Modeling and prediction of tool influence function under complex edge in sub-aperture optical polishing

Area of Science:

• Optical Fabrication
• Materials Science
• Manufacturing Engineering

Background:

• Edge mis-figures are a significant challenge in optical fabrication, hindering precision.
• Current models struggle with complex edge geometries and diverse tooling due to limited understanding of edge removal.
• Existing methods often rely on polynomial fitting for near-straight edges, lacking universality.

Purpose of the Study:

• To develop a comprehensive mathematical model for predicting complex edge tool influence functions (TIF).
• To elucidate the underlying mechanisms of edge effects in optical fabrication.
• To provide a unified 2-D analytical model for various edge workpieces and tools.

Main Methods:

• Proposed a nonlinear edge kernel concept to model nonlinear pressure by convolving with edge contours.
• Developed an algorithm for obtaining the edge kernel, adaptable to complex edge cases.
• Incorporated a moment balance formula for linear pressure and a basic pressure distribution to compensate for tool pad unevenness.
• Validated the model against Finite Element Analysis (FEA) results.

Main Results:

• Successfully modeled complex edge pressure efficiently, aligning perfectly with FEA outcomes.
• Demonstrated the nonlinear edge kernel's effectiveness in characterizing nonlinear pressure for complex edges.
• Verified the linear pressure component's adherence to moment balance constraints.
• Achieved accurate 2-D TIF predictions for diverse complex edge workpieces and tools through experimental validation.

Conclusions:

• The proposed comprehensive mathematical model accurately predicts complex edge TIF in optical fabrication.
• The novel nonlinear edge kernel and integrated pressure components offer a robust solution for edge effect modeling.
• This work advances the scientific understanding of edge removal behavior, enabling improved precision in optical manufacturing.