The homogeneity of filter media is important for material selection and quality control, along with the specific weight (nominal grammage) and the distribution of the local weight. Cloudiness or formation is a concept used to describe deviations from homogeneity in filter media. We suggest to derive the cloudiness index from the power spectrum of the relative local areal weight, integrated over a selected frequency range. The power spectrum captures the energy density in a broad spectral range. Moreover, under certain conditions, the structure of a nonwoven is fully characterized by the areal weight, the variance of the local areal weight, and the power spectrum. Consequently, the power spectrum is the parameter that exclusively reflects the cloudiness. Here, we address questions arising from practical application. The most prominent is the choice of the spectral band. It certainly depends on the characteristic "size of the clouds", but is limited by the size and lateral resolution of the images. We show that the cloudiness index based on the power spectrum of the relative local areal weight is theoretically well founded and can be robustly measured from image data. Choosing the spectral band allows to capture the cloudiness either visually perceived or found to be decisive for product properties. It is thus well suited to build a technical standard on it.

翻译：过滤介质的均匀性对材料选择和质量控制至关重要，此外比重量（标称克重）和局部重量的分布也很重要。云斑度或成形性是一个用于描述过滤介质均匀性偏差的概念。我们建议从选定频率范围内相对局部面密度的功率谱中推导云斑度指数。功率谱能够捕获宽光谱范围内的能量密度。此外，在一定条件下，非织造布的结构完全由面密度、局部面密度的方差以及功率谱表征。因此，功率谱是唯一反映云斑度的参数。本文讨论了实际应用中产生的问题，其中最突出的是光谱波段的选择。它当然取决于"云斑"的特征尺寸，但受到图像尺寸和横向分辨率的限制。我们证明，基于相对局部面密度功率谱的云斑度指数具有完善的理论基础，并且可以从图像数据中稳健地测量。通过选择光谱波段，可以捕获视觉感知的或被认为对产品性能具有决定性的云斑度。因此，它非常适合作为制定技术标准的基础。