distribution region, the effective range within the MR is adaptively selected according to varying noise levels for peak localization. This approach mitigates the disturbance from irrelevant noise in MR by analyzing the contribution of gradient changes in the captured information to the position of maximum modulation. Furthermore, the appropriate peak localization range is adaptively selected based on the noise condition, thereby minimizing redundant calculations and enhancing the reconstruction speed. The feasibility of the proposed method is verified through simulation and experimental validation, demonstrating its potential for high-precision and complex surface measurements.