Transmitted Light Measurement to Determine the Local Structural Characteristics of Paperboard: Grammage, Thickness, and Fiber Orientation

This study presents a novel transmission-based method for characterizing local structural features, including the grammage, thickness, and fiber orientation, of paper materials. Some non-destructive techniques, such as micro-computed tomography (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula>-CT), microscopy, and radiation-based methods, are costly, time-consuming, and lack the ability to provide comprehensive local structural information within a single measurement. The proposed method utilizes a single light transmission measurement to assess local grammage and thickness through histogram matching with reference data obtained via <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>-radiography and profilometry. The same light transmission images are also used to determine local fiber orientation, employing image analysis techniques. The structure tensor method, which analyzes gradients of light transmission images, provides detailed insight into the local fiber orientation. The results show that thickness and grammage measurements are independent of which side of the paper is evaluated, while the fiber orientation distribution varies between the front and back sides, reflecting differences in fiber arrangement due to manufacturing processes. Various distribution functions are compared, and the Pearson Type 3, log-normal, and gamma distributions are found to most accurately describe the grammage, thickness, and fiber orientation distributions. The study includes a variety of paper types, ensuring a robust and comprehensive analysis of material behavior, and confirms that the method can effectively infer the inhomogeneous features from a single light transmission measurement.