Focus variation technology as a tool for tissue surface characterization

For surface topography evaluation three different tissue grades were used. The values for the basis weight (EN ISO 12625-6) and caliper (EN ISO 12625-3) are given in Table 1. All three tissue grades consist of a blend of softwood and hardwood kraft fibres. The production however, is based on different manufacturing technologies. The most common type is the dry-creped toilet tissue, where the surface structure is mostly determined by the dry-creping process at the Yankee cylinder. The TAD surface structure depends on the machine configuration but mainly on the structure of the applied TAD fabric. Textured tissue is based on a hybrid technology of TAD and dry-crepe machine concepts. The surface structure is, like TAD, predetermined by the type of fabric, nonetheless the dewatering processes are not comparable. These differences in dewatering technologies yields different properties regarding bulk and surface structure. The surface analysis was always performed on the Yankee side of the 1-ply tissue samples.

For the surface topography measurements an infinite focus measurement (IFM) device from Bruker-Alicona (Graz, Austria, Model G3) was used. The mode of operation of the IFM is based on detecting the best focus position of an optical element towards the tissue sample, which is related to a certain distance (Danzl et al. 2011). By repeating the procedure for many lateral positions, a 3D height map of the sample is generated. Besides the obtained 3D data the optical depth field color image of the surface is also acquired. The color image can subsequently be used to determine the optical formation based on Fourier analysis. An overview of the used magnifications and the respective resolutions is given in Table 2. The same area is observed with three different magnifications (5x, 10x, 20x) to determine the various size-based structural patterns like roughness, crepe, fabric-based patterns and formation. For each magnification the vertical resolution depends on the size of the relevant structures (crepe, fabric, single fibres). The lateral dataset size takes into account the size of given structures, hence a certain periodicity is necessary for an accurate analysis.

Preprocessing The areal surface analysis of the measured 3D datasets was carried out with the MeasureSuite 5.3.5. software from Bruker-Alicona. All of the necessary surface topography features like roughness, crepe and structures were extracted using this software according to a defined procedure, including three preparation steps (see Figure 1). First, the main errors and artefacts due to optical interferences and tissue irregularities (e.g. holes) in the measurement data have to be corrected. Measurement artefacts are visible as isolated steep 3D peaks and have a tremendous influence on areal surface analysis, hence they were removed with the application of a maximum flank-angle condition. Areal surface analysis depends on a continuous 3D dataset, therefore missing data points due to holes in the tissue have to be filled by interpolation between the nearest adjacent data points. It has to be noticed that such irregularities, despite the correction, always have a minor influence on the results of the areal surface analysis and cannot be completely avoided. The second step contains the elimination of the nominal form (e.g. in-plane deviations) with the use of a so called F-filter (Form-filter). During the measurement the tissue sheet is fixed with an adhesive tape to a black background paper (for optical reasons), thus small planar variances occur. The last preparation step includes the definition of a spatial reference plane, which is the base for all subsequent calculations.

Filtering Following the preprocessing of the 3D dataset, further filtering techniques are applied to obtain the required topographical information. Filtering is important for a proper surface characterization, since several common surface parameters like Sa, Sz and also the used Sdr could be erroneous due to superimposition of structural features. The effect of filtering on the Sdr is discussed in a further section in detail. The procedure from the preprocessed data to the final parameters is illustrated in Fig. 2. Based on the preprocessed primary data (P), the roughness (R) and waviness (W) profile is separated with a cut-off wavelength of \(80\ \mu \hbox {m}\), which is called nesting-index by Blateyron (2006). The applied nesting index of \(80\ \mu \hbox {m}\) is valid for all used tissue grades at all magnifications and is determined with an empirical approach specifically for the used dataset and measurement configuration. For the filtering process itself a second order robust Gaussian filter for arbitrary planes (ISO 16610-71) was used. The filter considers the edge effects of inclined, as well as curved planes and has a low sensitivity towards defects like outliers and holes. However, the computational effort is high.

Developed interfacial area ratio (Sdr) The developed interfacial area ratio (Sdr) is used as one out of two parameters to describe small scale structures (i.e. roughness). The principle of the Sdr (ISO 25178) is shown in Fig. 3 and is used as a measure of the surface complexity i.e. roughness.

