**8. Conclusions**

Overall, the influence of the forced air flow on the light deflection effect was shown. The BOS measurement showed a significant reduction in pixel displacement, which was considered to be proportional to the light deflection. However, the results from the reconstruction quality experiment showed an only marginal improvement through the forced air flow. The reasons for this were already stated in the previous section and seemed plausible considering the results from the cooling experiment and the improved time delay. However, the reconstruction quality for this setting was lower compared to the experiment at *Tc* ≈ 300 K. Therefore, the change of radiation color through cooling needs to be investigated as an additional influence on the optical geometry measurement of hot objects.

This indicated a superposition of effects: on the one hand, the reduced light deflection resulted in a reduced reconstruction error metric while there needed to be an additional effect to then increase the error metric again. The underlying effect here might be the change of the surface color during the air flow induced cooling. The fringe projection reconstruction technique based on Peng's multi-frequency phase-shift method [18] used requires a constant ambient illumination strength. This ambient light influence is compensated using the temporal average of the phase shift sequence of the highest frequency. A change of background illumination may cause an error in phase reconstruction for each camera and, therefore, a change in the reconstruction error metric. However, a further investigation of this matter is beyond the scope of this paper and is therefore omitted.

#### **9. Summary and Future Work**

In this paper, a setup was presented to reduce the light deflection effect when using optical triangulation systems to measure the geometry of a red-hot object. A simulation was used to estimate the velocity of the free convection around the hot object. The same tool simulated the interaction of a forced convection flow with the free convection to gain insight into the necessary flow velocities to suppress the development of the refractive index field around the hot object. That knowledge was used to simulate and implement a forced air flow actuator to be used in combination with a fringe projection system. The effect of this actuator on the light deflection effect was indirectly estimated using a BOS-based method and directly measured using a reconstruction error metric. While the indirect method showed a minimization of the refractive index field, the direct method showed a reduction of the reconstruction error while not reaching the quality level of the measurement of a cold object. Different reasons for this behavior were discussed, but not further investigated.

Overall, the aim of the developed setup (reduction of reconstruction error) was reached while not being sufficient in comparison with a standard measurement. While the design method resulted in a successful development of the setup, it may not be generalizable due to changing boundary conditions when varying the geometry of the measurement object. The developed setup in the present configuration may be used to inspect shaft-like components.

In the future, an investigation of the changing surface color due to the cooling effect of the forced air flow needs to be conducted. Findings of this investigation can then be used to compensate for a changing background color, if the effect is found to be significant.

**Author Contributions:** Conceptualization, L.Q., C.R. and R.B.; Data curation, L.Q. and C.R.; Formal analysis, L.Q. and R.B.; Funding acquisition, M.K. and E.R.; Investigation, L.Q. and C.R.; Methodology, L.Q.; Project administration, M.K. and E.R.; Resources, L.Q.; Software, L.Q.; Supervision, M.K. and E.R.; Validation, L.Q.; Visualization, L.Q. and C.R.; Writing—original draft, L.Q.; Writing—review & editing, C.R. and M.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Deutsche Forschungsgemeinschaft (DFG); Collaborative Research Centre 1153 (CRC) Process Chain to Produce Hybrid High-performance Components Through Tailored Forming (252662854); Subproject C5 Multiscale Geometry Inspection of Joining Zones.

**Conflicts of Interest:** The authors declare no conflict of interest.
