**2. Background**

In this section, the literature for the methods to estimate the light deflection effect is revisited. The content includes the concept of the background-oriented Schlieren (BOS) method to reconstruct a refractive index field, as well as a presentation of a multi-camera fringe projection system (FPS) to quantify the influence of refractive gradients on triangulation measurements.

#### *2.1. Background-Oriented Schlieren Method*

The background-oriented Schlieren method was introduced to estimate density differences in a transparent medium from a set of images [12]. To this end, a contrast-rich and unique background was set up in front of a camera. An image was taken at zero-state as the reference, and additional images were captured during the measurement sequence. The displacement of image points due to the light deflection induced by the density gradient was quantified using suitable algorithms, e.g., Farnbäck et al. [13]. The estimation of the density gradient through the refractive index gradient required extensive knowledge about the measurement setup [14], e.g., the size and position of the refractive index field. This knowledge might be difficult to obtain in changing or unknown measurement conditions.

#### *2.2. Using a Multi-Camera Fringe Projection System to Estimate the Direct Influence of the Light Deflection Effect on Optical Triangulation Measurements*

In a previous paper [15], we used redundantly reconstructed 3D points of a multi-camera FPS to estimate the magnitude of the light deflection that was occurring when measuring a red-hot object. There, we concluded that the deviations of redundantly reconstructed points were a valid metric to quantify said effect. The validity of the method was shown using a discrete refractive index influence in the form of a glass plate. While we were not able to use the comparison of single object points, an analysis of all available reconstructed points using a histogram showed resounding results.

#### **3. Proposed Method and Necessary Constraints**

It is proposed to use a forced gas flow in order to reduce the light deflection effect of an inhomogeneous and dynamic refractive index field in an industrial environment. Beermann et al. [9] successfully used a forced laminar gas flow to lower the geometry deviations when measuring a hot rod using a laser light section method. From said article, it was concluded that the forced gas flow needed to be powerful enough to suppress the developed refractive index field while not cooling the hot component too much. To solve this conflicting interest, the velocities and flow parameters were simulated, as well as the cooling effect of such a forced gas flow to a hot component. To this end, the free convection of hot air above a hot cylindrical component needs to be simulated to gain insight into its characteristics. Additionally, the interaction of a forced gas flow with said free convection also needs to be analyzed. The result of that design process yields the necessary construction parameters for the nozzles, as well as the optimal solution for the necessary flow velocities in relation to both the suppression of the refractive index field and the cooling of the component.

The apparatus used for the forming of the forced convection should include an electronically triggered magnetic valve to open and close it conveniently from the same computer that controls the measurement system. To enable operational space for a handling system, as well as for the

measurement light, the setup should use nozzle pipes to form the desired air flow at a set distance away from the specimen. The minimum distance was postulated to be approximately 500 mm.