The Sdr describes the difference between the developed (true) and the projected surface area in percent (see Eq. 1), with a totally flat and smooth surface having a \(\hbox {Sdr} = 0\)

Power spectral density (PSD) In a comprehensive study Jacobs.et al. (2017) defined the power spectral density (PSD) as a tool to obtain the different spatial frequencies of a surface by Fourier transformation of the autocorrelation function signal. In surface topography analysis the PSD provides information on the appearance of periodic structures, like crepe and fabric patterns, which can be related to a certain spatial frequency range respectively structural size. These periodic structures are obtainable as peaks in the PSD curve. The surface roughness can also be determined and is defined by the height of the curve within the roughness frequency range. The peaks are summarized over the frequency range and are depicted as a distribution over all frequencies. When comparing the roughness of various tissue samples, differences in the height of the PSD curves occur. The higher the level of the PSD curve, the higher is the surface roughness and vice versa. For a 1D line profile the concept is explained schematically in Fig. 4.

In case of our work, the analysed surface data contains 3D structures, therefore the logarithmic power spectral density (logC) on y-axis changes to a power of four (\(\mu m^{4}\)) while the logarithmic spatial frequency on x-axis remains as \(\mu m^{-1}\). For simplicity reasons the surface is represented by a 1D PSD curve as it is shown in Fig. 4d. Due to the simplification and the anisotropic features of tissue a separate evaluation in machine direction (MD) and cross direction (CD) is necessary for the examination of structural properties like e.g. crepe or fabric patterns.

For roughness related properties a combined and averaged PSD curve is suitable, as roughness features occur in all directions randomly. The maximum structural size that can be assessed depends on the field of view (see lateral dataset size in Table 2). The minimum structural size that can be reasonably assessed depends on the lateral pixel size, which is also listed in Table 2 for the specific magnifications.

The field of view of the infinite focus device and the ability to acquire optical images simultaneously with the topography measurement allows optical variance analysis using a Fast-Fourier Transformation (FFT). The optical image from the lowest magnification (5x) is suitable to obtain optical variances at a scale of 2-5 mm. Image normalization and variance analysis based on the FFT algorithm were carried out in MATLAB (MathWorks, Massachusetts). The results are shown displayed as a variance distribution, where the unit-less logarithmic variance is plotted over the logarithmic wavelength \(\lambda\) (mm).

As already discussed (see Figure 2) roughness (R) and waviness (W) datasets were separated with the nesting index of 80 \(\mu \hbox {m}\) from the primary (P) dataset. By the use of this filtering technique, typical patterns and structures like e.g. crepe can be determined and described, as presented by Rosen et al. (2014). On the other hand the surface roughness is accessible for analysis without the underlying topographical structure that might affect the used roughness parameters. This allows for example the evaluation of the effect of the morphological characteristics of different fibre types on the surface roughness. While the PSD, as it is applied in this work, does not provide any numerical values like e.g. Sa, Sz or Sdr it does allow evaluation of the complete structural size spectrum of the given surface within one curve. Figure 5 shows the spatial averaged PSD curves for a dry-creped tissue surface, which was acquired at a magnification of 10x. In this figure the - in terms of direction - averaged PSD data is used for simplicity reasons. Still, when assessing structural properties, a detailed discussion in terms of MD and CD is necessary as it is shown below when comparing tissue grades. The diagram shows the PSD curve from the primary and also the incidental roughness and waviness data and gives an overview of the affected frequency ranges. The primary curve (red) includes all frequencies and has an overlap with the waviness curve (green) at lower frequencies (inverted x-axis), while the roughness curve (blue) has an overlap with the primary curve at higher frequencies.

As described in the “Methods” section, the surface roughness is characterized by the height of the PSD curve in the roughness range. Periodic structures like crepe or patterns from the fabric can be obtained as peaks in the curve. Such a dominant peak is, for example, visible in the averaged primary and waviness curve at a frequency of \(4*10^{-3} \mu \hbox {m}^{-1}\) which equals a structural size of \(250\ \mu \hbox {m}\) (40 crepes/cm). The crepe appears very regularly at this structure size. Deviations in the creping process, as observed by Ismail et al. (2020) due to blade wear, could be determined as peak shifts towards a higher or smaller frequency or to a less dominant and wider, or even to several small peaks. To detect possible effects attributed to formation in the PSD, the chosen magnification is only partly suitable as the lateral size is too small. This matter is discussed in the following section. In summary, the primary dataset contains the surface information within the whole frequency spectrum and thus shall be used for PSD analysis.

