High-precision centroid localization method for Shack–Hartmann wavefront sensors in low-density plasma diagnosis

Background For electron density diagnostics of low-density plasma in the load region of pulsed-power devices, Shack–Hartmann wavefront sensors with long-focal-length microlens arrays are commonly employed to enhance the detection sensitivity to weak phase-deflection signals. However, long-focal-length configurations make system imaging mismatch more pronounced. This may cause centroid boundary crossing, sub-aperture mismatch, and crosstalk, thereby degrading centroid localization accuracy and limiting the sensitivity of electron density inversion.

Purpose This study proposes a high-precision centroid localization method for Shack–Hartmann wavefront sensors based on object detection, aiming to achieve robust and accurate centroid coordinate regression under strong noise and large spot displacement conditions.

Methods A global offset correction mechanism based on full-field feature estimation was first established to correct the global spot-array offset caused by system imaging mismatch. Subsequently, an object detection framework performing localized sub-aperture detection was integrated with a continuous differentiable centroid operator to achieve sub-pixel centroid coordinate regression. To evaluate the proposed method, simulated and experimental datasets with varying complexity levels were constructed through physical modeling and laser imaging experiments for network training and validation.

Results The proposed method achieved mean centroid estimation errors below 0.26 pixels across all simulated and experimental datasets, with the minimum mean centroid estimation error reaching 0.158 8 pixels. Compared with the traditional threshold center-of-gravity method, the localization accuracy was improved by more than 2.8-fold. Ablation experiments further demonstrated that the introduced localized detection and differentiable centroid modules effectively suppressed compound noise and cross-boundary interference, reducing the mean centroid estimation errors on simulated and experimental datasets to 0.207 3 pixels and 0.180 0 pixels, respectively. When applied to low-density plasma diagnostics in electrical wire explosion corona experiments, the proposed method successfully reconstructed two-dimensional electron density distributions and improved the line-integrated electron density sensitivity of the system to 1×10¹⁵ cm⁻².

Conclusions The proposed method improves the localization accuracy and robustness of long-focal-length Shack–Hartmann wavefront sensor systems under strong noise and large displacement conditions. It significantly enhances the diagnostic capability for low-density edge plasma and provides a reliable approach for high-sensitivity electron density measurements in pulsed-power experiments.