*6.2. Experimental Results*

The results from the cooling analysis are shown in Figure 6. The thermographic images (Figure 6b–d) are excerpts from the full sequence of images at specific points in time (see the green spots in Figure 6a). To estimate the cooling rate Δ *Tf f* , linear functions were fitted into the sectors with constant gradients. The slope of these functions was the cooling rate and summarized in Table 2.

**Table 2.** Cooling rates before and during compensation.


The results from the BOS experiment are shown in Figure 7. The high displacement values in Figure 7b–d in the lower middle were a result of the hot cylinder not being in place when the reference image was shot. Therefore, the distance from a similar looking pixel group in the reference image was high.

**Figure 7.** Results from the BOS experiment. (**a**) shows one of the regular images used to calculate the pixel displacement; (**b**) shows the result of the displacement calculation for an uninfluenced convection field; (**c**) the result for an air flow at *pff*= 2.5 bar; (**d)** the result for an air flow at *pff*= 6.0 bar.

The estimated influence of the refractive index field was observable in the comparison of the measurement of the cold object and the object in the red-hot state (see Figure 8) using the direct estimation method and the multi-camera FPS. The mean values of the shown histograms are found in Table 3 and Figure 9. The reconstruction error *Em* in the reconstruction quality maps (Figure 8a–c) was not homogeneously distributed, with higher *Em* values in the upper parts of the images, corresponding to points further away from the FPS. Both the reconstruction quality maps and the histograms showed only marginal differences between the experiments. An example of the reconstructed 3D datasets is shown in Appendix B.

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**Table 3.** Mean deviation of the evaluated corresponding 3D points from the multi-camera fringe projection system.

**Figure 8.** Evaluation of the results from the reconstructed corresponding points of the FPS. (**<sup>a</sup>**–**<sup>c</sup>**) show an excerpt from the full measurement with an activated forced flow actuator, in which the cylinder can be observed from all used cameras. (**a**) is taken at *Tc* ≈ 300 K; *pf f* = 6.0 bar; (**b**) is taken at *Tc* ≈ 1300 K; *pf f* = 6.0 bar, *td* = 0.3 s; (**c**) is taken at *Tc* ≈ 1300 K; *pf f* = 2.5 bar, *td* = 3.3 s; (**d**) shows the summary of the conducted experiments as histograms. Dashed lines indicate an activated flow actuator, while solid lines show no external influence on the refractive index field.

*Em* in mm

(d)

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**Figure 9.** Summary of the measured reconstruction errors *Em* (cf. Table 3) as a bar diagram of the average values. The solid area indicates a deactivated flow, while the hatched area is the result of an activated forced air flow.

Other observations during the experiment included a noticeable cooling of the component during the measurement as observable through a change of color. The applied force of the air field did not cause any visible vibration or movement of the object.
