In the Result Viewer, under the Plots subtab, you can find histogram plots of the fiber length distribution and, for Identification Method Machine Learning, the distribution of fiber diameter.

On the left panel of the Results subtab, the number of bins for all distributions shown in the plots can be changed. Click Apply to generate the plots for a different number of bins.

Also available are curvature and orientation information, under the Results - Plots subtab plots of the Fiber curvature distribution, the Curvature autocorrelation and the Fiber curl-index distribution as well as three plots showing the fiber orientation as histograms of projections of the fibers to two-dimensional planes can be found.

The Curvature autocorrelation indicates how strongly the changes in curvature at different point of the fiber are related.

• A high positive autocorrelation suggests that if the curvature is strong at one point, it is likely to repeat after a certain length distance (i.e., similar curvature behavior at a later point of the fiber).
• A negative autocorrelation suggests that strong curvature at one point is followed by opposite curvature at a later point.
• The autocorrelation of curvature values can reveal periodic behavior or cyclical variations in the curvature, helping to identify regular structures or trends in the underlying data

For the above example, the autocorrelation diagram shows that the curvature changes its direction after a length distance of 0.27 µm on average, i.e. if the curvature is positive at one point of the fiber, the curvature is negative again on average after a distance of 0.27 µm.

To compute the three orientation histograms, each fiber is projected to the two-dimensional plane. The angle of each fiber segment, weighted with the length of the segment, gives an entry in one bin of the histogram, i.e., in one segment of the circle.

The number of fiber segments for an orientation in the plane is given by the size of a segment of the circle. Since the histograms are normalized, this number is always a value between 0 and 1. The histogram is symmetric since fiber orientations of 0° and 180° are undistinguishable.

Fibers in this example are oriented mainly in the X/Y plane with a bias in X-direction. Histograms of X/Z plane and Y/Z plane show large segments for 0° and 180°, and segments in Y-direction are even a bit larger. In contrast, the plot of X/Y plane shows a more homogeneous distribution of fibers in this plane, but the preference for X-direction is also visible there.

Besides the bin size for each of the histograms shown, that can be selected by the user, additional post-processing options are available.

In the histograms of fiber length and diameter, the fibers can be classified with respect to many fiber properties.

Select a Fiber Property for the classification and define the number of different classes by choosing the Number of Fiber Types.

In this example, the fiber diameter distribution (plotted above) implies that fibers are of mainly two different diameter classes. To classify the result accordingly choose Diameter for Fiber Property and the number 2 for Number of Fiber Types.

Select a Thresholding Method for the differentiation of fibers of different type (k-Means, Otsu’s method or define a Manual threshold) and the Number of Bins used for the separation of fibers.

Here, 100 bins are used to separate the fibers according to the Otsu’s method. Click Apply to change the Fiber length distribution histogram and, if available, the Fiber diameter distribution histogram. These histograms are shown now with stacked values for both fiber types additionally.

An additional tab (Threshold by scalar value), containing the fiber diameter distribution with the number of bins defined for the thresholding, the resulting threshold(s) for the selected method and a Gaussian fit for both fiber types, is created.

Note that the threshold (the green vertical line in this example) changes for different Thresholding Methods or can directly be defined by the User after choosing Thresholding Method – Manual.

The classification of fibers is also included in the Results Report tap.

The structure with the separated fiber types, can be loaded to the Visualization Area under the Fiber Identification Visualization tab.

To create an additional tab, showing the layered values in z-direction for a fiber property, select a Layered Fiber Property from the pull-down menu. With Layered Fiber Property Weighting define if the mean in each layer is computed with respect to the number, the volume or the length of the fibers.

Click Apply to start the creation.

A new tab for the layered distribution is added to the Plots subtab, according to the values selected.

For the example shown here, the tab Layered fiber curl index distribution is created, showing the mean fiber curl-index (weighted with respect to the fiber volume) for each layer in z-direction of the structure.

Click on Plot Options and select one of the histograms available, to access directly the dialog boxes for changing the Axis Settings or Graph Styles. These dialogs can be accessed as well by a right mouse-click in the histogram.

For more details on modifying plot settings, see the Result Viewer user guide.