Bipolar Spectral Analysis of Paper Formation Using Wavelet Transforms (2007)

In the last half century, considerable effort has been given to analyzing paper formation and interpreting the secrets of its patterns to understand how raw materials and the forming processes affect the structure. Many formation analytical methods have been developed to quantify web structure in order to provide for an objective comparison between papers, with the ultimate goal of replacing expert panel evaluations. The finest of formation analyses would serve to accurately predict product quality and performance and to identify process steps or material blends that would provide an optimal distribution of material for a given use. Conventional methods used for the characterization of paper formation are based on the statistical or spectral analysis of data sets (vectors or images) that represent the spatial distribution of optical density or grammage. The distribution of material forms regions of greater or lesser mass that are referred to as flocs or light weight zones (lwz), respectively. Patterns reflect the tendency of fibers to form aggregates under the conditions of forming. Optical density is further influenced by the non-uniformity of local optical properties. The uniformity, scale and intensity of mass distribution determine various properties and performance of paper, paperboards, and other fibrous web materials. Conventional methods used for the characterization of paper formation are based on the statistical or spectral analysis of data sets (vectors or images) that represent the spatial distribution of optical density or grammage. The distribution of material forms regions of greater or lesser mass that are referred to as flocs or light weight zones (lwz), respectively. Patterns reflect the tendency of fibers to form aggregates under the conditions of forming. Optical density is further influenced by the non-uniformity of local optical properties. The uniformity, scale and intensity of mass distribution determine various properties and performance of paper, paperboards, and other fibrous web materials. There are two generally practiced methods of spectral analysis that provide information about the scale and intensity of structural features. The methods, variance vs. zone size [1]and wavelength spectral analysis [2], are both predicated on an underlying assumption that the spectral characteristics of the flocs and lightweight zones are the same, or inseparable. In essence, the web structure is comprised of an ideal distribution of fibers in a random network, and any externally imposed perturbation of this ideality, for example forming hydrodynamics or chemically induced interfiber forces, will have no influence on the equivalence between the nature of the flocs and the light weight regions that exist between them. While for many web structures, this approximation appears valid, the existence of skewness in the probability distribution of mass or optical density for various papers and even a cursory inspection of the gray-level images of formation suggest otherwise. The objective of this work was to address the bipolar nature of paper formation by developing a method to separately characterize the heavy and light regions of formation images (data arrays). A continuous wavelet transform of the data set is bifurcated into separate spectra that expose the scale and intensity of each. It was hypothesized that the bipolar spectra will indeed be different, and can be useful for distinguishing flocculation mechanisms that have mechanical or chemical origins. This new approach will be demonstrated by analyzing simulated 2D fibrous networks and formation images from paper samples.