Morphometric Roughness of Nanostructured Surfaces

描述复杂的、非重复出现的地形是具有挑战性的，并且经典的方法（如快速傅立叶变换和均方根粗糙度（RMS））在捕捉其复杂性方面不足。然而，特定的地形极大地影响物理，化学和生物特性。因此，对地形进行准确的表征和精确的描述至关重要。许多具有特定形貌的不同纳米结构已被设计用于各种材料特性，但仍然缺乏直观的，跨学科的公认和全面的粗糙度描述。来自实验（生物）物理，理论物理和数学的科学家团队旨在填补这一空白，并为纳米技术中使用的一系列非常不同的样品开发最合适的分析和表征方法。原子力显微镜是在纳米尺度上记录形貌的主要实验方法。数学工具包括先进的形状描述符，基于闵可夫斯基泛函，和新开发的空间模型（纳米）粗糙表面和聚集模型，使用分形和随机几何的方法。

Describing complex, non-recurring topographies is challenging and classical methods like Fast Fourier Transform and root mean square roughness (RMS) fall short in capturing their intricacies. However, the specific topography greatly influences physical, chemical, and biological properties. An accurate characterization and precise description of topographies are therefore essential. Numerous different nanostructures with specific topographies have been designed for various material properties, yet the lack of an intuitive, interdisciplinary accepted and comprehensive description of roughness persists. The team of scientists from experimental (bio)physics, theoretical physics and mathematics aims to fill this gap and has set itself the goal of developing the most suitable analysis and characterization methods for a range of very different samples used in nanotechnology. Atomic force microscopy is the main experimental method for recording topographies on the nanoscale. The mathematical tools include advanced shape descriptors, based on Minkowski functionals, and newly developed spatial models for (nano)rough surfaces and aggregation models using methods from fractal and stochastic geometry.