FFT-Based 3D Gaussian Rough Surface Generation

The FFT-based methodology for generating 3D Gaussian rough surfaces enables rapid simulation of surfaces with Gaussian height distributions, providing significant advantages for advanced research applications. This approach leverages Fourier transform properties to accelerate the surface generation process through efficient spectral synthesis techniques, where random phase matrices are combined with predetermined power spectral density functions in the frequency domain before applying inverse FFT operations.

Key implementation aspects involve generating complex random matrices with Gaussian-distributed real and imaginary components, applying appropriate windowing functions to control spectral leakage, and utilizing zero-padding strategies to achieve desired spatial resolution. The computational efficiency of this method allows researchers to efficiently conduct in-depth studies by generating multiple surface realizations with controlled statistical properties, including specific correlation lengths and RMS roughness parameters.

The primary advantage of this FFT-based approach lies in its ability to rapidly generate large ensembles of 3D Gaussian rough surface samples, facilitating comprehensive statistical analysis and Monte Carlo simulations for subsequent research investigations. The method achieves O(N log N) computational complexity compared to traditional direct convolution methods, making it particularly suitable for large-scale surface generation requiring high spatial resolution and statistical accuracy.