Surface Characterization via Modal Decomposition

The patent segments the surface characterization process into three distinct stages: shape component (low-frequency modes), undulation component (mid-frequency modes), and roughness component (high-frequency modes). This segmentation allows each component to be processed and analyzed separately, reducing the computational burden compared to analyzing all measurements simultaneously. The modal decomposition naturally separates the measurement data into frequency-based groups that can be handled independently.

The patent extracts and removes the shape component from the total surface variation before analyzing undulation and roughness. By taking out the low-frequency shape modes first, the subsequent analysis of mid-frequency undulation and high-frequency roughness operates on a reduced dataset with lower computational requirements. This sequential extraction approach prevents the need to process the complete high-dimensional measurement set at once.

The patent applies periodic action through Fast Fourier Transform (FFT) algorithms to process the measurement data. Instead of performing sequential calculations on each measurement point, the FFT method processes the entire dataset in a periodic, parallel manner that exploits the frequency-domain structure of the modal decomposition. This dramatically reduces processing time while maintaining the ability to handle high-density measurement data.

The patent replaces traditional mechanical/sequential computational methods with frequency-domain transformation methods. By substituting direct spatial-domain calculations with FFT-based frequency-domain operations, the system achieves faster processing of high-density measurements. The modal vectors are computed and applied through efficient matrix operations in the frequency domain rather than through slow sequential spatial calculations.

The patent applies local quality by assigning different levels of modal decomposition detail to different spatial frequencies and surface features. Low-frequency modes (shape) use fewer computational resources, while high-frequency modes (roughness) that require more precision for manufacturing are processed with appropriate detail only where needed. This localized approach to modal analysis ensures manufacturing precision is maintained for critical features without uniformly increasing calculation time across the entire surface.

The patent changes parameters by transforming the problem from spatial domain to frequency domain, and by selectively truncating the modal series at different cutoff frequencies for different surface components. The number of modes retained for shape, undulation, and roughness can be independently adjusted based on manufacturing requirements. This parameter control allows optimization of calculation time by reducing the number of high-frequency modes needed for roughness characterization while maintaining sufficient precision for the application.