An unambiguous cloudiness index for nonwovens

TL;DR

This paper introduces a mathematically grounded, practical cloudiness index for nonwovens based on the power spectrum, demonstrating its advantages over other methods like the Laplacian pyramid.

Contribution

It derives a new cloudiness index from the power spectrum, clarifies its mathematical basis, and shows its practical superiority in measuring nonwoven cloudiness.

Findings

Power spectrum closely relates to cloudiness measures.

The power spectrum is easier to measure analytically.

The proposed index provides more information than alternatives.

Abstract

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 is easy to be measured image analytically and carries more information than the alternatives.