# Cloudiness – The Homogeneity of Filter Media

The homogeneity of filter media is important for material selection and quality control. Cloudiness or formation is a term that describes deviations from homogeneity.

There are different image analytical methods to measure cloudiness reproducibly. However, cloudiness measured with different instruments is usually not comparable. We have developed a theoretically based cloudiness index and a method to measure it from the power spectrum. Our paper »Assessing Cloudiness in Nonwovens« (FILTECH, 2022) covers more practical aspects of estimating the cloudiness index. We applied the cloudiness index in the project »ProQuIV« (Production and Quality Optimization of Nonwoven Infection Control Clothing).

#### An Unambiguous Cloudiness Index For Nonwovens (Journal of Mathematics in Industry, 2022)

Cloudiness or formation is a concept routinely used in industry to address deviations from homogeneity in nonwovens and papers. Measuring a cloudiness index based on image data is a common task in industrial quality assurance. The two most popular ways of quantifying cloudiness are based on power spectrum or correlation function on the one hand or the Laplacian pyramid on the other hand. Here, we recall the mathematical basis of the first approach comprehensively, derive a cloudiness index, and demonstrate its practical estimation. We prove that the Laplacian pyramid as well as other quantities characterizing cloudiness like the range of interaction and the intensity of small-angle scattering are very closely related to the power spectrum. Finally, we show that the power spectrum can be measured easily by image analysis methods and carries more information than the alternatives.

Authors: Michael Godehardt, Ali Moghiseh, Christine Oetjen, Joachim Ohser and Katja Schladitz

#### Figure 1:

Four microscopic images of a nonwoven layer from a face mask. Several fields of view taken in transmission mode, 2 048 ×2 048 pixels of size 3.367 μm. The total area of the four images is 190.2 mm2.

#### Figure 4:

Realizations of random fields generated by segments of exponentially distributed lengths, 1 024× 1 024 pixels of size 4.0 μm, thickness of the tubes 6.0 μm: a) mean length 0.5 mm, b) mean length 1 mm.

#### Figure 7:

Pixelwise mean of the normalized local grammages of the nonwoven FL1 for four lateral resolutions. The images consist of 2 048×2 048 pixels: a) pixel size 6.734 μm, b) pixel size 3.367 μm, c) pixel size 1.684 μm, d) pixel size 0.842 μm.

#### Figure 10:

Images of the anisotropic nonwovens a) FL2 and b) FL3, 2 048×2 048 pixels of size 6.734 μm. The image area is 190.2 mm2.

#### Figure 11:

Pixelwise mean of the normalized local grammages of anisotropic nonwovens a) FL2 and b) FL3, 2 048× 2 048 pixels of size 6.734 μm. The mean was computed from m = 10 separate images of a total area 1 902.0 mm2.