*Device Calibration*

It is necessary to calibrate the data recorded by the camera for accuracy. Data evaluation is based on the theory of 3D scanning (triangulation).

The laser beam projects a planar curve onto the material to be measured. Taking a picture of the projected curve on the material surface is a plane-to-plane perspective transformation as a bijection. A perspective transformation by homogenous coordinates is a linear transformation [40] projecting a quadrangle to a quadrangle. The transformation matrix has eight independent coordinates (*p*0, *p*1, ... , *p*7), as shown in Equation (4):

$$\begin{array}{c} P = \begin{bmatrix} p\_0 & p\_1 & p\_2 \\ & p\_3 & p\_4 & p\_5 \\ & p\_6 & p\gamma & 1 \end{bmatrix} \tag{4} \\\tag{4}$$

Corners of rectangular calibration equipment are appropriate to define the matrix coordinates (Figure 8).

**Figure 8.** Planar perspective projection.

The corners of the calibration equipment are *tix*, *tiy*, and the corners of its picture are *vix*, *viy*(i = 0, 1, 2, 3); based on this, the transformation is shown in Equation (5):

$$
\begin{bmatrix} v\_x^i \\ v\_y^i \\ 1 \end{bmatrix} = \begin{bmatrix} p\_0 & p\_1 & p\_2 \\ p\_3 & p\_4 & p\_5 \\ p\_6 & p\_7 & 1 \end{bmatrix} \cdot \begin{bmatrix} t\_x^i \\ t\_y^i \\ 1 \end{bmatrix} \tag{5}
$$

There are eight unknown coordinates and eight equations, Equation (6):

$$
\begin{bmatrix} v\_x^i \\ v\_y^i \\ 1 \end{bmatrix} = \begin{bmatrix} p\_0 & p\_1 & p\_2 \\ p\_3 & p\_4 & p\_5 \\ p\_6 & p\_7 & 1 \end{bmatrix} \cdot \begin{bmatrix} t\_x^i \\ t\_y^i \\ 1 \end{bmatrix} \quad \text{i} = 0, 1, 2, 3 \tag{6}
$$

Knowing the real positions of four points in the lighted plane (*t<sup>i</sup>*) allows the real coordinates of other points on the lighted plane to be computed.

The system is calibrated with a rectangular device with an LED in each corner (Figure 9a). During the calibration process, the rectangle is positioned in the laser lighted plane. This means that the device is aligned in the picture frame in such a way that it is positioned centrally and planarly in all planes, sagittal, transverse and frontal, with the frontal plane corresponding to the position of the shear specimen in the initial state. Figure 9b shows an image of the calibration tool. With the measured picture coordinates and the real coordinates of the LEDs, the eight coordinates of the homogenous transformation matrix can be calculated.

**Figure 9.** The calibration device (**a**) and its image during calibration (**b**) with its real dimensional coordinates.

In order to validate the hardware and software for recording and evaluating the shear deformation that occurs during the picture frame test, a reference geometry with a defined height profile (Figure 10a) was designed and manufactured. The aim of validation is to ensure that the height profile is measured correctly. Since shear deformation is only measured centrally, based on the deflection of the projected laser beam, the dimensions of the reference geometry do not need to correspond to the sample geometry, only allow the projection of the laser beam. For this purpose, the reference geometry was positioned on the lateral pivot point of the square picture frame and the laser beam is projected. The optical measurement of this height profile and its comparison to nominal dimensions is made stationary state and requires all measuring system components to be properly aligned and a validated calibration.

**Figure 10.** Reference geometry with defined peaks (1 to 5) adapted to the picture frame (**a**) and its measured height profile (**b**).

For experimental investigations, different reinforcing textiles which are widely used, e.g., in automotive and wind power plant engineering, were selected, Table 1. They vary in terms of fabric construction and/or fiber material, e.g., CF, glass fiber (GF), polyamide (PA) or polyester (PES), thus representing the group of commonly investigated materials.


**Table 1.** Material specifications.

1 For non-crimp fabrics the front and back and for woven fabrics, only the fronts are shown
