Middle-high spatial frequency error suppression of a self-organizing map pseudorandom path planning method in complex...

Area of Science:

• Optical Engineering
• Computational Science
• Materials Science

Background:

• Traditional pseudorandom paths reduce spatial frequency errors but require complex 2D to 3D mapping.
• Existing methods can introduce computational complexity and spatial frequency distortion.

Purpose of the Study:

• To propose a novel pseudorandom path generation method using self-organizing maps (SOM).
• To achieve adaptability to complex geometric shapes on surfaces.
• To reduce computational complexity and spatial frequency distortion in polishing.

Main Methods:

• Developed a pseudorandom path generation method based on self-organizing map (SOM) neural networks.
• Utilized neural network topology optimization to construct continuous 3D paths.
• Compared surface topography and power spectral density (PSD) curves of SOM, raster, and spiral paths on planar surfaces.

Main Results:

• The SOM path demonstrated superior performance in reducing middle-high spatial frequency errors compared to raster and spiral paths.
• The SOM method showed comparable effectiveness to raster paths in improving surface topography after polishing.
• SOM mitigated mapping distortion and local curvature mismatch on complex surfaces.

Conclusions:

• The SOM path effectively suppresses middle-high spatial frequency errors, inheriting advantages of traditional pseudorandom paths.
• The SOM method significantly reduces computational complexity and spatial frequency aberrations.
• This method holds great potential for polishing ultra-precision optical devices with complex surfaces.