Trigonometric-spline dwell time scheduling and real-time interpolator under dynamic constraints for deterministic...

Area of Science:

• Optics fabrication
• Precision engineering
• Manufacturing processes

Background:

• Deterministic polishing is crucial for ultra-precision optics manufacturing.
• Existing dwell time algorithms face challenges in efficiency, dynamic constraints, and interpolator compatibility.
• Industrial application of current methods is hindered by computational limitations and feedrate profile smoothness.

Purpose of the Study:

• To develop a highly-efficient dwell time algorithm for deterministic polishing.
• To address limitations of existing methods, including dynamic constraints and feedrate profile smoothness.
• To enable precise and efficient fabrication of large-aperture optical components.

Main Methods:

• Calculates initial dwell time density (DTD) using non-blind deconvolution.
• Generates feasible DTD profiles with a trigonometric-spline model.
• Employs self-adaptive offset algorithm for DTD repair under feedrate and acceleration constraints.
• Develops a real-time interpolator based on the C1-continuous DTD profile.

Main Results:

• Achieved a C1-continuous feedrate profile that strictly adheres to dynamic constraints.
• Demonstrated high computational efficiency compared to previous methods.
• Successfully suppressed multi-frequency errors, outperforming existing techniques.
• Preserved ideal dwell time gradient distribution, leading to improved residual error.

Conclusions:

• The proposed dwell time algorithm offers superior efficiency and dynamic constraint adherence for deterministic polishing.
• The method is suitable for the high-precision, high-efficiency fabrication of large-aperture optical components.
• The developed real-time interpolator ensures smooth feedrate profiles and accurate polishing paths.