This article presents a method for inferring and synthetically extrapolating roughness fields from electron microscope scans of additively manufactured surfaces. The method utilizes an adaptation of Rogallo’s synthetic turbulence method, which is based on Fourier modes. The resulting synthetic roughness fields are smooth and compatible with grid generators in computational fluid dynamics or other numerical simulations.

One of the main advantages of this method is its ability to extrapolate homogeneous synthetic roughness fields using a single physical roughness scan. This is in contrast to machine learning methods, which typically require training on multiple scans of surface roughness. The ability to generate synthetic roughness fields of any desired size and range using only one scan is a significant time and cost-saving benefit.

The study generates five types of synthetic roughness fields using an electron microscope roughness image from literature. The spectral energy and two-point correlation spectra of these synthetic fields are compared to the original scan, showing a close approximation of the roughness structures and spectral energy.

One potential application of this method is in computational fluid dynamics simulations, where accurate representation of surface roughness is crucial for predicting flow behavior. By generating synthetic roughness fields that closely resemble real-world roughness structures, researchers can improve the accuracy and reliability of their simulations.

Further research could focus on validating this method with additional roughness scans from different surfaces and manufacturing methods. It would be interesting to explore how well the synthetic roughness fields generalize to different types of surfaces and manufacturing processes.


The method presented in this article provides a valuable tool for inferring and extrapolating roughness fields from electron microscope scans. Its ability to generate smooth synthetic roughness fields compatible with numerical simulations using only one physical roughness scan is a significant advantage over other methods that rely on machine learning and multiple scans for training. By closely approximating the roughness structures and spectral energy of the original scan, this method has the potential to improve the accuracy of computational fluid dynamics simulations and other numerical simulations that involve surface roughness. Further research and validation will help establish the generalizability and robustness of this method across different surfaces and manufacturing processes.

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