Deterministic method for generating removal functions through online beam density regulation

Ion beam figuring (IBF) technology, characterized by atomic-level material removal, has become a core process in ultra-high-precision optical manufacturing. The realization of ultra-high-precision optical element figuring necessitates full-band error control, in which the parameters of the removal function directly determine the figuring capability. Traditional methods for generating removal functions suffer from parameter drift in offline-calibrated removal functions and insufficient flexibility in parameter adjustment, making them difficult to adapt to the dynamic needs of error correction across different frequency bands. This paper proposes a deterministic method for generating removal functions through online regulation of ion beam density. By analyzing the regulation mechanism of stand-off distance and aperture values on beam density, a multi-task learning prediction model is established for the characteristic parameters of removal functions and beam current distribution. Through these efforts, a deterministic method for generating a removal function was proposed. Experiments show that adjustments to stand-off distance and aperture values conform to the laws of beam density regulation. The determination coefficient (R²) of the multi-task learning model after training exceeds 0.9716, and the mean squared error (MSE) is within 0.0079. In the validation experiment, the accuracy between the generated removal function and the target removal function exceeds 96%, meeting precision requirements. This study provides a new approach to address the limitations of traditional methods relying on fixed-parameter removal functions in full-band error correction, and its dynamic parameter adjustment capability can support the application of subsequent variable beam diameter modification strategies.