GPU Ray Tracing for the Analysis of Light Deflection in Inhomogeneous Refractive Index Fields of Hot Tailored Forming Components
Abstract
:1. Introduction
2. Materials and Methods
3. Simulation Setup
4. Results
4.1. Preliminary Investigation
4.1.1. Parameter Selection
- The number of viewing rays;
- The number of boundary layers;
- The number of polygons per boundary layer;
- The smoothing of boundary layers;
- The export configuration of the COMSOL simulation.
4.1.2. Quality Metric
4.1.3. Preliminary Results
4.2. Light Deflection on Optical Systems
4.2.1. Parameter Setup
4.2.2. Investigation Metrics
- The mean Euclidean distance between the IRIF-refracted and IRIF-unrefracted lines of viewing: ;
- The mean lateral and axial resolutions: und ;
- The mean angle of incidence between the line of sight and the surface: ;
- The computation time of the ray tracing simulation: ;
- The coverage of the measurement object’s surface by the lines of sight: .
4.2.3. Light Deflection Results
4.3. Complex Components
4.3.1. Hybrid Cylinder
4.3.2. Bevel Gear
4.3.3. Wishbone
4.4. Feature Analysis: Bevel Gear Tooth
4.4.1. Metrics and Methodology
- Normalization and Directional Alignment of Metric Distributions:Each metric distribution is normalized over the range defined by its minimum value and the 95th percentile value . This normalization maps all metrics to the interval , facilitating comparability. Additionally, the coverage metric is inverted to ensure that minimizing all metrics results in an optimized solution. The normalized metric for each is computed as
- Weighted Aggregation of Metrics:A weighted sum combines the normalized metrics into a single composite metric:
4.4.2. Results and Interpretation
5. Discussion
Limitations of the Method
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
GPU | Graphics Processing Unit |
IRIF | Inhomogeneous Refractive Index Field |
RMSE | Root Mean Squared Error |
Appendix A. Light Deflection Results
Appendix B. Histograms of Metrics and Methodology
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Mesh Resolution | Configuration Name | Isosurface Resolution | Configuration Name |
---|---|---|---|
Coarse | A | No Refinement | no subfix |
Normal | B | ||
Fine | C | Extra-fine | + |
Extra-Fine | D |
Scene | Camera | Ray Tracer | |||
---|---|---|---|---|---|
COMSOL Config. | C | Sensor Size | 6.7 mm × 5.6 mm | Evaluation | Yes |
Trimming | Yes | Resolution | 2448 px × 2048 px | Visualization | Yes |
Smoothing | No | Scaling | 0.5 | Storage | Yes |
Cylinder Diameter | 27 mm | Focal Length | 10 mm | ||
Cylinder Length | 170 mm | Position | Variable | ||
Cylinder Polygons | 2000 | Rotation | Variable |
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Kern, P.; Brower-Rabinowitsch, M.; Hinz, L.; Kästner, M.; Reithmeier, E. GPU Ray Tracing for the Analysis of Light Deflection in Inhomogeneous Refractive Index Fields of Hot Tailored Forming Components. Sensors 2025, 25, 1663. https://doi.org/10.3390/s25061663
Kern P, Brower-Rabinowitsch M, Hinz L, Kästner M, Reithmeier E. GPU Ray Tracing for the Analysis of Light Deflection in Inhomogeneous Refractive Index Fields of Hot Tailored Forming Components. Sensors. 2025; 25(6):1663. https://doi.org/10.3390/s25061663
Chicago/Turabian StyleKern, Pascal, Max Brower-Rabinowitsch, Lennart Hinz, Markus Kästner, and Eduard Reithmeier. 2025. "GPU Ray Tracing for the Analysis of Light Deflection in Inhomogeneous Refractive Index Fields of Hot Tailored Forming Components" Sensors 25, no. 6: 1663. https://doi.org/10.3390/s25061663
APA StyleKern, P., Brower-Rabinowitsch, M., Hinz, L., Kästner, M., & Reithmeier, E. (2025). GPU Ray Tracing for the Analysis of Light Deflection in Inhomogeneous Refractive Index Fields of Hot Tailored Forming Components. Sensors, 25(6), 1663. https://doi.org/10.3390/s25061663