Physical constraint flow field reconstruction method for immersion scan-step flow

The lithography immersion flow field is highly sensitive to minor variations due to the precision demands of lithography. The scanning flow induces pressure fluctuations on the lens surface, subsequently impacting the quality of exposure. Previous measurement methods have encountered sparse distribution measurements on the lens surface due to limitations in sensor size and flow field dimensions. In this manuscript, the authors propose a modal fusion flow field reconstruction method, effectively integrating sensor-based experimental methods and equation-based computational methods. This method achieves high-resolution measurements of stress distribution and velocity distribution. Initially, a simulation of the flow field under operational conditions is conducted to acquire a dataset, followed by decomposing the dataset into modes to establish a modal library. Throughout the measurement process, the modal library is dynamically restructured based on sensor signal using a sparse representation method to forecast the flow field, and subsequently, the flow field is corrected in accordance with the Navier-Stokes equation.