The level of detail of the obtained topographical data from the IFM depends on the vertical resolution of each magnification (see Table 2), thus the accessible surface information differs. The influence of the used magnification on the 3D surface data is shown exemplary for the textured tissue sample in Figure 6. The benefit of the lowest magnification (5x) is the possibility to detect large sized structures and patterns while providing a certain periodicity. On the other hand, information regarding small scaled structures, like protruding fibres, is not available. This information can be provided at the highest magnification (20x), where small structures at fibre scale can be observed. Due to the optical measurement method protruding fibres are visible as long, steep flanked regions on the surface. Protruding fibres and also the contours of the fibre network mainly affect the roughness region of the PSD. An extended and valid overview of the frequency spectra is possible when all magnifications are considered. Surface roughness is of course represented more accurately at highest magnification while the medium and lowest magnifications are more precise at lower frequencies. For detailed analysis on surface roughness a magnification of 20x and for structural properties a magnification of 5x should be used.

Considering all discussed aspects of PSD and its application, the three used tissue grades are characterized regarding their surface properties. The corresponding primary PSD curves for roughness evaluation (20x) are shown in Figure 7 as spatially averaged PSD and for structural evaluation (5x) in Figure 8 as separate PSD curves for MD and CD.

The surface roughness is examined in the frequency range from \(8*10^{-3}\) to \(2*10^{-1} \mu \hbox {m}^{-1}\) at the highest magnification (20x) for each tissue grade. Comparing the roughness PSD curves it is obvious that the textured tissue (blue) shows the highest values, hence the measured surface roughness is higher compared to the dry-creped (red) and TAD tissue (green). TAD shows slightly higher values for surface roughness than the dry-creped tissue. These differences may directly be related to the production process. The dry-creping step breaks the mechanical integrity of the network to some extent and therefore leads to fibres randomly protruding from the surface to create surface softness in standard dry creped products. TAD production excludes any mechanical compression and dewatering of the tissue web, which generates a looser network structure with a high roughness. Due to the structured surface of the TAD tissue, the contact area and hence the adhesion to the Yankee cylinder is reduced. The low adhesion between the Yankee and the tissue decreases the influence of the dry-creping step on the tissue surface and less fibres are protruding the network compared to other process configurations. In contrast to TAD, the textured tissue production process includes some mechanical dewatering, a wet-creping step and a dry-creping step, thus it combines the advantages of the TAD and dry-crepe technology regarding the surface structure (looser structure compared to standard dry crepe + protruding fibres due to extensive creping). In our case the increased amount of randomly protruding fibres are probably the reason for the textured tissues higher surface roughness compared to TAD.

For structural evaluation the PSD curves for the lowest magnification are illustrated in Fig. 8 separately for MD (continuous line) and CD (dash-dotted line). Additionally the filtered waviness height images of the three tissue grades are shown to provide context. Surface structure due to crepe and fabric patterns are visible in the range from \(5*10^{-4}\) to \(8*10^{-3} \mu \hbox {m}^{-1}\). Differences between the MD and CD PSD curve of the dry-creped tissue are evident. The MD PSD curve shows a higher level as the CD PSD curve in the frequency range around \(5*10^{-3} \mu \hbox {m}^{-1}\) which is directly correlated to the periodical MD dry crepe structure. Compared to textured and TAD the dry-crepe PSD curves show a certain maximum horizontal level in the range from \(1*10^{-3}\) to \(4*10^{-3} \mu \hbox {m}^{-1}\). The dry-creped structure is mainly affected by the crepe height and regularity (e.g. crepes/cm). The crepe height is low compared to the height of the patterns from the textured and TAD samples, which is also evident in the caliper values in Table 1. Differences in the surface structure between the TAD and textured sample can be detected via the amount and intensity of the peaks in Fig. 8. The textured tissue PSD curves are located above the curves of the TAD on average, which indicates a generally higher height deviance from the valley to the top of the patterns. In addition it shows several small peaks, which are related to various regular patterns in MD and CD with different heights and structural sizes. Especially in textured CD several peaks appear over a broad frequency range, which depend mainly on the used fabric. The PSD curves of the TAD sample show intense peaks, which appear at a broad frequency range in CD, while the peaks in MD are shifted to a lower frequency. These differences can be attributed to the molding process during the dewatering and the used fabric on the TAD tissue machine. The analysis and comparison of topography based PSD allows an enhanced view on the characteristics of tissue surfaces and provides a powerful tool for further optimization of tissue surface structures.

