Virtual dual-difference zero-crossing localization for fast and noise-robust surface topography reconstruction in structured illumination microscopy

Structured illumination microscopy (SIM) is a promising technique for areal surface topography measurement, but its reconstruction performance is often limited by the computational cost and noise sensitivity of axial modulation response (AMR) peak localization. This paper presents a virtual dual-difference (VDD) localization method for SIM surface reconstruction. The method constructs a zero-crossing response from the measured AMR using a virtual axial offset, and combines this reformulation with adaptive weighted linear fitting to replace conventional nonlinear Gaussian peak fitting. An analytical criterion is further used to determine the virtual axial offset that maximizes the zero-crossing slope, thereby improving localization stability. Since the proposed method operates directly on the experimentally measured AMR and does not require additional hardware or modified acquisition, it can be readily integrated into conventional phase-shifting SIM. Simulations under different noise levels and experiments on a calibrated step, a planar mirror, a copper surface, and a precision bearing ball were carried out to evaluate the method. For the calibrated step, the root-mean-square measurement error was reduced from 2.93 nm to 2.12 nm under appropriate axial sampling conditions. For the planar mirror, rough copper surface, and precision bearing-ball datasets, the reconstruction time was reduced by 92%, 98%, and 97%, respectively, compared with Gaussian fitting. The copper-surface and bearing-ball experiments further demonstrate improved robustness under low-SNR and large-slope conditions, including reduced measurement noise and fewer reconstruction outliers. These results indicate that the proposed VDD method provides a practical and efficient alternative to Gaussian peak fitting for fast and noise-robust SIM surface topography reconstruction.