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

Pseudorandom path is helpful to reduce the middle-high spatial frequency error, but existing methods require 2D to 3D mapping, which introduces computational complexity and spatial frequency distortion. To this end, this study proposes a pseudorandom path generation method based on self-organizing map (SOM), which directly constructs continuous 3D paths through neural network topology optimization and achieves adaptability to geometric shapes on complex surfaces. The surface topography after polishing and power spectral density (PSD) curves of the raster path, the spiral path, and our proposed SOM path on planar surfaces are comparatively analyzed to evaluate the effectiveness of the SOM method, which shows that the SOM path outperforms the spiral path while performing comparably to the raster path in improving the surface topography after polishing, and that the SOM path outperforms the other two paths in reducing the middle-high spatial frequency error. In addition, the SOM method mitigates the mapping distortion and local curvature mismatch caused by conventional pseudorandom path projection for complex surfaces. The above study concludes that the SOM path inherits the advantages of the traditional pseudorandom path over raster and spiral paths in terms of the suppression of middle-high spatial frequency error, and at the same time reduces the computational complexity and spatial frequency aberrations. Therefore, the SOM method shows great potential for application in polishing the complex surfaces of ultra-precision optical devices.