Structures for the topographical variance analysis can be obtained only at the lowest magnification (5x) due to the necessary lateral size. The variation in local mass is crucial in tissue production as it affects the creping and moulding process and thus the surface topography (see Raunio et al. (2012)). The effect of large scaled structures on dry-creped tissue will be discussed separately.

Compared to the roughness evaluation with the PSD curve, the developed interfacial area ratio (Sdr) expresses the surface roughness as a figure in percent based on a different principle of surface roughness characterization (see Fig. 3). As it is common in surface analysis to describe and compare surface roughness with a numerical parameter, the Sdr is very suitable for tissue paper. In Table 3 the mean Sdr values for the magnification of 20x are listed. The Sdr values were evaluated for the primary (P), roughness (R) and waviness (W) profile, which are separated by a Gaussian filter (see Fig. 2). For each tissue grade three arbitrary areas were observed and the results were averaged. The corresponding standard deviations (SD) for each measurement are also shown in Table 3 and indicate a high reproducibility. Advantageously, the Sdr is nearly independent from textures and patterns on the surface (low Sdr (W) values), thus allowing the comparison of different tissue grades regarding their surface roughness. In contrary to Sdr, height based values like Sa or Sq have their limits in comparing tissue with deviations in caliper and structural patterns and should be avoided for characterization of such complex surfaces. Since structures have only a minor influence on Sdr analysis the difference between Sdr (P) representing the unfiltered topography and Sdr (R) representing solely the roughness profile is hardly significant. This shows that the interfacial area ratio (Sdr) does allow roughness measurement on tissue surfaces without pretreatment of the primary profile. Comparing the samples the textured tissue shows by far the highest Sdr, followed by the TAD and the dry-creped tissue which is in accordance with the results from PSD analysis (see Fig. 7).

The IFM provides a large field of view at lowest magnification (5x). This allows in addition to the described analysis of surface structures and roughness an optical and also a topographical analysis of large-scaled structures. Large structures in topographical variance analysis are identified by repetitive use of the Gaussian filter on the waviness dataset of the lowest magnification (5x) to eliminate smaller structures (e.g. crepe, fabric). In Fig. 9 the optical greyscale image (a), the corresponding filtered topographical height map (without the crepe-structure) (b) and the primary surface height map (c) for the dry-creped tissue are shown. In the primary height map (c) the crepe is visible as the dominant structure, with the frequency of the crepe varying throughout certain regions (such as in the region marked in red). It does seem that the crepe frequency is somewhat related to the underlying structure. The kind of relation would have to be clarified in future work. The inhomogeneity in the underlying structure of the paper is accessible with focus variation as is shown in the height map (b) and could have different reasons like e.g. formation effects in the wet end of the tissue machine or in-plane deviations due to the drying process. In the optical greyscale image (a) similar large scale variations are visible due to differences in light reflectance. This similarity in structures of the topographical and optical data is shown in the structure analysis in (d). In this analysis the primary topography image (c) was converted to a greyscale image and both, the optical and topographical image, were subsequently normalized and subjected to FFT based structure analysis. Beside the peaks at a wavelength of \(2.5*10^{-1}\ \hbox {mm}\) (which represent the crepe), there is an increase in variance for both datasets at a wavelength of 2 mm. This indicates a coherence between the optical grey scale image and topographical data that may be related to e.g. formation. Still, further work regarding topographical and optical large scale structure analysis and the reasosn for its coherence is necessary.