power spectral density analysis

**PSD** (Power Spectral Density) analysis is a **frequency-domain technique for characterizing surface roughness** — decomposing the surface height profile into its spectral components, revealing the contribution of each spatial frequency (wavelength) to the total roughness. **PSD Methodology** - **FFT**: Apply the Fast Fourier Transform to the surface height data — convert from spatial to frequency domain. - **PSD Function**: $PSD(f) = |FFT(z(x))|^2 / L$ where $f$ is spatial frequency and $L$ is the scan length. - **2D PSD**: For 2D surface maps (AFM images), compute the 2D PSD and radially average for isotropic surfaces. - **Units**: PSD is typically expressed in nm⁴ or nm²·µm² as a function of spatial frequency (µm⁻¹). **Why It Matters** - **Multi-Scale**: PSD reveals roughness contributions at every spatial wavelength — identify which frequencies dominate. - **Process Signatures**: Different processes create roughness at different spatial frequencies — PSD is a process fingerprint. - **Stitching**: Multiple measurement techniques (AFM, optical, scatterometry) can be stitched in PSD space to cover the full frequency range. **PSD Analysis** is **the fingerprint of surface roughness** — revealing the spectral composition of surface texture for comprehensive roughness characterization.